Kirzner Fervor

The Difficulty of Backtesting

2009-03-31T20:31:00.003-04:00

One of the benefits of momentum based systems is that you don't have to deal with the vagaries of fundamental data. Leaving aside revisions to economic data, when they appear in real-time, and changes to their methodology, earnings data is difficult enough. You would think it would be a simple enough thing to just add up companies earnings to get a P/E or to use operating earnings instead of as reported earnings, but some even criticize those two points. Also, you have to deal with changes to index methodology.

Let me explain. In the late 1990s, MSCI changed the methodology by which they calculate indices. In the past, they used simple market-cap weights and tried to include 60% of the publicly traded firms (by market-cap) in the index. At the time, most other indices were float adjusted, where they only recognized shares available for trading in computing weights. Countries like Japan, which saw massively overvalued multiples in the late 80s and early 90s, also had companies that were not widely held as part of their indices. Since they weren't widely held, they should have had less weight in the index. Less weight in the index would have meant that prices wouldn't have gone as high and stocks wouldn't have been as overvalued in the early 90s.

The other main change was increasing the weight 60% limit to something like 80-85%. For instance, in the U.S. GM had 60% of the U.S. auto market so only GM was included, but Ford (despite being huge) was not.

How does this matter? Well, if the index methodology is changed to correct a massive overvaluation in Japanese stocks, it means that you cannot compare historical price or PE ratios to the current levels for most historical indices. For example, let's say I build a global tactical asset allocation model with a 50% weight on momentum and a 50% weight on value. I determine momentum for a country's equity index by how its momentum compares against the other countries and then I compare it to its history (using a z score). Then I take 5 pieces of valuation data (like P/E, P/Cash flow, P/B, RoE, RoA) for each country and compare each country relative to each other and again to the history for each series. In each case, comparing the multiplies to each other should have no bias. However, if I'm using an index that has changed its methodology and was severely biased upward, all my valuation and momentum data shouldn't mean much when I compare it historically. For instance, the standard deviation of P/Es would be much larger and the average value would be higher (due to Japan being overvalued, for instance). The z-scores could be telling me something that isn't true. So what might appear to be historically cheap now, after correcting the bias, actually may not be cheap. As a cross-check, it would make sense to also look at alternative indices that have not substantially changed their methodology over the period.

If Siegel is right (from WSJ article above), then even the earnings data should be biased.

My Solution to the AIG problem

2009-03-21T13:23:00.003-04:00

TPM put up a timeline of the collapse of AIGFP. Most of the information is gleaned from the WaPo series from last year. One thing that is interesting to me is the video (I think this is the one, HT: Ritholtz) of Hank Greenburg when he comments about the extent of their CDS portfolio. He gives a bit of a different timeline than the WaPo piece. Since there are all these self-interested parties trying to shore up their reputations, I'm really not sure who's right. One thing I would note is that the CDS market was growing by like 100% a year at the time when they stopped writing CDS according to the timeline. From the time Greenberg began to be under investigation by Spitzer (when his influence probably began to wane), to the time they stopped writing CDS, their exposure could have doubled or more.

Anyway, to my solution. My reading of the problem is that AIG has suffered more from additional cash sent to counterparties as the result of ratings downgrades than it has from losses on their CDS portfolios. Now, I'm sure that they were aggressive in writing these and did face significant actual losses on these portfolios, but sending money to Goldman et al is the big source of their trouble. If AIG were AAA due to government backing (like Fannie or Freddie), then less capital would be required and AIG (and the government) could get their money back.

I see two main problems with this, first, AIG brought in people to wind down their contracts. If they've already taken a loss on the contracts, then they're SOL. The other problem is the political economy problem. Wall Street firms received most of this money and they would likely lobby Congress, the Fed, or Treasury department so that they don't have to give the money back. I think Spitzer was right saying those firms should have had some kind of haircut, but he usually isn't so it might just be an abberration.

My solution is really simple enough that I'm not quite sure why no one has brought it up. The firm is essentially backed by the government, so why not?

Is the BoE reading the Money Illusion

2009-03-18T16:28:00.003-04:00

I was reading the March BoE minutes when I came across the following statement:

"There was a high degree of uncertainty over the appropriate scale of purchases
necessary to keep inflation at target in the medium term. The Committee noted
that their February Inflation Report projections suggested that a significant
shortfall in nominal GDP was possible over the forecast period. Nominal GDP had
grown by, on average, around 5% since the inception of the MPC – a period over
which inflation had been close to the target on average. In contrast the
Committee’s February projections implied a small decline in nominal GDP in 2009,
with growth remaining below 5% in 2010. Therefore the projections suggested a
shortfall in nominal GDP of at least 5%."

The BoE is basically saying that they chose the amount of assets to purchase under the APF by figuring the gap of nominal GDP relative to the historical average. Since nominal GDP in 2009 will be close to 0% and the average is 5%, they should buy assets equal to 5% of GDP. Barclays has already noted (in MPC Watching) some of the problems with this methodology (like the money multiplier), but I was struck at how similar this is to Scott Sumner's nominal GDP targeting idea. You usually don't hear central banks talk about nominal GDP gaps.

Condor Options

2009-03-17T00:07:00.003-04:00

I thought this post at Condor Options was very good. I think one thing that makes testing these types of option strategies difficult is that you really need some kind of software package to do it. I can test a simple mean-reversion strategy on S&P500 on excel that gets returns close to what they have, but it would be a pain to test bull and bear spread strategies without something at least like Trade Station and preferably something better. That being said, I think it will make a lot of sense to pursue this type of strategy further. Just like mean reversion strategies tend to work in spurts, so do trending strategies. Most strategies could use additional chances to earn some premiums.

50 shapers of Finance

2009-03-12T16:27:00.003-04:00

The FT has released 50 shapers of finance, and not surprisingly KF is not among them. I count 31 of 50 (not counting Lou Jiwei, so it could be 32, but I don't really know what he does) as members of government organizations. Three are practicing private-sector economists: Krugman, Shiller, and Roubini. I think they are putting too much faith in private sector CEOs, you could probably narrow the list to ten. Bernanke, Obama, the three economists listed, and then five dead economists.

Greenspan is wrong

2009-03-11T10:09:00.004-04:00

I don't think he's completely wrong here, but he's certainly wrong on the impact of low short-term rates impacting long-term rates. First, I could point him to the FRB at San Francisco that gives a little primer on the determinants of long-term mortgage rates. Mortgage yields tend to track government yields and long-term government yields are certainly affected by what happens to short-term government yields. Granted this relationship tends to break down, like it did when Greenspan notes, but historically the long-term decline in the discount rate has some effect on the mortgage rate.

Second and more importantly, the chart above of the effective interest rate charged on ARMs vs. FRMs says it all. Note the dramatic decline in ARM rates relative to FRM rates around the time when the bubble began to expode in 2002-3. Indeed, Greenspan himself said in a 2004 speech that, "recent research within the Federal Reserve suggests that many homeowners might have saved tens of thousands of dollars had they held adjustable-rate mortgages rather than fixed-rate mortgages during the past decade." The research from my (unpublished) M.A. thesis showed (among other things) that ARMs account for a significant portion of new subprime loans and the rise in delinquencies. Since the spread of subprime borrowing and ARMs were also a contributor to the growth in the housing boom, Greenspan's low interest rate policies (and speeches) fueled the interest in ARMs and hence the housing boom*.

I don't deny that increased investment from overseas was a factor, but it really doesn't make sense for the housing boom to be mostly caused by the global savings glut. They might have invested in MBS, but most of the decisions were first made by people buying homes in California, Nevada, and Florida and those who sold 'em to 'em.

* not a conclusion from my thesis, but it was a team project

Component TAA Update

2009-02-08T22:19:00.008-05:00

Given its a start of a new year, I figured I would update my Component TAA model (for more see: here, here, and here) results to give an idea of how it performed out of sample.

For a brief refresher, I took Mebane Faber's Tactical Asset Allocation strategy and looked at adding risk-parity portfolio weights and then also at looking at within sector momentum strategies. So the basic strategy outlined by Faber (2007) is to go asset classes that are above their 10 month moving average and remain in cash the rest. Classes are equally weighted (and he uses US stocks, foreign stocks, commodities, real estate, and 10 year US bonds).

My addition is to weigh different asset classes so that each contributes equally to the risk. The idea is that bonds are much less risky than stock, so that the contribution to overall portfolio risk is dominated by stocks. If you leverage up the portfolio, then you're basically long US stocks and the other positions don't really matter so much in determining your returns.

The second part is to look within the asset class instead of as a whole. Given the research by Jegadeesh and Titman, my decision for choosing what sectors to invest was determined by momentum. For the purposes of this study, I have been concentrating on the past four months worth of momentum and holding at least for two months. The top 25% of individual securities are used. As an example, instead of going long only Commodities, I might be only long oil and gold.

So the information I am going to present are first the 2008 returns of each strategy (and leveraged 100%), followed by tables with the historical returns, and their historical charts (scaled by natural logs). I'll follow up at the end with a summary of the performance of the CTAA and what it was holding at the end of the year.

The following are the historical charts, investing $1 in each strategy (and scaled by the natural log).

So, at the end of 2008, you would want to be in bonds (though you would be losing money in them now, suggesting TAA is off to a bad start), and that's about it. Risk Parity Weights are approximately at 37% bonds, 18% Commodities, and close to 15% in the rest of the asset classes. The Component TAA is invested in SHY, IEF, AGG, TLT, and MBB equally weighted in bonds (avoiding corporate, international, municipal, and TIPS ETFs).
Obviously, I don't think the Component TAA is something that should be blindly followed, the way that most people could blindly follow the TAA. It is designed to perform best when momentum is a factor (like during booms) and is expected to underperform at times when the TAA adds most value (by being in cash). It was particularly hurt in 2008 due to the collapsing energy prices. Risk-parity weights as a tool to reduce risk, however, worked well in 2008.

Kaizen ECB quotes

2009-02-04T19:38:00.000-05:00

In a speech titled, "(Under-)pricing of risks in the financial sector" by Jean-Claude Trichet

"The periods of crisis bring to light the major shortcomings of the
underlying mathematical [risk] models. In those periods the behaviour of
amrkets and prices does not appear to follow any probabilistic model ex
ante but rather reflects a more fundamental Knightian uncertainty in which
even probabilities are unknown."

Buy and Hold (Part 2.5)

2008-12-19T19:38:00.002-05:00

This post will eventually get merged into a Part 3. I've had some programming difficulties with the final part of the project and I've spent too much time watching Lost to resolve them before the Christmas break.

Continuing on with the Buy and Hold series (part 1, part 2) I've been writing. I was first curious to look at a long-term history of what a Markowitz Mean-Variance portfolio would look like over the years. Originally I planned on using about 90 years worth of data, but it seems really unstable for that period, so I only used the past twenty years (to get the weights, I used more data than that). I wanted to use this as a benchmark to compare strategies using similar Markowitz-type weights.

About three months ago, I did some research into interest rate environments similar to what has been done at MarketSci). After seeing their posts, I wanted to see if a long-term investor who solely identifies what interest rate environment they are in to determine their portfolio weights would outperform the typical Markowitz portfolio. I love what they do at MarketSci, but there is also value at creating rules that are simple enough for your Grandma to follow (like Mebane Faber's 200 day MA rule that I love so much).

Back to brass tacks, I have to concede that I couldn't operate the Matlab Mean-Variance optimizer. I could generate the portfolios, but then when I used those portfolios that I created in the optimizer it never worked. I'm still not sure why I was getting errors, but I decided that a simple approximation was to choose weights that maximize the Sharpe ratio, since that could replicate the optimizer's results. Unfortunately, this didn't let me use risk aversion to be able to change anything, but all I want to do is to compare one strategy vs. a benchmark stock/bond mean-variance-like strategy. I don't need things to get too crazy.

To identify periods of interest rates rising/falling/neutral, I looked at how much interest rates had changed over the past 6,12,18 months and if the difference was greater than some standard deviation multiples.

Then, I identified the returns in each period and separated them into different portfolios. As though they were investing in three separate strategies (ie expected returns and covariances for the positive interest rates were separate from the , I calculated weights using my Sharpe ratio optimizer. Where I'm stuck now is in error checking my lines of codes to combine them together (I might have the solution (pretty easy, just haven't gotten around to it), and will update after the holidays. Sometimes writing facilitates thinking.)

Again my hypothesis is that long-term investors could benefit just by investing differently depending on what interest rate environment it is.

Re: Hulbert

2008-12-14T23:48:00.002-05:00

Mark Hulbert wrote an interesting piece in Barron's about a week ago.

He notes that the 39 week moving average on the DJIA underperforms the buy and hold strategy since 1990. I wasn't quite sure why he used 39week instead of 40 week or 10 month or 200 day. But it's interesting how right he is.

I looked at weekly returns (using his 39 week, which is close enough to 40 week, but the data also does not include dividends) and I also looked at monthly returns. I then used rolling periods of close to 19 years (from 1990 to now) to check how average returns and Sharpe ratios looked. On weekly data, buy and hold average returns outperform the TAA strategy in only 28.8% of weeks, but Sharpe ratios are also higher in TAA than buy and hold in 76.6% of weeks. The general story is that in the early years of the strategy (until 1980), 19 year ahead arithmetic returns and Sharpe ratios are greater for the TAA strategy than for the buy and hold. After 1980, not 1990, things begin to reverse.

Looking at monthly results, average returns are greater in 46% of TAA 19 year(ish) rolling periods than buy and hold as well as 64% in the case for Sharpe Ratios. Monthly also pushes the reversal period back further, to 1974. I also looked at rolling 5 year periods for the monthly data. In 46.8% of rolling periods, the TAA outperforms the buy and hold on Sharpe Ratio, 40% for returns.

I freely admit that the 200 day strategy is not the most profitable and won't even outperform the buy and hold. However, it's key benefit (beyond simplicity that anyone can understand) is that it reduces risk. If you looked just since 1990, the monthly return on the 10 month DJIA strategy (ex dividends) is 5.75% with 10.8 stdev where the buy and hold is 6.5% with 14.5 stdev. Using a 4% risk-free rate, the buy and hold has a Sharpe of .17 while the TAA is .16. However, when you look at geometric returns, the TAA return declines to 5.3% while the b&h falls to 5.5% so that the TAA nudges out the b&h on a Sharpe ratio basis.

Overall, this does confirm what Thornton is saying when he notes that it underperforms recently. However, it's not necessarily as simple as he makes it. Yes, it underperformed recently, but on a risk-adjusted basis it doesn't. The 200day MA still provides a useful indication of when major markets trends have begun or end. They aren't great indicators for short-term traders, but if Grandma paid a bit more attention, then she would be able to reduce some risk.

Though it is obvious to me, I should also note that the 200 day average on just DJIA is not, by itself, what advocates of these TAA systems would use. It is TAA b/c you look at multiple asset classes that should perform well as others do not.

So as an additional treat, I looked at the 10 month TAA strategy using weights of 60/40 on stocks and bonds as represented by both the S&P500 and the DJIA (including dividends) since 1950. The TAA strategy is applied to both stocks and bonds. For reference, the S&P500 TAA strategy performs the best, with a Sharpe of .52, followed by .44 for the TAA DJIA, lastly the buy and holds were the weakest at about .39 each. Since 1990, both the DJIA and the TAA DJIA strategies including dividends and a 60/40 allocation have been roughly the same (Sharpes ~.56). However, the S&P500 TAA strategy has a Sharpe of .72 while the S&P500 version of the 60/40 is only .47. Over the whole period, using the roughly 19 year rolling average methodology from above, the buy and hold strategies outperform the TAA is roughly 72% of the months, but the TAA strategy has a higher Sharpe ratio in 72% of months as well.

So in general, the TAA strategy will likely reduce your returns. Know that when using it. However, it will also improve your risk adjusted returns, but reducing the volatility of your strategy. It also makes most sense to use the TAA strategy on a proper asset allocation strategy and not just looking at it as market timing one index. There is still value at looking at long-term trends when it comes to investing.

Kaizen BoE quotes

2008-11-24T23:55:00.002-05:00

I'm pretty much done writing the program for my next buy and hold post, but there's been some setbacks and it has taken longer than expected. I should be able to finish it the weekend after I get back from Thanksgiving holidays. In the mean time, enjoy some Kaizen BoE quotes. I love it when Central Bankers admit mistakes.

"Because a number of countries, most obviously China, chose to peg their currencies either to the dollar or to a basket in which the dollar featured heavily, the FOMC had to cut rates more aggressively to maintain domestic activity than would have been the case if the dollar had been free to depreciate against them. Moreover, by virtue of the currency pegs, this monetary looseness in the United States was transmitted overseas, despite attempts at sterilisation. Now the primary driver behind the surge in commodity prices over the past three years or so has been the rapid development of the emerging market economies and the consequent growth in commodity demand running up against relatively inelastic supply. But the general pickup in inflation worldwide, together with the appreciation of a range of asset prices, suggests that accommodative monetary policies may have also played a part.

"The pattern of global imbalances that resulted from this mix of policies has vexed policymakers for some time. We knew they were unsustainable and worried that the unwinding might be disorderly, though I don’t think anyone could have guessed the course that events would actually take. But we did see that there were vulnerabilities present. However, nothing very much was done about these imbalances. Why was that?"
...
"Indeed, a central bank seeking to stabilize inflation over a sufficiently long time horizon should necessarily recognize the possible adverse longterm consequences of a credit-driven asset-price boom in its policy deliberations."

All from Charles Bean - Deputy Governor for monetary policy of the BoE -
‘Some Lessons for Monetary Policy from the Recent Financial Turmoil’ -
Remarks at Conference on Globalisation, Inflation and Monetary Policy -
Istanbul, 22 November 2008

Kaizen Fed Quotes

2008-11-19T19:28:00.002-05:00

"In short, we still do not fully know what caused the run-up in house prices and over-building. Short-term rates were low in 2002-04 as the Federal Reserve countered the risks it saw to good economic performance, and these low rates probably had some effect on housing markets at the time. But the problems largely built up after policy rates were well on their way to neutral, and other factors appear to have played major roles. We have learned little about the likely effect that a somewhat higher funds rate would have had on the speculative element of prices. Of course, it is important to keep an open mind about the relationship of short-term interest rates and speculative activity. If it becomes clear that monetary policy can predictably influence the evolution of bubbles, central banks should take that ability into account when crafting policies intended to keep output rising in line with its potential and inflation low and stable." - Vice Chairman Donald L. Kohn At the Cato Institute's Twenty-Sixth Annual Monetary Policy Conference, Washington, D.C., November 19, 2008, "Monetary Policy and Asset Prices Revisited"

AQR and Leverage

2008-11-18T20:06:00.004-05:00

Damian over at Skill Analytics wrote a post on the AQR article from Allaboutalpha.

I agree with his sentiments regarding the way they determine their leverage. I would guess they don't use that formula to determine their leverage but it could be a simplification of something they do use. Nevertheless I would strongly advise not using it.

Let's use l as leverage. They have two portfolios A and B with correlation p and standard deviations stdev(A) and stdev(B). The standard deviation of the portfolio is
stdev(p)=[(stdev(A)/2)^2+(stdev(B)/2)^2+.5*stdev(A)*stdev(B)*p]^2

They set (stdev(A)+stdev(B))/2=l*stdev(p) or l=(stdev(A)+stdev(B))/(2*stdev(p))
Now, if I were to assume that stdev(B)=x*stdev(A) just for mathematical simplification
that would mean l=(1+x)*stdev(a)/(2*[(stdev(A)^2*(1+x^2))/4+.5*x*p*stdev(A)^2]^.5
and: l=(1+x)/[(1+2*x*p+x^2]^.5

So what we have from this little mathematical porn is that if there's no correlation then l=(1+x)/[1+x^2]^.5. In other words if the standard deviations of each asset are the same (x=1) and correlation is 0, then you'd use leverage l=2^.5 which is the maximum leverage you would use. Strangely, as the ratio of the two variances goes from something like x=.75 to 1.25, the peak is when x=1 and declines on either side. The same is generally true for other correlations except that the closer the correlation is to 1, the lower the leverage.

So why does this matter. Basically, if you were to use a system like this to determine your leverage, it is based on two things, the correlation between the two assets and the difference between the variances. In other words, the levels of variance do not matter in this framework, only the difference between the two assets' variances. The correlation part makes sense, but this seems a little too simplistic.

Buy and Hold (Part 2)

2008-11-09T17:29:00.005-05:00

This is the second part in a three part series. The first is here.

To look into why buy and hold doesn't work, I wanted to compare a relatively simple asset allocation strategy with the typical 60/40 stock/bond allocation. I obtained data from the Global Financial Database for the S&P500 and 10 year treasuries going back to 1921. Now the S&P500 wasn't actually published before 1950 or so, they use the methodology going back farther. Also there really wasn't a way to invest in the indices until the 70s or later. As with most things in finance, this isn't perfect by a long shot and is just showing what could happen.

The strategy I looked into compares stocks and bonds. I looked at whether bonds have outperformed stocks in the past 12 and 6 months. I gave a weight of 2/3rds to the 12 month ratio and 1/3 to the 6 month ratio. So if stocks outperform bonds in 12 months and 6 months, they get a value of 1, and bonds get a value of -1. If stocks outperform in 12 months, but bonds outperform over 6 months, stocks get a value of 1/3 and bonds get a value of -1/3.

Since I am comparing a strategy against 60/40 allocations, I decided that my starting point would be the 60/40. I use a base value of 60% for the stock allocation and the bond allocation is always 100%-stock. There is no leverage so stocks and bonds are capped at 0% and 100%. Finally, there is a multiplier against each of these values, so if stocks start at 60% with a multiplier of 20%, then if stocks have a value of +1, their allocation is 80% (and 20% bonds). A fairly simple, straightforward strategy.

Since there are caps, the efficient frontier is truncated at the top (as you increase the multiplier the stock level just goes to 100% or 0% immediately). However, the clear result is that you can improve returns by increasing allocations when different asset classes are outperforming relative to each other. The best Sharpe ratio I reported was actually with a multiplier of .6, indicating that if stocks are outperforming on both a 12 month and 6 month basis, you should be in 100% stocks and vice-versa for bonds. If over the next 6 month period stocks outperform (but bonds have outperformed over the 12 month period), then you should increase your stock position to 40% (according to this strategy). Since 1995 this strategy has outperformed the buy and hold by 50%, or an alpha of 3.2%. Since 1970, it would have lost money in 73, 81, and 87 (it was entirely in stocks in October 87, if you were wondering), but 73 and 81 were quite mild.

Another strategy to come in part 3, hopefully by next weekend.

Buy and Hold (Part 1)

2008-11-09T13:10:00.002-05:00

I can get behind the argument that the average investor should index. Security selection is difficult and most don't want to spend the time to attempt to outperform the index. Time spent trying to outperform the index might be better spent doing other things (esp. based on the size of their holdings).

However, the decision to index or not index is one part of the equation. The investor chooses not only the securities to invest in, but the relative proportions of different asset classes, or holdings in different ETFs/Index funds. If you believe in buy and hold, you might keep your asset allocation constant over time, changing them only as your risk aversion increases as you age (to hold more bonds). Given the cyclical nature of our economic system, this strategy is incredibly misguided. Different asset classes perform different over different time periods, suggesting that an investor should change their allocation as economic conditions change. Put more emphasis on stocks when the economy is doing well and pare back when it slows.

The mutual fund industry is interested in selling Beta, but due to the cyclical nature of the economy, many investors sell their funds as the market falls. In effect, the mutual fund companies receive more volatile, cyclical earnings as their AUM flucuates. However, if they were to focus on products taking advantage of cycles rather than just offering Beta, they would see less liquidation as markets fail, and investors would be less likely to sell their funds. Earnings would be less cyclical. Further, I would argue that this focus could result in a much more successful fund manager than normal. If people view their products as safer, not only would they be more willing to hold their assets with that firm in the long-term, but they would also want to hold more assets with them.

One concern you could have is that if all funds were structured as broad asset allocation funds that take advantage of the cycle, economic cycles would moderate. While I think returns to the strategy would be competed away in such a situation, I think there are three criticisms to that argument. First, not all funds would want to manage funds in that way. At present, most people are happy believing buy and hold is the best way to manage money or they believe their own method is more succesful, it would hard to convince everyone. Second, not everyone would structure their funds the same way. Some would focus on economic data, some might focus on valuations, some on technicals and momentum, while others could use a combination. Not all of the signals would come at the same time. Finally, for that argument to be true, the lack of participation of major investors would be a sufficient condition to smooth the business cycle. Personally, I am of the view that economic cycles are the fault of the Federal Reserve and they appear in specific sectors due to primarily technological change but also government regulations. The strategies I will look at don't try to time these changes, but use momentum data to figure out when others think it has changed. So if everyone were following this strategy, surely the momentum data would no longer be viable, but I doubt everyone would follow it.

I plan on following this post up with two more posts detailing two strategies I have looked at. One is simple enough that anyone could implement, but the second is more complex.

Presidential Inaugurals

2008-11-08T19:59:00.003-05:00

Following Obama's Victory Speech earlier this week, the news media informed us that it was one of his best speeches yet. I don't dispute that, despite my belief that ideas matter and his aren't that good. But I wanted to see how Obama's speech compares to other speeches in American history. Now it isn't always easy to get your hands on victory speeches, b/c American President-elects didn't always give them. I compared his speech to Bush's speeches and Clinton's victory speeches using a tool that calculates a bunch of statistics of how complex your language is. One statistic, more commonly quoted is apparently called the Flesch-Kincaid grade level. According to this statistic, Obama's speech wasn't that much different from the more recent Victory Speeches.

However, I decided to go further back, mainly out of an interest in finding old Presidential speeches/addresses to see how politicians used to talk to Americans. So I found all of the inaugural speeches for Presidents since 1896 (since McKinley bridges both centuries I included both of his) and ran them through this tool. The tool provides many different statistics of how complex different texts are and I don't really know enough to tell which ones are best. So I created a Z-Statistic for one and then averaged them all to create one single value for each President(the negative of Flesch reading ease tests were used). Z-statistics are a little unrealistic, but I'm just using them as the first-best method of simplification. I couldn't find Eisenhower's 1956 speech, so I just assumed they had the same values (not realistic, but only used for creating the statistic).

While his speech is not an inaugural address and this method isn't perfect, Obama falls in at 27 of 29. For a speech listed as his best, it fails the complexity of language test. Surprisingly, Bush's second inaugural used quite complex language, as well as Nixon's inaugural speech. Clinton's first speech was not as "good" as either of Reagan's (by this standard), but his second was.

A final problem I didn't note is that since we have had television, these speeches have definitely changed. Earlier speeches mostly ran in the newspapers, are longer and could be thought of as like a State of the Union Address that we would see today. I took the time to read Coolidge and Taft's speeches to get a feel for them and they lay out all sorts of policies in much further detail than current ones do. Compare that to Bush I's speech where he talks in generalities and a Thousand Points of Light, but nothing specific. Here's another surprising fact, Bush II's second inaugural was the most complex inaugural since television began.

A well-received speech doesn't necessarily mean it was well-written or at a high grade level. It is as much true that you need to deliver the speech properly. Based on my analysis, I think the MSM is thinking more of the delivery of his speech rather than necessarily the content or eloquence of his speech. I did my best to quantify the eloquence, but the content is left to you.

Or you could think that the media is just completely biased for this guy (mi amigo, my compatriot, that one, my friend).

Note: For reference, if you add in MLK's "I have a dream" speech, it is close to Reagan's second inaugural. This post would fall between T. Roosevelt and Bush II.

Corzine idea

2008-10-23T23:41:00.002-04:00

I was just watching Jon Corzine on the Daily Show and I got to thinking about an idea for a research paper. It would be interesting to trace the major Cabinet secretaries (like Defense, Treasury, etc) back to Wall Street. It would be interesting to look at their political ideologies and see how Wall Street has or hasn't influenced them generally over time and was there any bias to a certain political party (or ideology, since the parties have changed)?

Willing to admit it

2008-10-22T22:14:00.002-04:00

Arnold Kling posted today about how Economists as a whole do not know what is going on and that their textbook models are wrong. I couldn't agree more. However, I haven't spoken with anyone who has said, "wow this Rational Exepectations model really helped me forecast this crisis."

Two of my colleagues and I spent some time with Johnny Walker this afternoon... wait I mean John Walker of Oxford Economics. He seemed perfectly willing to admit that his workhorse economic model doesn't work well during this time period. I'm not sure how true this is for academic economists who build models, but I would think that most people who spend their time forecasting are perfectly willing to admit that they use them as a tool to think about the economy rather than something absolute.

In principle Kling is right, it is better to admit pseudo-knowledge than not admit it. I just think that professionals are more willing to admit it than he gives them credit for.

How the financial collapse killed libertarianism by partisan hack

2008-10-19T10:42:00.002-04:00

I love these death of articles by people ignorant of not just the political philosophy that is their subject, but also the conditions leading to its collapse.

Let us start with his claim that, "after LTCM's collapse, it became abundantly clear to anyone paying attention to this unfortunately esoteric issue that unregulated credit market derivatives posed risks to the global financial system, and that supervision and limits of some kind were advisable." First, credit default swaps as we know them today were still in their infancy in 1998 so it would be difficult to say they were as important to LTCM's collapse as Myron Scholes' shoes were. Second, he's attacking the wrong problem, to me, one of the biggest lessons from LTCM is that risk-models and excessive leverage are a dangerous combination. Those problems were never fixed, but it is hard to say that libertarianism is or isn't the culprit. Libertarians would say that banks who lend money to institutions who use excessive leverage might fail if the bets go wrong, and they should be allowed to fail. Harping on, the author notes that "the Washington Post ran an excellent piece this week on how one such attempt to regulate credit derivatives got derailed." Again, the author fails to distinguish between a credit derivative and a derivative. That article is as much about regulating currency and bond derivatives as it is about CDS.

So here again we are faced with the theory that conservatives, liberals, and a central banker who control the government, conspired together to halt attempts to regulate derivatives. The reader is left to his or her imagination to determine how regulating derivatives would have made a difference. I agree with Ritholtz that the decision to allow investment banks to lever up to more than 30x from their original 15x was a mistake. However, I'm not quite sure what else would have or could have been done. Much of the trade in CREDIT derivatives was to get bad assets or the impact of said assets off their balance sheet, a form of regulatory arbitrage. If they threw up some more regulations, I have little doubt that the industry would have tried to find new, exciting, and complex ways around it.

The author notes that consistent libertarians, as opposed to conservatives like Gramm that he is confusing with libertarians, opposed the bail-out and then he invokes the Great Depression that many could be employed in soup-kitchens. Implicitly he is tying the libertarians with the liquidationist view of the Great Depression. L. White has done a great job explaining how Mellon wasn't a liquidationist and Hayek and Robbins weren't liquidationists.

Finally he argues, "libertarians react to the world's failing to conform to their model by asking where the world went wrong. Their heroic view of capitalism makes it difficult for them to accept that markets can be irrational, misunderstand risk, and misallocate resources or that financial systems without vigorous government oversight and the capacity for pragmatic intervention constitute a recipe for disaster."
First, there are libertarians who believe the market is efficient and there are libertarians who do not believe that. I would say that there are many many more in the latter category. I'm perfectly willing to say that markets can be irrational, misunderstand risk, and misallocate resources. However, I would also be willing to say that almost all of the times when they do this, you can point to a government regulation or a government program that is leading to this. The ABCT doesn't really describe the depth of our current situation on its own, but it sure does a good job explaining how the government encouraged the market to misallocate resources into the housing boom. The difference between the author and I is that I want to see market oversight and market regulation where he only is looking to the government for the solution. Well, I think there are plenty of cases where you can point to the government being the problem.

What's interesting to me, is that the death of socialism was predicted by Hayek and the Austrians several decades before it happened. In all reality, I'll admit that what the Soviets had and Chinese (before Deng) had wasn't really socialism. It was only really tried in the WW1 War Economy in Russia and it failed miserably, as predicted. The system that grew out of it, at least in Russia, was more of a market socialism, mostly socialism, but a little markets and freedom thrown in. Libertarians, mostly Hayekians, have predicted that the global financial system is unsustainable in its current form. Many predicted that the housing boom would lead to a situation like what we're currently experiencing. That's because what we don't have is capitalism and anyone with a brain should realize that. Even before the bail-out bill, we were on our third-way, though not as far to the socialist side as Europe. It's not that this doesn't fit with our model, but when you take our government and say we live in a capitalist country. People like me need and have stood up and said we do not live in a capitalist country. Our theories aren't to blame, our theories told us we would end up in this mess.

Malkiel's Wambulance

2008-10-13T00:43:00.002-04:00

"It is very tempting to try to time the market. We all have 20/20 hindsight. It is clear that selling stocks a year ago would have been an excellent strategy. But neither individuals nor investment professionals can consistently time the market." - Burton Malkiel

My problem with this statement is that it is not specific. I would agree with him that investment professionals can't time the market on a short-term or medium-term basis, for the most part. However, pretty much everyone knew without 20/20 hindsight that there were big problems in the financial sector, more than a year ago. Some people, using insights from a variety of schools of thought or just plain, old common sense, got out of the market. You don't need to time the market when it goes up, you just need to know that business cycles happen and it pays to get out of the market when the downturn is coming. The regular investor can index away in the good times, but that doesn't mean that always indexing is the proper course of action.

Risk and Uncertainty

2008-10-08T22:57:00.001-04:00

What I don't like about Free Exchange is that I have no idea who the authors are who contribute to it. I don't know to always read and who to take with a grain of salt.

Here they note that modern finance "seeks to turn uncertainty into risk. You cannot quantify uncertainty, and you cannot trade it. It is pre-finance—and it can be corrosive. Risk, on the other hand, is a probability distribution. It is quantifiable. You can model it and analyse it and it has a value. Therefore, you can trade it." They are right on what modern finance seeks to do and the difference between uncertainty and risk. My problem lies with modern finance and actually turning uncertainty into risk.

I view uncertainty and risk from a Knightian lens. Risk is measurable, uncertainty is not: "The essential fact is that "risk" means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomenon depending on which of the two is really present and operating. ... It will appear that a measurable uncertainty, or "risk" proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We ... accordingly restrict the term "uncertainty" to cases of the non-quantitive type."

So, that leads me to wonder can you actually convert uncertainty into risk or can you only reduce and spread out risk? Knight says that risk has an ex-ante probability distribution. In trying to get life insurance, from my perspective I have uncertainty because I cannot measure my risk, but the insurance company can and from their perspective it's a problem of risk. Subjectively, after I get insurance, I would know that after my death, my family would be taken care of. I would no longer have uncertainty (on this one part of the uncertainty of my death, there's a minimum of two others, like how and when), but the insurance company has gained a risk. Actually that may not be accurate. Maybe it is also uncertainty when it hits the balance sheet of the insurance company? Perhaps it is the subjective determination of the insurance company that makes it risk rather than uncertainty? This explanation seems lacking to me. A probability distribution seems outside of value and outside of the human mind. A more satisfying explanation, to me, is that the payouts on the insurance contract are uncertain by themselves for the individual and when transferred to the insurance company. They become risk when there are enough of them that produce a probability distribution.

As an example from modern finance, if you take a bunch of MBS and pool them into a CDO, you have certainly pooled them, but the pool of assets or the structure do not become a measureable probability distribution. So what you have with CDOs is not risk diversification, but taking a bunch of assets with uncertain payoffs, pooling them in a complex structure, and then sending different levels of uncertainty to people. Risk is not diversified, but different levels of uncertainty are spread out among the owners of the tranches to the CDO.

Quotations

2008-09-21T14:36:00.001-04:00

"Bob Rubin as Secretary of the Treasury — I mean, if he was a Hindu and he was being reincarnated, he'd come back as a pail because this guy bailed out everything you can imagine." - Kevin Phillips on Bill Moyers show

HT: Big Picture

Taylor Rule

2008-09-17T19:39:00.002-04:00

If certain people used certain data series (like MacroAdvisors' Monthly GDP series and CPI) to make a Taylor Rule, they might be pleasantly surprised by investing when Fed Funds is above what is suggested by the Taylor Rule.

Why doesn't this exist

2008-09-04T20:47:00.002-04:00

By law, a hedge fund needs to avoid having too many (100) accredited investors in order to avoid coming under additional regulations. An accredited investor can include a pension fund, a bank, a hedge fund of funds, someone with a million dollars, and other rich persons. An investment company can also act as an accredited investor. However, people who make less than 200k dollars in either of the past two years are not accredited investors and therefore cannot invest in hedge funds. Also, a fund may require a large initial investment that more marginal investors cannot invest in. Furthermore, some of the better funds are hard to invest in, even for large investors. And I'll add in the fact that fund of funds charge an additional layer of fees that are pretty absurd.

So I think if it is legal, there should be structures like a closed end fund that solely invests in a particular hedge fund marketed to these marginal investors in hedge funds. The ideal organization to launch something like this would be an already respected fund of funds, a global investment bank, or some other organization with many contacts among large hedge funds. You could start with like the five or ten largest hedge funds that are open to investors and then expand into more.

Again it would be best sold to the marginal hedge fund investors. Someone with a 500,000+ portfolio and willing to invest 50k in a hedge fund might be willing to do it if they can buy in with a share in a closed end fund that is investing many millions more in a fund. Seems like a winning idea to me, if it's legal and the organization behind it has the relationships.

Resistance and Support

2008-08-31T12:59:00.003-04:00

This article has been mentioned on a few sites, I saw it first at Free Exchange.

It notes that prices that end in .99 induce customers to purchase a much higher percentage of sales than would be suggested. It is particularly true for lower priced items, but a purchase like a washer/dryer wouldn't have much effect.

While it is easy to design an experiment in a retail setting to test that theory, it would be much more difficult to test it in the financial markets. However, it seems to me that it would most evidently manifest itself in support and resistance points. I don't think support and resistance really translate well into trading systems. However, they can be useful in explaining behavior in the market (though I admit more value in hindsight than at the time). For instance, a stock might test its five year high several times and after breaking through on higher volume, it will surge significantly. A more active trader could see that and place buy stop orders above the resistance level. The problem with using a system is that sometimes it will go slightly above the resistance and then drop significantly. It is done more based on feel and that's also the problem with testing the effects of support and resistance lines using standard statistical techniques. A sustained, high volume move through a resistance point is more important than a weak one.

Getting back to the BBC article, a resistance line can be thought of like a price of 8 euro. The marginal asset manager might think that a stock is worth no more than 25 dollars. He would be interested in selling at 25 and willing to buy at 24.99. However, in the real world, the decision would really be how much of his portfolio to sell at 24.99 vs. 25.00 and not whether he is buying at 24.99. Due to the same effects noted in the BBC article, he would be much more willing to sell at 25 than at 24.99. The situation works in the reverse for a support line at 25, a manager might only be willing to buy a little at 25.01, but he might be willing to buy more at 25. You may ask shouldn't it be 24.99 where he wants to buy more to be consistent with the article? However, the real meat of the article is that people don't react linearly to these price changes, the same way that portfolio managers or traders might react.

There's one problem with this analysis that I can figure out so far, the prices in the BBC article are all small. While the prices of stocks can be reasonable on the face of it, even a retail investor would probably be buying 100 share lots and a PM would purchase significantly more. So the question is, is it the dollar value that matters or the price that matters? I'm not really sure of the answer, but I would say at the very least support and resistance are important enough that every technical trader would pay attention to them. There has to be some "inefficiency" here.

Testing this would be another problem, but I'm sure some finance professor is already looking into it. I really think that the key would be to look at when it comes to resistance points with light volume or heavy volume. For instance, after identifying resistance points, I would calculate whether they are above a moving average of volume to determine whether a day is a light volume or heavy volume day (might want to do relative to the market as a whole as well) and then I would look at how the stock performs relative to the market. I would identify resistance points using something like Average True Range relative to the stock price. For instance, a 6 dollar stock that moves 25 cents a day might have have support or resistance at the $1 level, but Goldman you might look 20 dollars away for support/resistance. That way you can do all the stocks together and then compare quartiles of stocks based on price or trading volume. Finally, all you have to do is look if high volume violations of resistance points or confirmations of support lines result in prices above those points over the next month (or 3) more so than the low volume.

That's probably a publishable paper right there, biggest problem is probably identifying the resistance points. It would make sense to do it in multiple ways to avoid the criticism that you measure it wrong. If you don't remove earnings days or something, you'll also need to make some kind of assumption to deal with them.

TAA and switching to bonds

2008-08-20T22:23:00.003-04:00

First off, anybody see the ads for Crusoe on NBC during the Olympics, makes me want to break out my MES.

Second, if anyone remembers/cares I took the level 2 exam of the CFA back in June and ended up passing. So congratulations to my brothers.

Third, some ideas come to me that are rather simple, but make a lot of sense looking back on them. I had tried using bonds instead of cash in the TAA model previously, but was unimpressed due to larger volatility. However, I hadn't considered using the TAA investment in bonds. In other words, use the return series that invests in bonds when above the 10 month average and cash otherwise instead of a pure cash index for some asset classes.

The two asset classes I meant to target with this strategy were the two that historically have performed the worst on a Sharpe ratio basis, commodities and foreign equities, in the TAA strategy. I still have the TAA rule for each, but before I evaluate that I look at whether the US equity or foreign equities are below the 10 month average, if that is the case, I will have them invest in the bond TAA strategy. Then, if above the 10 month MA, they invest in that asset class, otherwise they invest in cash.

For comparison, in recent years (since 1990), the TAA strategy for commodites returned 8.8% annually (16.69% s.d., Sharpe .27 with r.f. @ period average), this simple change increases the return to 13.6% (11.8% s.d., Sharpe .79). For foreign equities, the return goes from 7.6% (12.59% s.d., Sharpe .27) to 12.2% return (12.43% s.d., Sharpe .64). The overall strategy improves from 10.7% return (6.85% s.d., Sharpe .94) to 12.5% return (7.01% s.d., 1.17 Sharpe).

Again, the reason I focused on these two was because they perform the worst. Using the strategy on US equities seems to work (Sharpe goes to 1.16) and for REITs (Sharpe goes to 1.15). Overall Sharpe goes down slightly, but for the individual asset classes the Sharpe increases suggesting the decline is due to decreased diversification and higher variances. A 5% increase in the Sharpe ratio individually doesn't impress me as much as the ones for commodities and foreign equities.

I also tested my original intention, just using the bond TAA instead of cash (and nothing more complicated like above) and it works well for REITs, but works best for equities. A marginal improvement on a risk-adjusted basis for the portfolio, but interesting nonetheless.

TAA and commodity overheating

2008-08-18T23:36:00.003-04:00

Just wanted to do a quick blog on the TAA model noted earlier on this blog.

I created an extension to the model based on it achieving a certain return after a set number of months. After that, I looked at whether it makes sense to get out completely or to use a different exit rule (like a 5 month MA instead of 10 month MA). It doesn't get back in until the next time the 10 month MA crosses back over. The general idea is that if an asset class goes up that significantly in such a short period of time, it is unlikely that the returns in the future will be strong, despite being above the 200 day return

I started with a 20% return in a quarter and getting out completely. In that model, there is an improved return. However, closer analysis reveals that it is almost exclusively in the commodities sector. It stays out of almost five years worth trading (239 months vs. 294 months) changing an asset class with 8.8% return and 16.8% volatility to one with a 13.3% return and 13.12% volatility.

I also experimented with different combinations of returns, periods of time, and whether to use a MA average rule to get out or just permanently get out. Several of them perform better than the original TAA rule, but almost all the benefit comes from the commodities sector and the other sectors don't improve enough to be worth it.

I should note that my analysis didn't include the current period (ended in early 08), but the knowledge I take from my analysis is that when commodities rise 20% in a quarter, they historically have a correction.

Note: I also created a more complicated algorithm for the other asset classes that will get back in if the past three months did not have the quarterly 20% return which seems to help reduce volatility and improves the portfolios Sharpe ratio (though the individual ones don't appear that much better. Basically the same thing as the commodity strategy except it is willing to get back in (keeps the same returns for the commodity strategy). 11% return for the overall strategy here with 5.43% volatility. (compared to about 6.85% for the original TAA model).

The Economics of Registering to Vote

2008-08-03T12:28:00.003-04:00

Well, I should say that it is more the cost/benefit analysis of registering to vote. I recently moved from Queens to Jersey City and there were some thirty-ish professionals outside the PATH entrance who wanted to register me to vote. I am registered in Indiana (where KF's parents live and went to college) and still have my Indiana driver's license.

Walking to the registration table, I figured that (outside of time wasted filling out the form) I was making a cost-less decision. I probably won't vote, but I figure that the margin difference in New Jersey in the general election will be smaller than the margin difference in Indiana. So, if my vote matters at all (probably not), it matters a fraction more in Jersey than Indiana. So the benefits side of the calculus is the expected value of me voting and that influencing the election (probably of me voting times value of my vote and also all future voting decisions and their weight discounted to the present).

However, I didn't realize the costs of voting until a man who either was an unemployed, alcoholic construction worker or homeless (probably the latter) began to convince me not to register. His early arguments weren't that convincing focusing mostly on how much the vote matters and staying off the grid (the first I already knew, the second I didn't care about). However, he mentioned that one of two places they pull jury duty from is the voter rolls. If I am pulled to do jury duty twice a decade in New Jersey that means that I earn like $3.50 (how much the lochness monster takes) and lose a vacation day, I presume.

The problem of how to value the cost is difficult for two reasons. First, the call for jury duty is random and could be modeled like a Poisson process. An easy work around would be that I have jury duty in five years and ten years and discount the costs on those dates back at 6% or so. The second difficulty is valuing a vacation day. I can assume that the value of a vacation day would increase as my income increases since leisure would become more scarce and I would imagine that my income grows significantly five to ten years from now. I could probably model it, but it shouldn't matter that much, as will be seen. My gut feeling is that, in terms of dollars, a vacation day shouldn't affect salary (I get paid the same) and you could assume that it doesn't affect your bonus. However, if you don't use all of your vacation days, you might have worked harder and deserved a higher bonus by accomplishing more work. There is some probability that it will increase your bonus by not taking the vacation day, but it is small and would probably not be a big effect after discounting*. The real place to value the vacation day is in subjective value. The proper trade off is the net benefit of sitting in the sun or skiing out west or sitting in a jury room.

The subjective benefit to skiing with friends relative to sitting in a jury room, for me, outweighs the money (from bonus or the 3.50) and the benefits of being able to vote in New Jersey. I'll stay registered in Indiana and avoid jury duty like the plague.

I'm pretty sure they don't let people who think like me on juries anyway.

*It is small on the margin because it would probably only be if you had like leftover vacation days from the day before and just dropped out from work for like a month. That would probably affect bonus.

SEC exempts Market Makers

2008-07-19T10:26:00.002-04:00

This big news in the market these days has been the new SEC naked short sale regulations. According to this article, market makers in equities and options have been exempted from the short sale regulations.

In my view there are three main criticisms of the original regulations. The first is resolved by this adjustment. The options market, in particular, was effected by these regulations since it can disrupt hedging operations. Since activity in the options market feeds into the equity markets, if you create regulations that make it less likely someone will make markets in some options, there will be some big effects. The second criticism is the one pointed out by Mish several times that the firms exempted from the shorts has been chosen rather arbitrarily. Finally, is the whole this prevents these companies from going quickly to a fair value and serves as a form of relief for privileged, politically well-connected banks. People lost their life savings on internet companies and rules like this weren't put in place. And I'll leave it at that.

Merger Arbitrage

2008-07-17T21:12:00.004-04:00

*I generally don't post about specific stocks, but I haven't gotten around to some of the research I meant to do and something I am looking at is increasingly looking worthwhile.

Merger arbitrage is the art of buying companies that are getting acquired and selling companies that are acquiring. When the merger goes through, you collect the spread between them. If the merger doesn't go through, the spread widens and you lose money.

Alpha Natural Resources (ANR) is a coal stock and Cleveland-Cliffs (CLF) is an iron and coal stock. Cleveland-Cliffs announced on July 15th that it will purchase ANR for $22.23 and .95 shares of CLF. On the 16th, ANR opened up around 119 after trading around 95 the past few days and then proceeded to tank back down to a close of around 96 at the close of the 17th. CLF was trading around 110 prior to the announcement and has come down to about 97.25.

Based on current prices, 100 shares of ANR should be worth 22.23*100+97.25*95=$11,462 and only cost $9,580 on the market. Since the value of the ANR is dependent on the value of CLF, you would sell short the CLF in a merger arb situation. This way when you receive the 95 shares of CLF you can deliver them to whomever you borrowed the stock from.

For example, assuming the existing prices are where you buy and short and the merger closes, that means that ANR will be priced such that what you can buy equals 22.23*100+p*95, where p is the price of CLF. If CLF closes out at 100, ANR should be worth 117.23 per share. After your ANR shares are converted to CLF, you can close out your short (worth 95*100 dollars) and keep 2223 (22.23*100). The merger is supposed to complete at the end of the year and depending on how your margin account is handled, it looks like you could put up about 20k for an annualized return of about 20%.

That's not to say that this isn't risky. Merger arbitrage is a very risky business and it admittedly isn't mine. Given how that ANR has fallen fairly significantly since the announcement came out, the market is pricing (excluding shorting costs and TVM) that the stock is only worth three-quarters a share of CLF. I will be waiting for more details, particularly the proxy. Do your homework and certainly don't blindly follow me. I would have bought it on the open of 7/16 and have lost like 20 dollars a share already on ANR and not made it back on CLF. At these prices and this spread, I feel like it would be less risky given the potential gain.

SEC 8-K form
Press Release

edit: Harbinger Capital increased a position from 3/31 of about 8.73% to about 18.36% and announced in a 13D that they would oppose the merger.

Filed

2008-07-10T13:22:00.000-04:00

under who cares.

Increasing 200 day moving averages

2008-07-08T14:08:00.003-04:00

I did a quick study of what happens if you look at whether the 200 day moving average is increasing or not. I used the same asset classes and methodology as this which through February of this year showed a return of 11.98% (6.82% std, .875 Sharpe). I looked at three improvements which probably do not have different enough results to tell a priori which is better.

1. If the 200 day moving average is increasing a buy signal is generated, invest in cash otherwise.
2. Entry order is only generated when the price is greater than the 200 day MA, only exit if the 200 MA decreases.
3. Same entry order, but exit if below 200 day MA and 200 day MA decreases.

The first shows a return of 12.5% (6.9% std, .947 Sharpe), the second has a return of 12.8% (6.9% std, .975 Sharpe), and the final has a 12.4% return (6.6% std, .961 Sharpe). For the first one, the bond portfolio underperforms relative to the classical TAA model from Faber. In the second, the real estate portfolio underperforms. However, this is also dependent on the time period. Over the whole period the real estate underperforms, but since 1995, the second method produced strong returns in real estate (though the third method does better). The second method has the benefit of simplicity and surprisingly is in the market more often than the traditional TAA method.

I had originally assumed it would be in less. I wanted a method that would use the same entry and get you out quicker when the market begins to tank, but it appears that the benefit comes from keeping you in the market longer (roughly 70% of the months that are different are from the second method having a buy rather than a sell) and these months, particularly for commodities and stocks, generate strong returns and the handful of months avoided have relatively mixed returns. However, when they are down, they are down pretty significantly (real estate is an anomaly that acts opposite both effects). I was also surprised to find out that on average the TAA method generates on average 50 entry or exit signals per asset class whereas the second method generates about 45.

In conclusion, the TAA model can benefit by being in the market longer and not necessarily trying to avoid more periods.

Probit and Interest rates

2008-07-01T23:57:00.004-04:00

I'm curious how the historical shape of the yield curve can assist in the prediction of returns for holding government bonds. This is a preliminary post that plans to detail some of the basic lines of thought I am pursuing. I am heading to DC for the 4th, so I would like to perform an out-of-sample test to look into how this line of thought actually performs when I get back. I have some skepticism and doubts about this method that can only be confirmed upon more research (more on this later).

I began by collecting total return series for 1, 2, 3, 5, 10, and 30 year government bonds along with interest data that's available for bills, bonds, and corporate debt. Some of the series are active in some time periods and not in others, so I just stuck with 3 month t-bill and 1, 3, 5, and 10 year bonds, along with BAA corporate interest rates.

I first looked at the returns for the different bonds. In general, I am interested in holding for several months, so I took the geometric average three month returns and created holding 10 year (5 years back, five years forward) windows to evaluate each time period. The evaluation was simply which (not decile or quartile, but) quintile or 20% range the return would fall into. So if a time period is ranked a five, it would perform in the top 80% relative to the performance five years prior or forward. This way the select periods of time where bonds dominate don't outweigh the whole dataset and there are still runs where it makes sense to be in bonds. The only reason I don't do the whole series is that I believe doing so would result in too much trading.

The chart above is the average monthly (not 3 month) return for each of the bonds I looked at and each decile. Below that is the same chart except if given a 4 or a 5 above, the left-most column is a 1 and 0 otherwise. Since we expect that bonds with longer maturities should have longer durations it makes sense that the 30 year has the largest spread and the greatest opportunity to profit or lose. I also looked into the correlation of the returns to the 6 bonds. For the most part correlations like 3 year vs. 5 year are very high, but as you get larger differences, there are larger differences. However, what is striking is that the correlation between many bonds, even like the 10 year vs. 2 year, are higher than 80%. That suggests that for the most part if you can build a good model for one of them, the idea should work for all (with the 10 and 30 relative to the 1 year having lowest correlations).

I think it is interesting to look at conditional means (or categories) for different statistics. For example, what are the returns like on average over the next three months when the yield curve inverts (or steepens). The only problem with that is that I have so much data and so many different yield curves to compare. I didn't want to specify one way that would work best (ie. do I only look at when the 10 year inverts relative to the 1 year, or do I look at 2 and 5, do some outperform in different central bank regimes?). To give myself as much flexibility without doing something crazy like a neural network, I decided that it would be best (at least in a preliminary sense) to look into using a probit model to categorize the returns.

I described what probit models are and how to use them to look into the probability of a crisis or recession previously. Essentially, I have the series of 0s and 1s and the goal is to use the independent variables to estimate the probability that an event will occur (in this case, the event is that it is worthwhile to invest in bonds for at least three months). I estimated the model for each bond series using two methods, in the first I focused on the interest rates mentioned above without reference to their past values, in the second I used the interest rates and each of the past 12 lags. The first method is less successful than the second, but it also avoids a lot more curve-fitting problems than the first method. The first method classifies 63% to 72% (from 30 year to 1 year) correctly whereas the second method is up to 73% to 80% (from 30 year to 1 year). For comparison, using the binary decision of greater than the 10 month MA or less, classifies at about 60% for each bond (and including it in the decision-making doesn't help). Note that I consider classifying correctly to mean a probability greater than 50%.

What will be interesting is to look at the false positive rate and the returns in situations when there is a false positive. In other words, I think the value of the probit model is identifying risk/return better than other models. If I can identify situations with good average wins relative to average losses, then I can control my risk better. Using the model incorporating 12 lags (which I am worried about), I calculated the times where there are false positives for the 10 year bond and found a 2% annual return with 3% volatility compared to a 18% return with 9% volatility for the normal (note that this is just what the returns are and ignores the fact that it will be in cash for significant periods of time, just want to get an idea of the conditional means). As expected, the periods when the model says to get out of the market, there are negative annualized returns(-10% with 7% volatility). However, I am a little worried about false negatives, but after looking at how often the model invests (since it invests for three months), it appears that the problem goes away. Obviously the problem with this is that I use the whole series to develop the probit model rather than going with information available to develop the coefficients. I would suspect that these good returns would get slightly reduced by using the actual trading model (which is what I intend to test when I am back from DC). In comparison, the 10 month MA rule, returns 8.5% with 8.5% standard deviation (ignoring interest) though it is invested more often. Incorporating commercial paper yield into the second model would reduce its return (though risk/reward stays high) though also reduce volatility by more in this model than in the 10 month MA rule.

Nevertheless, it appears to be an interesting development, I am worried that the coefficients are a bit difficult to interpret (too black boxy) and that they won't be stable enough to generate significant returns. I also don't doubt there are problems with autocorrelation, but fixing that in probit models can be a pain.

Bear Stearns in Vanity Fair

2008-06-30T13:16:00.003-04:00

The article in Vanity Fair regarding the collapse of Bear Stearns was fascinating. Particularly for an essentially anonymous trader who was able to profit (by shorting other financial stocks as Bear went down) from their collapse. The day that Bear did the final drop (I can't pull up the ticker on any of my normal methods so I can't be sure which day it was) it was up 10 dollars at about 9 o'clock only to get beaten down to flat by 9:30 and then got smoked (pretty sure it dropped at least 25%-50% the next half hour). My only insight is that most traders just see what is happening and react.

Though the entire article is worth a read, I found the following quote particularly enlightening.

It was then that Gary Parr and the bankruptcy attorneys patiently explained that bankruptcy was actually not an option, not for a major securities firm. Changes to the bankruptcy code in 2005 would force federal regulators to take over customer accounts. All its securities would be subject to immediate seizure by creditors.

The 2005 BAPCA bill was a giveaway to credit card companies, but it seems like this statement doesn't really make sense. First, it depends on if the securities are in margin account or traditional customer accounts. Margin accounts are held in the name of the brokerage, so it makes sense that those would be able to be taken in bankruptcy. Though I'm not an expert, by any means, I would assume that this hasn't changed. Within customer accounts, SIPC protects cash and securities less than numbers only lawyers remember. So based on the statement above, the 2005 BAPCA would allow the immediate seizure by creditors of the customer's cash and securities held at Bear Stearns. To me that just means that if Bear declares bankruptcy, it would be forced to liquidate. It couldn't go into bankruptcy protection and eventually hope to emerge. The equity would be worthless. In other words, senior management would never consider bankruptcy for Bear. I could be totally mistaken, but it appears that if it weren't for the BAPCPA bill, Bear could (big assumption) have tried bankruptcy and not purchase by J.P. Morgan. I'm not an expert enough to know if this is the case, but it would be interesting to look further at the influence of this bill and the collapse of the company.

Natural gas inventories

2008-06-19T11:57:00.004-04:00

Natural Gas inventories were surveyed to change by 58 and came in at 57 (prior was 80). Natural Gas proceeded to fall 3% (at writing). For those who aren't traders, generally the natural gas inventories usually don't move the market enough to be worth trading (though they were three and four weeks ago), but I haven't seen such a strong, lasting move on this number when the inventories came in essentially in line. It looks like around 11 there was news (according to Briefing.com) that China would raise some prices of gasoline and crude, but this decision wouldn't affect natural gas. I guess I'm kind of at a loss to describe it.

Generally the trend is your friend, but I can't help put think that this is oversold (the front contract is at 12.72 and UNG is as 60.30 as of this writing). However, bottom picking this kind of strength on the downside can be vicious unless you are looking to hold for a long enough period. Thankfully my only position in UNG was in a play account on updown because I have been wanting to bottom pick this for at least an hour and it just keeps going down. The futures are at 12.65, down 4.3% from the open.

Edit: Looks like I was about ten minutes off the bottom. Also edited for grammar.

Volatility Smile

2008-06-16T17:35:00.002-04:00

The Black-Scholes-Merton model makes the assumption of constant volatility. In practice, we observe something called the volatility smile. Basically, options struck at the money have less volatility if you solve for volatility in BSM than options struck far in or out of the money. This is an interesting phenomenon that finance professors like to write about and hedge funds try to exploit.

I wonder whether equity index options (in particular just b/c I know that the 10 month MA strategy works on them and they have a long history) experience different volatility smiles when above the 10 month MA or below the 10 month MA. If the volatility doesn't change, I would look to a situation where calls are cheap when the market is trending up and puts are cheap when the market is trending downwards. I imagine it would take significant work to look into this. If no one else does (let me know if you do), then I might take a stab at looking into this problem sometime within the next six months. Nevertheless, I think it is an interesting question and could present arbitrage opportunities. Volatility is traditionally higher when equity markets are below 200 day moving averages, but I wonder if it is high enough given historical volatility during these times and the small (mostly negative) returns.

Beta and Sectors

2008-06-12T23:58:00.008-04:00

I meant to post something about the interest rate environment and tactical asset allocation, but I haven't gotten around to it since the results aren't that spectacular. Still kind of interesting. Anyway, I've been reading Eric Falkenstein lately over at the Falkenblog and his website DefProb.

One point that he makes is that historically buying low Beta stocks has better returns than buying high Beta stocks (though there are periods of significant underperformance such as the internet bubble). I found this result interesting (risk is inversely related to returns, how could that not be interesting?) and so decided to look into a similar strategy using sectors.

I used weekly dividend adjusted data of the 9 Sector Spiders since they began at the end of '98 along with SPY. I calculated Beta vs. SPY using at least a year's worth of data and no more than 5 years worth of data. At the start of every year I ranked the Sectors on the basis of Beta and formed a high Beta and low Beta portfolio with three Sectors each. I also calculated a portfolio investing equally in each Spider to serve as comparison (SPY is market-weighted).

Over this period (from Jan. 2000 to the end of last week), the equal-weight portfolio return 2.4% annually (15.7% std), the high beta portfolio returned -.14% (20.7 std), and the low beta portfolio returned 4.3% (14.3% std).

I then calculated the 40 week (200 day) moving average and considered a signal at the beginning of the month good through the end of the month (since that is how the 10 month TAA works and I wanted it to be somewhat comparable). The results are reported below:
(After accidentally inflating the returns of the high portfolio) The results indicate that the low Beta portfolio outperforms when the market is above the 40 week moving average and slightly outperforms when the market is below the 40 week moving average which confirms the argument that Mr. Falkenstein had made (note that the Sharpe ratio is higher for the high than the low in the below 40 week, I think that the Sharpe ratio is an incorrect method of comparison when returns are below 0). That doesn't change the fact that investing when below the 200 day moving average is very risky.

CFO advisory posted yesterday regarding the sector momentum strategy (which I have covered before on this site) and noted that a significant portion of the return has been due to XLE. The low Beta portfolio included XLE from 2000 to the beginning of 2007; however, from 2007 until recently XLE return 35% annualized compared to 11% from 2000 to 2007. So I would argue that the performance of the low Beta portfolio doesn't suffer from the XLE criticism (note that I really agree with it anyhow).

TAA and avoiding pullbacks

2008-06-05T13:31:00.002-04:00

I should probably be studying, but this didn't take me that long to work out and was pretty interesting.

This could be considered another extension of the tactical asset allocation system developed by Mebane Faber that I have blogged about several times. The original strategy is to invest in five asset classes (US bonds, US stocks, Foreign stocks, Commodities, Real Estate) when they are greater than their 200 day moving average and commercial paper otherwise.

I modified the system slightly, maintaining the 200 day moving average requirement, but I added an additional constraint: it could not be the case that it was above the 5 month (4 and 6 have similar results) moving average and the return over the previous month was negative. The point of this was to take into account periods being overbought and then getting back in quickly. The periods above the five month that have negative prior month returns have very poor risk to reward ratios, most significantly for stocks and REITs. So making this simple addition can take a system with an 11.9% historical return with 6.8% standard deviation (.867 Sharpe at 6%) to 11.8% with 5.68% standard deviation (1.026 Sharpe). Though there is not a statistically significant difference in means, there is a significant difference in standard deviations according to an F test.

Not only is this improvement a significant, easy to implement improvement, but it is based on logic. Most trends do not continue up continuously. There tend to be pull backs. This strategy maintains the idea that the trend is your friend and attempts to stay out of a pull back if it happens two months in a row.

Note: the portfolio leveraged 50% has a 14% return with 8.5% standard deviation compared to 13.5% with 9% standard deviation for the original version. The best benefit in reducing standard deviation is in keeping the risk to reward statistics strong when using leverage.

The Hedge Fund strategy that wasn't?

2008-05-22T14:54:00.005-04:00

One of Crossing Wall St's more recent posts refers to an older post regarding the returns to trading when the previous day was a large or small return. They conclude that big days lead to more big days in either direction. In order to avoid any biases, I looked at the average daily return and standard deviation each day and created a strategy to buy if it is more than one standard deviation positive and sell if it is more than one negative. I used a ten year lead up and began the strategy in 1960 without including the returns of dividends (12178 observations). I also looked at portfolios using the same strategies for two standard deviation envelopes. For the 1 up and 1 down portfolios, the return (of just the days invested, ignoring risk-free returns) is 53.9% (15.5% standard deviation, 1728 observations) and 26.06% (20% standard deviation, 1817 observations), respectively. For the 2 up and 2 down portfolios, the returns are 82.4% (18.75 standard deviation, 462 observations) and 18.04% (27.5% standard deviation, 501 observations). Also note that these are annualized figures and on average they might make only 35 trades a year.

All things considered, they look like strong strategies. It makes more sense to combine the long strategies since their returns historically are the strongest. My combined strategy was to be long above the 1 standard deviation and use 100% leverage when above the 2 standard deviation. the returns are 79.05% with 23% stdev over 1728 observations.

Just on the basis of my recent trading, I felt that these returns looked too good to be true (granted they are only investing some 15% of the total observations). I hadn't seen this many big days together in the past 5 months or so. So I decided to look at the rolling 10 year cumulative returns to confirm how it has performed historically and how that would appear relative to today.
The chart above plots just that. Particularly back in the 70s the market trended very well. Furthermore the returns to the strategy were strong from the 80s to the 90s. However, the strategy seems to have lost its edge in recent years. The ten year cumulative return most recently was only 17.7%. I'm sure this is greater than the markets return ex-dividend, but my point is that just because a strategy worked in the past, doesn't mean that it will continue. For example, waiting to start the strategy until 1985 cuts the average return from about 70% to 36% with only 500 fewer observations. What is also interesting is that the sign of the minus 1 and minus 2 standard deviation strategy has flipped since 2000. They are buy signals and not sell signals. 13% return (23% stdev) for the down 1 standard deviation if you buy and 50% return (27.7% stdev) for the 2 standard deviation. The up 2 standard deviation strategy still has worked since 2000 (though with dramatically lower returns, 22% with 21% standard deviation), but the 1 standard deviation strategy has not.

The returns to the strategy appear to be stronger if you use 10 year rolling averages and standard deviations for the entry points, but the success of the strategy follows the same trend. For example, this strategy (the one graphed above) since 2000 returned 8% annualized with 28% standard deviation compared to essentially flat with 27% standard deviation the way originally calculated.

Stops

2008-05-20T14:43:00.002-04:00

I was directed to IBDIndex through Quantifiable Edges. The more recent posts are also interesting, but this older post on stops is fascinating. Essentially, he tests using an 8% trailing stop and then if you have gained 17% on a trade, he uses a 25% trailing stop. It seems to be pretty successful when trading stocks and would be worth it to check out. In part 2, he gives the results on a robust backtest.

TAA update

2008-05-19T23:29:00.003-04:00

I probably will not be posting that often for the next three weeks or so. I have the level 2 C.F.A. coming up and I have got to hit the books.

Anyway, unless there is a correction, May will show a signal to invest in equities according to the TAA model. I was interested in the returns in time periods when the previous signal was to not invest and the following month closed above the 200 day moving average. By comparison, the excess monthly TAA return is 5.16% historically with a 6.94% standard deviation (12% normally) and5.8% excess return (13.76% standard deviation) for the S&P500 timing model. When there are two consecutive months of buy signals, the similar statistics are 6.25% return (13.48% standard deviation). For the S&P500 when there is a sell signal in the month prior and a buy signal in the present month, the average excess return has been .09% with a 12.81% standard deviation. However, if you look at all of the assets, commodities and foreign stocks have very strong returns that keep the overall strategy strong. Excluding the S&P500 dates until there are two buy signals slightly reduces the standard deviation while keeping returns positive, though it doesn't appear to be statistically significant.

For the 24 times since 1974 that if you bought the S&P500 at the beginning of the month when price crossed above the 10 month SMA, you probably wouldn't have any return, but the standard deviation of equities.

Spurious

2008-05-14T19:58:00.003-04:00

I generally like Bespoke. They make some good recap posts of what sectors or countries are performing relative to each other. However, I was disappointed with today's post. Their point is that if you graph the S&P500 since October and compare it to June1990 to July1991, we follow a pretty consistent pattern.

I've seen arguments like this made before, "this is just like the conditions leading up to the '87 ('29 or what have you) crash." To the extent that some market participants believe this (as it can be generally be heard in the financial media), there might be some predictive power in that. I'm not sure, I would have to test it. However, my complaint is that simply graphing one time series onto another and positing a special relationship that could indicate future returns is sloppy statistics and bad practices all around. At a bare minimum, you should report the correlation today vs. that time period, how many times there has been similar correlations over time, and the returns in those situations. There's certainly more you can test, but I would suspect that it would make sense to check whether or not the relationship is spurious.

Well, I decided to look into this a little deeper. I use the weekly S&P500 data and compute the correlation of rolling time periods with May of 2007 through the end of the first week of May. Out of 3,011 weeks that correlations were computed, 457 (15.2%) showed correlations with the recent time period greater than 50% and 135 (4.5%) showed correlations with the most recent time period greater than 75%. The most highly correlated periods showed 90% correlation only 3 other times and two happened in 1953 and the other was 1990. However, if you look at the 75% correlation periods, it is clear that every time there has been a downturn, the market tends to look like it is now. They're right that on average, the market has bounced when it was highly correlated with today, 1.7% over the next three months (7% annualized). However, the standard deviation was also 8.5% (17% annualized) which means that it isn't statistically different than zero. On a six month basis, the return increases to 4.87% (9.7% annualized), but the standard deviation increases to 14.7%(20.8% annualized). So if you wanted to take advantage of the historical correlation, you would also be looking to take on a lot of risk.

Another point I wanted to note is that when you have a series like stock returns that have unit roots, you generally need to difference the series or log difference the series to tease out relationships. A unit root basically means that the process is not stationary, it doesn't have a consistent mean and standard deviation. But, if you put the returns in the form of percentage increases, then the returns might have the same mean and standard deviation over long periods of time. The problem is when you compare two series that both have unit roots (as both comparisons are here) and if you regress one on another and find a large R^2 value and positive autocorrelation. If the residuals are also integrated order 1, then you have what is called spurious regression. If the residuals are integrated order 0, then you have cointegration. Cointegration is like the relationship between gold and gold mining stocks (or oil and oil services stocks). Spurious regression would be like the relationship between defense spending in the U.S. and the population of South Africa. Both go up, but there's no fundamental reason. I can't think of any reason why the stock market would necessarily behave exactly the same way twice, but the way to test this would be to set up a Matlab program that iterates through every week of data and looks at the returns of highly correlated months and invests when they're significant. All things considered, it wouldn't be hard to test (this is just one time period).

For example, if you were looking at 6 month correlations on October 5th, 1987 and would hold for 3 months if the correlation were greater than 75%, then you would find an annualized return of about 10.6% with 11.4% standard deviation (pretty consistent even including the awful 1987 data with the whole series). You might choose to invest and lose 20% over the next three months. The risk/reward ratio looked even better on a 85% basis. Interestingly enough, the situation of greater than a 90% correlation with the 6 months leading up to the 1987 crash has never happened and neither has it happened looking at it including October (despite what anyone else will tell you). My point is that a correlation with a previous time period, or a chart pattern similar to what happened before, may or may not be robust, but it should be statistically tested and caveats given before being used as a buy/sell.

Donchian Channels

2008-05-14T13:33:00.002-04:00

A Donchian Channel is the formed by the high and low of the past n days. For my purposes, I used weekly data on the S&P500 from 1950 through May. I ignored interest compared the returns (w/o considering dividends) with a strategy investing when the market is above the 40 week (200 day) average. I checked several different ns, but 20 weeks (100 days) seems fairly standard. The results are generally consistent no matter how many weeks are chosen. When a 20 week high is hit, then a buy signal is generated and similarly a sell signal is generated for the 20 week low. I used a 10 week ATR to measure a trailing stop (high-2*ATR or low+2*ATR) as my exit.

When in a position, the SMA strategy generates a 10.6% annualized return with 12.05% standard deviation (1983 weeks).

The short side of the strategy generally underperforms. In other words, equity markets (as represented by the S&P500), do not tend to trend downwards after hitting 20 week lows. The long side of the strategy generates a 7.6% return with a 14.1% standard deviation in 3005 months. I wouldn't be surprised if additional filters would allow the long-side to have strong profits. For example, an additional requirement for a buy signal (not as an exit) with price greater than the 20 week moving average increases return to 8.3% and a 12.3% standard deviation. Combining the two original strategies together generally results in a return not significantly different from 0%. Since this is the basis for the turtle trader strategy, I would consider this pretty important. Unless you're a short-term trader, quant, or hedge fund, I would recommend staying away from shorting equities. Since the turtles mostly traded commodities and currencies, I wouldn't be surprised if this type of strategy works better on the individual components (as this would probably work better on individual stocks rather than equities as an asset class). I still feel that keeping things simple with the 200 day would probably be your best bet.

Since the short strategy generally results in the underperformance, I considered flipping a long when at the 20 week low and the market is greater than the 25 week SMA (no cases when this occurs for the 20 week). This strategy by itself produces a 14.9% return with 14.1% volatility. Unfortunately, over more than 50 years, this happens in only 55 times. I did some other tests in TradeStation with the ADX which also seems to be a successful filter, but the data I was using wasn't nearly as long a time period. I wouldn't be surprised if short-term reversals in equities generate strong returns, but those strategies generally require strong risk management

OverBought/OverSold part 2

2008-05-08T11:41:00.002-04:00

Regarding yesterday's post with OverBought and OverSold indicators, I combined that with the TAA model from before (5 asset classes, buy above 200 day, invest in Commercial paper otherwise). I just wanted to add in RSI since that had a tendency to be most effective (can't use lower bollinger band since already out, not enough data for stochastics). I started with the method from yesterday (only invest when RSI is less than 75) which works very well with equities, but this method does not work as well with the other asset classes and it significantly underperforms as a diversified strategy. However, it remains significant for equities, so I will leave it in place for them. EAFE benefits from staying away when there is an RSI less than 50, but the other asset classes are already out of the market enough due to the TAA that it really doesn't improve their situation that much (25 results in no change for any of them) and the change just for commodities won't change the results significantly (statistically or economically). Ignoring the OverBought RSI figure for everything except equities also improves returns (different time periods are slightly improved by reducing them to 98 or 95, but it is not statistically or economically significant).

In other words, what is true for yesterday was likely true just for the S&P500 and not something applicable to a diversified strategy. However, just including it for equities can raise the Sharpe ratio from .88 to 1 over the entire time period and from .94 to .99 since 1990. Not a statistically significant difference for the overall strategy, but since it is statistically significant for the underlying, it might be worth considering an addition. A strategy that avoids situations where the monthly return is greater than the 2 (or 2.5 or 3) stdev Bollinger Band does not improve returns overall.

OverBought/OverSold

2008-05-07T13:32:00.004-04:00

One of my interests is looking into ways to improve investing returns. I decided to look just at the S&P500 on a monthly basis since 1967. Mebane Faber has noted that the returns to a 10 month simple moving average strategy earns significant returns. In this sample, the returns are statistically significant with a 12.2% return (13.5% standard deviation) compared to a statistically insignificant 5.8% (18.3%) when below. I wanted to test three common OverBought/OverSold indicators on a monthly basis and then check to see if they would be any benefit when combined with the 200 day strategy.

The three indicators I used were Relative Strength Index, Slow Stochastic, and Bollinger Bands. I would imagine that most people who would come to this site has heard of these concepts (which you can google if my explanations aren't good enough), but I'll explain their basic concepts anyway. The Relative Strength Index scales the ratio of the size of recent up moves to down moves. If there are more up moves, then the ratio will tick up which is then scaled from 0 to 100. The %K fast stochastic indicator measures where the most recent close is relative to the range the stock has been trading in. If it is trading near recent highs, then it will be closer to 100 and closer to 0 when trading near lows. Slow Stochastic is a 3 month MA of the fast. Bollinger Bands measure 2 (or n) standard deviations away from the moving average. For all of these, I use ten months as the initial range. I'm only able to do the slow stochastic since 1988 since I couldn't get highs or lows before then.

The biggest problem with these is that compared to the 10 month strategy, these have relatively few occurrences. So instead of being concerned with Sharpe ratios, I'm mostly concerned with statistical significance.

The results are that few of the indicators result in statistically significant returns. Overbought/oversold points on the 2 stdev Bollinger Bands are not significant with almost zero return when greater than the 2 and too few observations when less than the -2 (though that return is about 20% annualized). With breakpoints at 20 and 80, the oversold RSI is not statistically significant, but the Overbought is statistically significant in the positive direction. In other words, when the RSI is greater than 80, the market generally keeps going up. However, at the 90 breakpoint, it is no longer statistically significant. Combining those two signals (greater than 80, less than 90 (or 95) is statistically significant and occurs in about 72 months (14.5% of total). This indicates to me that the RSI does work as a momentum indicator and as an OverBought/OverSold indicator. Finally, the Slow Stochastic with 20 or 80 is significant (though both are positive). There are only five cases where the Slow Stochastic was under 20 (including March) and the average return in the next month has been 5.4% (this April did not disappoint). Increasing the low breakpoint up to 25 still gives significance and increasing the high breakpoint all the way up to 95 still shows significance with positive returns (I expected negative). This would indicate to me that Stochastics are not particularly good as OverBought/OverSold indicators on a monthly basis. However, it is really the most extreme readings that really generate statistically insignificant results. So it might make sense to look at a stochastic of 98, but a stochastic of 85 or 90 is probably more indicative of momentum than anything else.

So how would an investor incorporate these into a strategy? In general, you would want to stay away from situations where you do not generate statistically significant returns and invest when they are. Including the strategy when the slow stochastic is greater 80 or 90 combined with the 200 day MA does not change returns. The 200 day covers the momentum effect already. Avoiding the situations where it is above 98 does not result in a statistically significant difference between the two results. The below 20 or 25 is not statistically significant either. However, both of those two increase the Sharpe ratio of the strategy (note I use since 1988 for this part, but since '67 for the rest).

For the Bollinger Bands, you may as well ignore the OverSold indication since it always comes when you are out anyway due to the 200 day. The OverBought indication increases the Sharp ratio, but its inclusion is not statistically significant compared to the 10month SMA strategy.

What is true for the OverSold in Bollinger Bands, is also true for the RSI. The 200 day already gets you out of the market. Even the best combinations of the OverBought indicator (noted before at 80 and 90) do not improve significantly on the 200 day MA. However, if you reduce the break down to 75 and do not invest when the momentum is greater than that, then you will significantly increase returns at the 10% level. I just kind of pulled that number out of the air so I was surprised it works and am more afraid that it was a bit of curve fitting. The only problem is that if you are an investor looking for total returns, you will reduce the months of investing by almost 50%. Even still, though, if you include the risk-free return, then the historic returns for this strategy are at 11.5% (10.7% SMA) with a standard deviation of 8.1%(11.6% SMA). That ratio of return to risk is consistent over multiple time periods. The ratio is also fairly consistent going down through 70 (and below, though the returns suffer since you are in that many fewer days). The good thing about the RSI is that it is easily incorporated into other strategies since it only uses closing prices.

One additional improvement (that could be some curve fitting action) would be to make three requirements for a position, the first is SMA or below 25 on the stochastic, the second is RSI less than 75, and the third that the stochastic is not greater than 95. This return is significantly greater than the original SMA almost at the 2.5% level. After incorporating the risk-free return, the Sharpe ratio is .71 vs. .63 for only the RSI requirement, and finally .43 for the SMA. I plan on backtesting the TAA strategy with the RSI requirement, but I cannot backtest the complete method since I don't have high/low information for total return indices on bonds and REITs. ETFs have the information, but the time frame is smaller which makes comparisons difficult (though implementation is still possible).

In conclusion, OverBought and OverSold indicators can have some value in pointing out time periods to avoid (or get in), but they seem to have the most value when used in conjunction with each other. There are many dangers with curve fitting when using this kind of analysis, so the general rule is to keep it simple stupid and test a strategy that works on one set of data on other sets and look for some kind of consistency in the returns.

BRK

2008-05-05T12:38:00.003-04:00

Berkshire Hathaway held their annual meeting over the weekend. There has been some news about how lower returns on the insurance business and their derivatives positions (specifically equity index puts) hurt their bottom line. I love to take the time to gloat that I called it (it being losing money on the puts in the short-term).

However, I don't think the coverage of the loss has been that great. He only has European puts which require payment at expiration, so the loss is unrealized. He has paid out no money and won't have to pay out any money for many, many years (if at all, which is what I argued). I'm by no means an expert in the way that derivative contracts are accounted for (see FAS 133 if you want to figure it out), but traditional equities or fixed income can be classified as held-to-maturity, available-for-sale, or trading securities. If a derivative contract were classified under the fixed income or equities held-to-maturity method, then the historical cost would be recorded on the balance sheet and any realized gains or losses would be recorded as they occur. Short of bankruptcy, I can't imagine a situation where Buffett would get out of these positions. I guess I don't understand why he isn't allowed to use this method of accounting since it most fairly represents the value of the position. FAS133 seems to require any derivative that is not part of a hedging operation to have the gains or losses recorded each quarter. That seems inaccurate and misleading. If I were performing equity analysis on Berkshire Hathaway (or any company with large derivative positions that they could never possibly lose money on if they held to maturity and are well-capitalized), then I would restate that part of the balance sheet as if they were held-to-maturity.

Also, I should note that the numbers on the balance sheet that are reported as liabilities and occasionally mentioned in the press for his derivative positions, might also include new positions. A quarter of the increase in liabilities (383 million of 1.6 billion) on equity index puts is due to new positions, and a third (229 million of 667 million) of the CDS losses. I don't know much about the underlying content of the CDS positions, but losses on these positions could be outweighed by the (unrealized) profits on the index puts if the market improves. A little strange that he would lose money on both (market still collapsing in March, but credit conditions improving). Overall, he lost 1.2 billion on the equity index puts that he will never have to pay out. That would make Net Earnings per common of about 1382 instead of 1682 (decline of 18% instead of 64%). Considering other financial firms have performed significantly worse, I would say that isn't that bad. And Berkshire Hathaway will be able to show much greater (unrealized) profit if the market improves, even though we know that they really just gained back money written off.

Wish you were here

2008-05-02T11:26:00.004-04:00

Here's for wishing that the BLS had an easier method for pulling data on the birth-death model from their website.

Anyway, this might just be pulling stuff out from nowhere since I didn't extend the series for long enough, but I did some manipulation of the Establishment survey data that came out today to get an idea of what the results would have been if the birth-death model hadn't been adjusting the data. Here's my big problem, when we compare results from now to the last recession, you're not comparing the same thing since the Birth-Death model has been adding jobs. There have been different methodologies over the past 8 years or so, but as they have changed, they have been adding more and more jobs through the BD model. Ideally if you wanted to compare all of the data, you would completely remove the influence of the BD model from non-farm payrolls.

For example, several financial reporters have noted that the decline in this month was not nearly as large as from March to April 2001 when the economy shed 281,000 jobs. The birth death model added 52k in March and 75k in April of 2001 which would mean that the net effect would be losing 304,000 jobs (note that this comparison may not be perfect since the Birth Death figures could be non-seasonally adjusted and I'm looking at seasonally adjusted payroll data). In comparison, the April figure for this year was -20,000 before taking into account the Birth Death model, but -145,000 after. In other words, we lost about half as much as many jobs as the beginning of the last recession. The numbers for Feb-Apr have all been negative and for the year we have lost 457,000 jobs compared to adding 1,090,000 all of last year. In comparison, the first four months of 2001 didn't shed as many BD adjusted jobs. (though most of the job losses came in the second half of that year).

Again, I'm not sure if this analysis is the best, but my point is that you can't compare historical recessions to this one using job data that has been manipulated. So when you hear financial reporters say that the job report isn't that bad, know that they really don't know what they're talking about.

Addendum: if you take everything in non-seasonally adjusted figures (Dec and Jan are vastly different), then March showed 573 after B/D adjustment and April showed 578 afterwards. This is compared to 571 and 382 in March and April of 2001, respectively. Again, you really need to then re-seasonalize the data (by whatever method the BLS does it) to really compare it to what generally gets reported in the financial press.

Here's for not understanding GDP numbers

2008-04-30T09:41:00.004-04:00

In addition to the plethora of economic information coming out today, advance GDP numbers came out for quarter 1 early this morning. I'm not surprised that the current account deficit narrowed, that is to be expected with a weaker dollar. Looking at the percentage change table, it is clear that inventories were strong and services were strong. The increase in inventories was responsible for a 20 billion dollar increase, but the increase in services was responsible for a 40 billion increase. The Q4 inventory data was pretty awful, so I'm not surprised there was a bit of mean-reversion. However, I'm more surprised at services being as strong as they are.

If you go into table 2.3.1 (or 2.3.6), you will see why services are strong. Basically, in spite of a housing recession, spending on housing (services, not to be confused with residential investment) goes up. I'm not surprised that housing operation is going up (electricity is increasing at a 15% rate), but I'm a little baffled why in the middle of dramatic decreases in home prices and sales that spending on housing would be increasing. Medical care and household operation (electricity mostly) make up a big percentage of the increase in services (and therefore services), roughly half. And another large increase is due to other. The big question I have is, why isn't spending on housing services decreasing in the GDP numbers rather than consistently increasing? The durable goods section showed only a small decrease, but the average increase since 2006 in the housing services number has been .6% and increased by .55% this time. Effectively in line. Granted that the ISM non-manufacturing index was below 50 the entire quarter, it makes even less sense why services would be increasing.

Ultimately, if you use better inflation numbers or per-capita figures, this would probably be the second quarter of a declining GDP. Not the best definition of whether we are in a recession, but it's what the financial press usually talks up.

Long-term Component Timing Model

2008-04-23T12:17:00.005-04:00

My primary concern here is to test a component (subsector) timing model going back more years than ETF data is available. Total return data isn't available for sub-sectors for all asset classes in a way that could be approximated with ETFs available now. However, there are total return series available that replicate them well enough to be comparable with prior results developed in this space (here). For domestic equities, I was able to use the S&P indices (used in Rydex ETFs). For commodities, I was able to use the DJ-AIG indices (just using futures is not comparable to total return indices. I used total return series for a number of foreign equity indices. Finally, I added a AAA corporate bond index to the 10 year treasury since none of the other bonds really are that impressive for the long-term (30 year has strong returns, but too much volatility). Reits are kept the same.

The general strategy is as simple as the TAA strategy. If the subindex is above 10month SMA, invest, otherwise stay in commercial paper. For equities, I also entered the entire asset class in CP when the broad index is below the SMA. They have much stronger correlation to the index than the other asset classes. Asset classes are equally weighted. I'll only report since 1991 (when I have data for commodities). The returns are consistent over time, they tend to slightly decrease, but with consistently lower volatility.

For reference, the AA strategy has a return of 9.65% (7.8% stdev) and the TAA is 10.8% (6% stdev). Extending the strategy with the component timing model gives 10.4% (4.7% stdev). Adding in a currency strategy similar to this* will reduce returns to 9.9% (4.2%).

*including interest rates from holding foreign currencies, but not counting the movements of currencies when in domestic currency since other asset classes do not control for value of the dollar which makes it not comparable to past strategies, all this does it lower the return and keeps volatility relatively constant, just wanted to be conservative

For the unlevered strategies, the alpha of each strategy is highly significant (<.01%) at 3% (.64 Beta) for the original, 3.6% (.46 Beta) timing w/o currencies, and 3.2% (.42 Beta) with currencies. The alpha of the timing (w/o curr) vs. the TAA strategy is significant at 1.7%. Using 2:1 leverage (except for the currencies), the TAA strategy has an alpha 4.86% (1.2 Beta), 6.3% (.92 Beta) timing w/o currencies, and 5.4% (.8 Beta) with currencies. Note that the levered returns are 16.1% (12% stdev) for the TAA, 15.6% (9.4% stdev) for the timing w/o currencies, and 14.3% (8.1% stdev) with currencies. Using even more leverage (1.5x), would give an even larger return for the timing model with roughly the volatility of the 2:1 TAA strategy.

Note that I did not use a momentum strategy, just the timing model. This means that there would be relatively small transaction costs, but you could not use futures contracts to implement it (except commodities and foreign indices). Nevertheless, it shows that there is significant evidence that this strategy has worked over a significant period of time with a variety of asset classes. I expected the returns to be different since I am using more equally weighted portfolios than cap-weighted as the indices are (within each it is cap, between each it is equal), but I was pleasantly surprised at how well it performed over the past 18 years or so (and 30 years) which gives further evidence that the momentum strategy for the component TAA strategy or a strategy like this with much less in trading costs.

Value Investing

2008-04-22T20:27:00.002-04:00

I would recommend that anyone who thinks the markets are efficient should read this research.

Commodities and Countries Update

2008-04-16T14:52:00.007-04:00

I added in the combined the j/k momentum model and the TAA model for the commodity and currency strategies I described yesterday(before it was only TAA, but I know follow the guidelines described in this post). The results confirmed the reasoning in yesterday's post. Commodities historically (tested since 83) do not have a very powerful momentum strategy. However, the j/k strategy with countries and the TAA model combined outperforms using the TAA model individually on each country. However, the TAA model generates very few signals and would be better for a longer-term investor. The j/k model (with j=4, k=2, and investing in the top 25%) with TAA overlay has a CAGR/Stdev of 2.18 (CAGR: 9.5%) compared to .99 (CAGR: 12.4%) for the EAFE TAA strategy. The EAFE without currencies in the TAA has a Sharpe of about 1 and 1.14 with them. Those increase to 1.07 and 1.23 (1.04 and 1.19 for yesterday's). However, regressing the new excess returns on the individual TAA excess returns does not generate significant alpha (annualized 26 bps), but the Beta is only .81. Unlike yesterday's strategy (ex-currencies), this strategy does have a significant alpha (at 10%) of 50 basis points relative to the original TAA strategy with a Beta of .78 (it improves to significant at 5% with 55 basis points with the currencies relative to TAA with currencies compared to 30 bps for the strategy yesterday).

* 50% decreases the Sharpe of the foreign strategy by themselves, but increases the Sharpe of the OVERALL strategy, I just wanted to be consistent with previous posts

addendum: I should note that the returns to this strategy are over a long period of time, particularly since the currency strategy benefits from high interest rates. The Sharpe ratios come down significantly over the past ten years compared to the past thirty years. Since the strategy has maintained a more constant growth path (ie not the early/mid 80s), the country strategy improves the Sharpe from .83 to .96 for the TAA strategy (individual country TAA is .93). However, the inclusion of the currency strategy has a smaller effect (I don't take into account the declining value of the dollar on any assets besides currencies, so this could be understated) increasing the Sharpe ratio by .04-.05. It seems that compared to the 50% momentum strategy over the past ten years, the EAFE has outperformed historically so that the momentum strategy is relatively constant, but the EAFE outperforms. (.4 10 year Sharpe vs. .1 30 year) in the past few years. I'm not sure how long the EAFE will continue to outperform, but I would prefer the less volatile Sharpe ratio. Right now my thinking is that after taking into account the depreciation of all of these assets in dollar terms, the best cash strategy would be the currency strategy, but I'm not sure yet.

Not impressed with JPM

2008-04-16T09:51:00.002-04:00

JPMorgan put out earnings before the open today. It opened up 4% and despite the initial squeeze, it is up about 1% from that point as this statement is being written (9:55). JPM has traded from a low of around 37 to around 47 since November so a two dollar move in this range (after getting beaten down the past week) isn't all that impressive. Even though it is roughly at the average price since November, I still am unimpressed by results that "beat estimates."

Of course Wall Street cares more about coming in line with estimates than actual figures (EPS down 50% yoy, 20% qoq, "could have been worse, buy"). However, if you actually look at the 8-K instead of looking at the headline number, you would notice that JPMorgan made about a billion dollars on the Visa deal. The Corporate/PE division had 1.027 billion in net income which is actually 72 if you subtract out the Visa deal. I don't expect them to make any one-time deals with this much profit over the next year so I would guess that the next earnings will come out much lower than this quarter's. I would expect the remaining quarters to be closer to an average of last year's profit for this division and then a rosy estimate would be that the other divisions keep net income constant (or growing/declining at the rates from Q4 to Q1, effectively flat overall). In this case, Net Income would be 600 million lower (assuming same level of credit losses which I really have no way to estimate, could be lower could be higher and would have a big effect on Net Income) or at 1.8 billion. That would put a crude estimate of EPS for next quarter at .50 or down about 25% qoq (or similarly for this quarter assuming the IBanking revenue was not above average and down 43% qoq from that perspective).

These are crude assumptions, but an exceptional one-time event like the largest IPO in history should not be the saving grace during the credit crunch. I care about earnings going forward.

Note: WFC actually does have a pretty good business model. Over 90% of their loans are prime. They're going to lose some money, but be in a much better position coming out of this crisis. All of their business segments showed declining yoy, but that will likely turn around better than other banks.

JPM is still up .75% from the open (10:20).

Commodities and Foreign Countries

2008-04-15T20:51:00.004-04:00

Continuing on with my theme of finding ways to improve the TAA model (here, here, and here), I thought I would do some more research into a longer examination of a timing strategy, but breaking apart an index into its component parts. I don't use the momentum strategy described in my Component TAA, Part II post (noted above), but just the normal timing model after breaking apart the EAFE and GSCI into their components. The strategy is to go long the components above the 10 month SMA and be in cash otherwise, just like Mr. Faber's TAA strategy.

I'll start with the GSCI. I used data available from the Global Financial Database on Commodities futures since 1983 (except Natty Gas which is since 1990). Unfortunately, they didn't have all of the energy contracts and were missing a few of the other contracts. I kept each commodity subgroup (livestock, ag, energy, ind. metals, precious metals) the same weight and scaled up the components. I confirmed that this index has about a 94% correlation with the GSCI. I was a little disappointed with this figure (preferring higher than 97.5%), but I will make due with what I have. I tested just performing the timing on the sectors (since 91) and on the individual components (since 83). One thing is very clear, the GSCI is dominated by energy you cannot compare an equally weighted TAA strategy with the market-weighted portfolio in GSCI. If you compare the strategies, use weights close to GSCI.

With sectors and a buy and hold strategy, my returns are initially different than the GSCI, so I don't expect the best comparison for the timing, but with 94% correlation, I would expect similar trends. However, I found that the return/sd ratio increased for the GSCI strategy, but not the component strategy. Variance decreased, but returns decreased as well and the effect was not economically significant. On the other hand, the returns to the GSCI strategy are enhanced considerably. The returns and correlations are roughly the same if you break it down into all of the contracts weighted by what is in GSCI. I wouldn't be surprised if some of this result is due to the fact that many of these commodities contracts show considerable seasonal variation that cannot be reduced easily by using the 200 day MA the way that an equity indices returns are improved (they lack the seasonal variations) and that the aggregate figure trends better. A more complex strategy, such as taking advantage of contango or backwardation, might be more appropriate for the components of the GSCI. There are other indices that I could use to test this method since I didn't have all the contracts (I will use the CRB indices except energy which I will have to recreate).

Countries, on the other hand, do trend well and the timing strategy works very well on them. I used total return data and replicated the EAFE index since 1994 with a 99% correlation. Before that time period, I replaced the FTSE-100 with the All-Shares index and some other total return indices are used that don't have futures contracts for them.

(begin digression: I had to use alternative indices for some countries that didn't have total return indices for the whole period, however, the question is how the strategy improves on this Buy and Hold strategy and not necessarily on the EAFE. If it improves returns over a long period of time, you could reasonably assume that it would continue to outperform in the future with futures contracts available and that the returns that you have are highly correlated with what you would have had with futures contracts. The returns are probably slightly better since the indices used are all-share instead of focused, but you would also expect the variance to be higher, it is equivalent to using the Wilshire 5000 instead of S&P500: end digression).

I also didn't use all of the indices in the EAFE since some of them have very small weights and the countries don't have actively traded futures. The top 12 or so are good enough. In general the equal weighted strategy outperforms the EAFE weights (due to the 25% weight on Japan). The difference isn't large enough to concern ourselves about over the long-term (1.26 CAGR/STD vs. 1.25). Over the long-term, the buy and hold returns were different between the EAFE and weighing the individual components (since there are times when I don't have France or Singapore's total return indices), but again the comparison I want to make is between the trends and not the absolute levels. From 1970 to February of this year, the Buy and Hold for the EAFE had a CAGR/std ratio of .715 (CAGR=11.7%) and the component strategy was .82 (CAGR=13.1%). Overlaying the timing strategy increased the Sharpe ratio on the EAFE to .99 (CAGR=12.4%) and the component to 1.25 while increasing the return to 13.6%. Since 1988 (when I have data on France), the spread between the strategies has stayed strong although overall returns aren't as strong. The Buy and Hold on EAFE went from .43 to .64 and with the component strategy it went from .62 to .95.

The 6% Sharpe ratio of the original TAA strategy was about 1.0 (12.4% CAGR) since April of 1980 and 1.14 (12.3% CAGR) with a currencies strategy. Replacing the EAFE increases the Sharpe to roughly 1.04 (12.5% CAGR) in the original and 1.18 (12.4% CAGR). The excess returns show an insignificant alpha over the original TAA strategy, but with the currency strategy included there is a significant alpha of 30 bps which reduces to about 25 bps when currencies have a 3x weight (Sharpe of 1.31 vs. 1.27 originally).

Also note that this is a timing model just like the one before. There isn't the excessive trading costs of a momentum strategy. You would be in each country about 60-75% of the time and frequently for years at a time. Someone with a large account could use this strategy to help reduce risk while keeping returns constant (meaning more leverage could be used).

The Simon Hypothesis and Investing

2008-04-14T20:18:00.003-04:00

I try to attend the weekly NYU Colloquium on Market Processes when the market is relatively boring (it was after the business with PBR). This week I learned of something called the Simon Hypothesis (named after the Nobel Prize winning economist). It is stated thus, "Human beings, viewed as behaving systems, are quite simple. The apparent complexity of our behavior over time is largely a reflection of the environment we find ourselves in." He comes to the hypothesis by describing an ant needs to arrive to a destination. Does the ant go straight to the destination? No, it lives in a complex environment of ups, downs, and possibly dangerous run-ins with birds. The ants system could be as simple as see block, go left (or see bird, hide). The ant's path is complex not because the ant is complex, but because the environment the ant finds itself is complex. The hypothesis is asking if there is any way to predict which way the ant will take on a second journey?

That is an empirical question, but I think most people's first hunches would be that it would be impossible to predict. I would argue that this much is true for many walks of life, particularly investing. We might know the ant's final destination ahead of time (or the subprime crisis, or the internet bubble to burst), but how we get to that conclusion would be different every time. So while a backtested strategy might look sound on paper, ultimately, there is no way to tell if the path which reached a destination in the past will reach the destination in the future. The most important aspect of long-term investing is thinking about why the fundamental economic reasons why the strategy should earn abnormal returns in the future (if you can't think of any good ones, put your money in index funds and T-Bills). In the TAA case, I believe it takes advantage of the boom/busts inherent in markets (with central banks). A deep value investor or distressed debt investor survives through their entrepreneurial foresight (much more important to the Austrians than the neoclassicals which could be one reason why they don't teach value investing with a tenth the attention payed to CAPM), and so forth.

I guess the key insight is that you need to be flexible. You're not sure where the path can take you, so you should always try to find the shortest route when you can. You're never sure what surprises can force you to take twice as long a route, but in markets like this, it isn't hard (WB, BSC,ABK, WM,etc).

Currency Strategies

2008-04-13T23:12:00.007-04:00

Just to note: compared to the previous post, this post looks into currencies with proper data and more importantly, accounts for interest rates.

There are four main sources of currency beta: value, momentum, carry, and volatility. Value is described as the PPP strategy, taking advantage of relative differences in long-term reversals to the mean of currencies with overvalued or undervalued currencies (on the basis on inflation and interest rates). Momentum is a trend-following strategy. Carry is investing in high interest rate countries and borrowing in low interest rate countries. A volatility strategy uses options on currencies and would be more exotic than a retail investor would want to use (and is most likely used to take into account exotic strategies a hedge fund manager uses and show that they are most likely just long/short volatility).

Well, I have been interesting in including the Beta of currencies in tactical asset allocation portfolios (see here for original post) and I wanted to experiment with these strategies. I generally am skeptical of the mean-reversion strategy since I've seen the charts of countries deviating from PPP estimates for decades. It's too hard to compare a basket of consumption goods between the countries to measure PPP accurately enough for me to be confident enough to invest using it. Volatility would also be too difficult to test and I've never traded currency options. It might be something to add in the future, but I'm guessing that strategy is too volatile for me...

So I set my eyes on the carry and momentum strategies. The carry strategy is particularly interesting to me since there already is an ETF which does that for you. DBV goes long the highest yielding currencies and short the lowest yielding ones to profit from the spread of the interest rates so long as exchange rates do not move very far. I replicated the strategy using all of the currencies that the ETF uses (and before the Euro I used France and Germany) going back to 1980 (when I could get decent interest rate data for some of the smaller countries). I replicated the DBV strategy as best as I could, except that I had to use some alternative interest rate data with longer histories instead of Libor (and then I continued to use that instead of switching to the country's interbank rates after the interbank data becomes available). I got a 95% correlation with the DBV since it has been in existence with a 10% return with a 7.8% standard deviation since 2000 (however, they report a cumulative return of 518% (14.67% annualized) since inception and I only showed 354% (8.5%), not sure how they account for the Euro, this could be the reason why). It's not perfect, but it's good enough (mine is crude since it may not always be market neutral b/c I'm lazy and don't plan to use it to invest with)

Taking the strategy further back (to 1980), there was a smaller return 6.3% (with 9% std) which could be attributable to wider (or more volatile) interest rate spreads during the 1980s which converged to roughly .4% in recent years. Ultimately the strategy has a very low correlation with the timing strategy that's been developed here and at WorldBeta and with the momentum strategy I will detail below. Also, based on my crude analysis, applying a 10 month moving average to this strategy increases the return:risk ratio from .694 to 1.15 (without including the benefit of being in CP when not using it it is .89). This strategy increases the correlation of the carry trade with both the initial TAA model and the momentum strategy. The increased correlation with the momentum strategy is due to the large influence of currency movements on the carry trade. Interestingly enough, the worst declines in this strategy have been when the market in general goes down (like in 1987 and 1998). However, the momentum strategy does not have the same volatility or exposure to what happens in the equity markets.

The momentum strategy is basically the same as the TAA strategy. I bought currencies above their 10 month MA and stayed in dollars when not in a foreign currency. However, due to the nature of the currency markets, except by hedging, you can never really have no exposure. If I bought euros and converted them to dollars, I'm effectively taking a position in dollars even though it is my home currency. The benefit of this strategy is that I'm always receiving an interest rate, it is either the dollar interest rate or a foreign one, and unless I lever this strategy, I don't necessarily have to borrow in any of them (unlike the carry trade). Anyway, this strategy has a return of about 11.4% with a standard deviation of about 6.6% with practically no correlation to the timing strategy.

Based on the returns and correlations of the two currency strategies, (and between only these two), I originally thought I should allocate about 70-80% of the currency strategy to the carry trade since that is where the Sharpe ratio is greatest for those two strategies. However, that isn't what happens in the context of the entire portfolio. Since the carry trade has greater correlation with the components of the timing model, the Sharpe ratio in an equally weighted TAA portfolio including currencies is maximized when the carry trade has no weight in the currency strategy. Giving this strategy equal weight in the TAA strategy* since April of 1980 would have decreased returns from 12.4% (with std of 6.42%) to 12.3% (with std of 5.5%) and increased the Sharpe ratio from about 1 to 1.14. Giving the currencies double or triple weight would increase the Sharpe ratio further. Even a triple weight on the currency momentum strategy will only reduce the returns by about 20 basis points historically and drops the standard deviation down below 5. Not sure yet the effect on leveraged portfolios, but that is my next step.

Since it was effective to include currencies in the TAA strategy and it is essentially a way to invest in cash, I wondered if it should it be included as the default cash strategy (eg. when the TAA model goes to cash, should it invest in currencies instead)?

Well, that answer is no. Despite the fact that the model outperforms cash with little correlation to TAA, it still will go with the market in the worst periods when the TAA strategy in general should be in cash. However, the cash returns (esp. standard deviation) do not take into account the depreciation of the dollar. All in all, it would probably be a wash and better to just keep the strategy separate, but it might be interesting to test after including the effect of depreciation (and volatility!) of the dollar.

* To be clear, what is tested is using the 10 month strategy on the countries and then investing in that as BH strategy itself. Additionally applying the 10 month strategy to the currency strategy does improve returns and Sharpe ratios for the currency strategy, but does not improve the Sharpe ratio for the overall strategy for some reason. I tested this as an afterthought, but I never wanted to test that as an original strategy, the 10 month MA is already applied individually and it makes little sense to complicate things further, IMO.

Checking your assumptions

2008-04-11T21:21:00.006-04:00

Let's say you develop two investment strategies. One is based on tried and true methods and the other is new and innovative. If you discover that you can maximize your excess return:risk by allocating a large portion of your portfolio to the new strategy, check your assumptions.

I've been researching strategies for currencies and adding them to the Tactical Asset Allocation strategy (here). This strategy is already very successful so I was surprised to find out how good a simple currency momentum strategy was when added to the portfolio. I didn't realize at first how important it was to check the assumptions regarding the data. I downloaded the data from the St. Louis Fred website and it was monthly data, I assumed it would be fine. The problem was that the data isn't end of the month data, it is the average of a month's daily data. This is a good thing for running regressions with exchange rates or using them to adjust accounting information, but it's not good for trading strategies. Even creating new month time series with the end of the month or middle of the month dates will dramatically underperform the average series (Global Financial Database has the numbers based on end of month which I will be using in the future). You can only know the average rate for the month at the end of the month so by assuming you get out at the average rate you're assuming that you know the entire month's returns sometime that is not the end of the month.

I originally performed this research by looking at several different currencies until I realized what I did wrong, but it is easier to illustrate with one currency.

Just to illustrate how far off it is, using the strategy (L/S 2 period MA timing) on the Pound going back to 72 (including interest rates), will give a return of about 15.6% (8.1% std) on the average of the month data, 9.64% (10.3% std) on the end of the month data, and 12.4% (9.7% std) on the middle of the month data. The best thing about the strategy is that it has virtually 0 correlation with the TAA model (why it deserves such a huge weight in it originally) using any of the datapoints. That alone leads me to believe that currencies should have a position in a well-diversified portfolio. With the British pound strategy as a proxy for how well the complete momentum (it isn't, but I suspect that strategy will be better), the Sharpe ratio will be increasing with a positive weight on the currency strategy until about 40% (for the middle of month, 25% for end of month). I'm comparing it with the basic TAA model with equal weights on the remaining assets. I can only guess that the well-diversified currency strategy will perform even better and should receive a larger allocation.

To test this without compiling all of the interest rate data and combining everything (next project: recreate the carry trade) I tested a j=4, k=2 momentum strategy on the currency ETFs that are available since September of 2006. This is a very short time frame when all of these ETFs performed very well, but it would represent at least the long-side of the strategy accurately. The strategy would be in either two or three currency ETFs and has a CAGR of 13.8% with a 5.6% standard deviation. I would reiterate again that this is a period of a massive decline in the dollar and it is not expected that this kind of risk:return ratio would continue in the future (the return is expected more than the risk). Over this time period, the strategy (absolute returns) has a correlation with the TAA model of 19%. 19% isn't 0, but it still should be important enough to add to the portfolio after completing a more rigorous long-term examination of the strategy.

Tactical Margin Overlay

2008-04-09T22:59:00.006-04:00

I recently posted to try to improve on my probit model by tactically adjusting margin, but it appears that there was an error in my calculation and the results are not as good as I had posted.

However, if you fade my previous results, that will tend to be have a stronger Sharpe ratio. In other words, my previous results were that you could increase your Sharpe ratio by increasing leverage when the model is in more assets. The new results are that you can increase the Sharpe ratio relative to what you would have had otherwise by increasing leverage when you're supposed to be in few assets. In the original results, the risk-parity portfolio underperformed since you were using more leverage on assets like bonds, but in this case the risk-parity portfolio performs much better. The 50% margin portfolio that uses 0 leverage when in 4 or 5 asset classes and 100% leverage in 1 or 2 asset classes has a .0364 better Sharpe ratio in the risk parity portfolio (.012 for equal weighting). Some of the cost of leverage can be made up, but the excellent returns I originally posted are not the case. Unless I combine the probit model with this model and the results are impressive, I would prefer to stick with the original model without leverage rather than these.

Momentum Average and TAA

2008-04-08T20:46:00.008-04:00

Damian in the comments asked if I could use the average of four returns: the 1 month, 3 month, 6 month, and 12 month to rank the components of the momentum strategy from the previous post.

The results were as I expected. The momentum strategy isn't that good more than six months out and averaging the good Sharpe strategy with the bad Sharpe strategy really doesn't improve the returns. Intermediate trends are strong enough for ETFs that that should be the focus. I was able to improve on his idea by changing it to an average of 1 month, 3 month, and 4 month returns and the 1 month and 4 month are an improvement still above the momentum average. They still don't outperform the j=4, k=2 model in backtests, but they could outperform other models and there's no reason why it can't outperform in the future. The two bottom strategies at least relieve some of the burden on the 4 month.

I should also note that I am continually refining these strategies including the calculation of interest, margin, and the risk parity weights. I'll always post a comparison to a base model whenever it is different from anything posted in the past. The difference in returns from this model to the original reflects better accounting of interest returns. I also took out the previous inclusion of the style ETFs. Sector momentum has previously been far more important than style momentum and I expect that to continue in the future.

Another Post regarding recessions and TAA

2008-04-04T00:20:00.007-04:00

I previously posted regarding the connection between returns of a TAA portfolio and when a recession occurs. This follow up with discuss the methodology and results from adjusting an investment strategy based on a quantitative estimate of the future probability of a recession.

The TAA models are good at reducing risk, but to increase return to something comparable to an equity index it seems silly to use the same amount of margin at all times. The post above gives evidence that lowering the amount of leverage in times when there is a prediction of a U.S. recession will increase the Sharpe ratio relative to a similarly levered model.

To incorporate this insight into the TAA model, as I used the same probit modeled I discussed in the first post I made regarding probit models. To use this model in an investing environment, I used a warm-up period of 200 months and then estimated the model each month to get a probability of a recession 12 months out. Since the NBER doesn't have dates for recessions in the past two years (I guestimated), I stopped the model 24 months prior to the end of February and used the coefficients as of that date with the data available to get the remaining predictions. Using this data I created two possible ways to scale in and out for leverage. I looked back four months for predictions in both cases. I did this for three reasons: the data constantly gets revised, I'm not sure always what is available on any given date and I want to be safe, and the lag time seems optimal (12 keeps you unlevered during the rebound, 1 is too sensitive, 6 works just as well, but I wanted to keep it shorter). So looking back four months, the first method will lever the portfolio when the estimated probability is greater than 50% and not lever the portfolio below that. The second method is similar except it provides three baskets levering a full amount, 50% of the full amount and none at all.

The results for the first and second method are comparable, but the second method slightly underperforms the first on a Sharpe ratio basis (the return is lower and the standard deviation is lower, but not by enough to offset the return). It's possible to fiddle with the parameters to improve the results, I'd rather just ignore it for the simplicity of the first model. The chart below gives the portfolio statistics for the first model with 0 leverage (and no probit data), 50% leverage, and 100% leverage. The first two columns are the base 0% and 50% and the probit columns represent the model with dynamic leverage ratios. Similar to before, I report the evenly weighted portfolios and the risk parity portfolios.

The results confirm my original intuition(!) and then the models even outperform what I had suspected would happen. Essentially the model reduces your leverage heading into a recession and then quickly puts it back on. Surprisingly, comparing these returns with the raw results from the last post on TAA and probits, shows an even better return for this method using the model than reducing leverage when a recession happened. I do use domestic equity volatility as a factor in the model which could help the investor get out when volatility increases (it is a small component compared to interest rates and money supply data though). Anyway, the results show an increase of the 50% leveraged portfolio's Sharpe ratio by almost .1 by reducing standard deviation substantially and keeping the returns constant. The 50% portfolio, previously with a horrible Sharpe ratio relative to the 0%, now is roughly comparable (with equal and risk parity weights). With 100% leverage, the risk parity probit model now has a Sharpe ratio equivalent to the equal weight 0% and 50% equal weight portfolios (but with more return and risk). However, the 100% leveraged probit models dramatically outperform their cousins without the probit model. Again, this is due to substantially reducing volatility by reducing leverage in periods leading up to recessions.

Given the success of the probit model in reducing volatility and keeping returns high, I now plan to investigate leverage as a function of the volatility of each asset class (individually). I'm guessing there would be similar results, but without some of the messier complications of using the probit model (not sure when data is released and it's relatively intensive computationally). Assuming I can find daily data from the site I got the monthly data, it shouldn't be that much of a problem and I can just use the percentage of large up and down days in a quarter as a proxy for volatility of each asset class.

When will an American presidential candidate talk like this?

2008-04-03T20:44:00.005-04:00

From what I know about Morgan Tsvangirai, I would say he is a man of courage. I could be totally wrong since my only real knowledge comes from wikipedia and this WSJ editorial. That WSJ article is really impressive. As an economist and someone who tries to keep up with international events, I've been following the tragedy of Robert Mugabe since he kicked out the white farmers several years ago. His Presidency in the past 10 years ago has basically been one stupid decision after another. Tsvangirai talks the talk and hopefully he has a chance to walk the walk. Unfortunately there is news today that the offices of the MDC were raided today. I'm not sure how this will turn out, but either Mugabe will step down or he needs to be assassinated and overthrown. If Tsvangirai has a chance to turn the country around, I'm convinced he'll do his best and at least has the right solutions. It will definitely be a difficult road, but as they start creeping up the Economic Freedom Lists the country might be a buy since their companies have almost no value whatsoever. However, it would take real changes in the country for it to actually be a buy (3-5 years from now).

HT: Robert Lawson

A Preliminary Post regarding recessions and TAA

2008-04-03T00:45:00.004-04:00

I was hoping to incorporate my recession model into decisions about margin into the TAA model previously blogged about (here and here), but things got away from me. The model is in Matlab and output recession predictions based on the information available at the time which was the big challenge so it really won’t be that much work beyond that. Hopefully, I can post that information tomorrow, but today I wanted to just give a brief update on the returns of the even Asset Allocation (20% in US stocks, Foreign Stocks, commodities, bonds, and REITs) vs. the returns of the Tactical version during times of recession.

I regressed the returns of the TAA strategy and the returns of the 50% levered TAA strategy against the returns on the comparable AA strategy (unlevered or levered) and a binary variable equal to 0 if the economy is not in a recession and 1 if the economy is in a recession. I’m saving the reader the time of reviewing the results, but the AA returns are highly significant (as expected) and the coefficient on the binary variable is not significant at the 5% level, but is at the 10% level for both levered and unlevered. I’m willing to concede that the effect on the adjusted R squared of the binary variable is very small, but the important thing is the sign of the coefficient and not necessarily how much of the variation is explained.

In both versions, the coefficient on the AA variable is roughly .61, but the intercept and the coefficient on the binary variable are roughly .003 and .004 in the unlevered and levered versions, respectively. These numbers are based on monthly returns, the annualized numbers are roughly 3.5% and 5%. For those without a statistical background, that means that in CAPM terms, the alpha is positive and larger for the levered version and, more importantly, both models outperform the passive strategies during recessions by a statistically and economically significant margin.

I tried to alternative strategies that could be considered a middle road. I developed two new returns variables based on the TAA data, the first was the unlevered TAA returns when there was no recession and levered otherwise and vice versa for the second. Looking at the regression results for these two gives evidence of being able to target which coefficient will be higher. Avoiding leverage in a recession increases the intercept to .004 and keeps the other coefficient flat, but avoiding leverage unless in a recession keeps the intercept, but the coefficient on the binary variable goes up to .004. Which is more important and why does it matter?

Ultimately looking at the return characteristics (below) yields the answer. As expected, the TAA model has the best Sharpe ratio; however, by avoiding margin during times of recession, you can increase the Sharpe ratio relative to a similarly leveraged portfolio. I haven’t been sure if I calculate the margin returns properly. Intuitively you would think that it would be double the returns minus the cost of debt, but with the TAA model you only margin the positions that you are in since the cost of margin is greater than the cost of cash. Furthermore, there are historical periods where the broker’s call rate gets so insanely large that it wouldn’t make sense to use margin, but this model, at present times, still uses it.

To conclude, by using a model that can predict recessions (which I conveniently have), you can improve the Sharpe ratio of leveraged portfolios. One possible note is that my model works to predict a recession within the next 12 months. It begins to show indications several months prior to a recession with plenty of time to take some off. Unfortunately this also means that there are several different ways to test it. Finally, I suspect that controlling the use of margin based on expected returns of the portfolio will also prove to enhance returns.

Component Tactical Asset Allocation: Part 3

2008-03-28T16:16:00.002-04:00

This is the final of three posts on Tactical Asset Allocation. Part 1. Part 2.

The subject of this post is the theory of the market process and tactical asset allocation and why I believe that the former implies the latter will be a more successful strategy than buying and holding index funds.

The fundamental implication of the Efficient Markets hypothesis is that if information will be quickly incorporated in security prices. Mathematically this implies that stocks follow a random walk with jumps when new is absorbed by the market. Based on this assumption, the ideal investment strategy under the Capital Asset Pricing Model is to hold the market portfolio for the long-term (I know I’m ignoring Treynor-Black).

Beyond the typical objections to EMH, there are two main insights from the market process school that leads me to reject the EMH and I believe they are the most important observations of the school.

First, there are significant government interventions that make the market remarkably inefficient. The most important is the business cycle and monetary problems that in the 20^th century has almost always been caused by central banking. The standard Mises-Hayek theory of the business cycle is that by pushing the interest rates lower than the natural rate of interest, a central bank encourages investment beyond what would happen in the free market. Eventually the investment works its way into a boom for the producers of consumers’ goods and prices begin to increase. In order to stop the boom (to prevent runaway inflation), the central bank must raise rates. This action ends the boom and the process to correct the malinvestments made in the boom period. Since capital intensive industries are more exposed to interest rates, they typically feel more pain than consumers’ goods industries.

Moreover, governments intervene in other ways that are frequently not understood well enough by investors or they don’t always understand the implications. Economics is not a terribly difficult discipline and figuring out the implications of dumb government policies isn’t that difficult. If the government subsidizes ethanol production, farmers will use less land for the production of the typical agricultural products and those prices will have to rise. If there is a war in the Middle East, it is likely that oil (unless they have refineries in the country in question) and defense stocks will typically increase in value. Investors react in the short-term, but over the course of 6 months to a year or longer, these plays are still profitable. I’m not sure whether it is the uncertainty of these situations or that investors systemically do not think the government is as bad as it is (possible given the state of business school economics courses, also it is very difficult to quantitatively test), but investors do not react strongly enough.

Second, the market process school emphasizes the role of the entrepreneur in moving the market to equilibrium prices. EMH doesn’t care about why prices behave in certain ways, it merely attempts to model them. However, what is seen as a random walk are actually deliberate actions taken by entrepreneurs engaging in speculation and arbitrage. Entrepreneurs who have greater foresight will outperform those who don’t. Furthermore, the investing, particularly derivatives, are referred to as zero-sum games. The profits are zero-sum; however, ex ante, all of these trades are positive sum in terms of utility. These trades show ex post profits or losses depending on the skill in forecasting of the entrepreneur.

Finally, as Hayek notes, there’s no such thing as perfect knowledge, as is assumed by the actors in CAPM. Knowledge is dispersed throughout society and the purpose of the market is to organize that knowledge. Market prices reflect the knowledge of all market participants.

Combined these three factors make tactical asset allocation an attractive prospect. Since there are cycles that can be observed by students of the Austrian School, it makes little sense to buy and hold equities when there are lengthy periods of time where you can lose a significant sum of money. Also, not only is there a purpose to being an entrepreneur which is ignored in the EMH, but paying attention to what happens to prices can reveal knowledge about other market participants’ knowledge and opinions in the market. Michael Covel notes in his book about trend following that trend followers tend not to be in the business of predicting trends, they have imperfect knowledge and as a group they have no opinions on the market. However, if the market is going up, they would be more than happy to buy and vice versa to sell. The logic is essentially the same for TAA. Mr. Faber isn’t providing a service in predicting the market, he’s trying to improve on the buy and hold passive strategy by staying out of the market when market participants have a negative outlook. Nothing wrong with that.

Component Tactical Asset Allocation: Part 2

2008-03-27T22:32:00.013-04:00

This is the continuation to the previous Component TAA: Part 1 post.

First I will present the results with a single momentum strategy comparing the AA, TAA, and Momentum TAA strategies with 0 leverage and with 2-1 leverage. Then, I will present alternate momentum strategies using different js and ks, but investing in a constant number of ETFs followed by a constant j and k with a different % of ETFs available. I will conclude with work in progress to improve it further. I might add an additional post describing why the economist in me prefers Tactical Asset Allocation as an investment philosophy to the Efficient Markets Hypothesis and the Capital Asset Pricing Model.

Before I begin, I should note that the Domestic ETFs I invest in a separated into two groups, sector and style. Whichever one I can invest in earlier (sector), I will use that return and then later, I average the two's returns. I might get a better return without doing this, but that particular market is so broad that I wanted to investigate the combined effect. Not only do some sectors out perform, but sometimes value outperforms growth and large-cap outperforms small-cap. I wanted to be able to include this relationship as well, I'm just not sure how much stronger this effect is compared to the sectors. I also had a longer list of sectors that I cut down on prior to running these returns, so the ranking since I updated the data can actually choose from more sectors and gets better returns. I'm only reporting a sector basket with the 9 Spider select ETFs.

The first table represents a unlevered comparison of the AA, TAA, and Momentum TAA (with j=4 and k=2 investing in the ETFs ranking in the top 25%) with equal asset allocation between the 5 asset classes and the Risk Parity weights discussed in the previous part. The TAA beats the AA which is the conclusion reached by Faber. However, the Sharpe Ratio (@ 6% for all) increases with a more normal kurtosis (3=normal, greater than 3 indicates fat tails) by using the risk parity weights. There are similar results comparing the TAA and Momentum TAA, however it seems like the Kurosis for the TAA portfolio is relatively constant. This makes sense since the data is cut off prior to 1998 and excludes some of the larger price movements.

The next table is the same strategies and comparison as above, but with 100% leverage. It is more for general interest than comparison. The method used in the paper by Panagora was to use the Risk Parity weight and then lever the portfolio to a desired return (such as the S&P500's average return) so that variance would be minimized. In this case, the return on the TAA without Risk Parity Weights would be greater than the standard deviation on something like the S&P500. You could use roughly 20% leverage to increase the return of the TAA Risk Parity to roughly the return on the normal TAA (this same argument works to target the standard deviation as well). However, the Sharpe ratio in this case would be less than if you had not used leveraged. The return is the same, but the variance is actually greater (the same holds true for AA, TAA, and Momentum TAA). So even without the large 2-1 leverage reported below, if you measure your investment success by your Sharpe ratio, then it won't make sense to use leverage. However, relatively speaking, the risk parity weights outperform the equal weighted portfolio. If you're an investor seeking to maximize profit or would be willing to accept more risk in exchange, then you should use the risk parity instead of the equal weight portfolios.

The third table presents the CAGR, Standard Deviation, and Sharpe Ratio comparing different momentum strategies. Recall from the previous article that j represents the number of periods to look back to and k represents the number of periods to hold (since k can be greater than 1, then even if you hold 6 ETFs when k=1, it will be variable for k>1). Using more complete data, it is clear that the Sharpe Ratios increase as j comes to 3 or 4 and declines after that. However, there is no clear trend on what happens with k. It usually increases to 2 and declines after that, but it is not consistent. If at all possible, I would prefer a larger k to a smaller k since it guarantees that I will have less turnover.

Finally, the last table shows the returns with j=4 and k=2, but investing in a different percentage of the ETFs that have sufficient return histories. The trend in this case is clear, return increases as you increase the percentage until it tops out between 25 and 33.3%. However, these returns are all gross and the others could relatively increase if transactions costs are included. Furthermore, I would suspect the tax consequences are greater. Instead of picking the best sectors, at 75% you're getting out of the worst. For portfolios with less than half a million dollars, there might be too many ETFs to be able to use the 75% or 50% to make it worth it. However, I should also note that the benefit of the original TAA model is that each position can be approximated with futures contracts which could possibly reduce costs and provide an easier method to use leverage.

To conclude, gross returns and gross Sharpe ratios are greater using the Momentum TAA with risk parity portfolios. However, there are still additional ways that it could be improved. This strategy can be considered a component in a larger overall strategy. For example, Mr. Faber discusses alternative strategies such as mean reversion and following hedge fund managers that produce significant returns. I think that there are strategies in options, distressed debt, value investing, macro investing, mean reversion, and statistical arbitrage (or investing in hedge funds that specialize in stat, risk, or convertible arb) that can add to this return while not being correlated with the TAA or Momentum TAA. Unfortunately, with the exception of mean reversion, these strategies are either not quantitative (macro, distressed debt, value) or are difficult to backtest (options - competence, and arbitrage are arbitraged away).

Next, there are additional beta factors that can be considered or thought about in different ways. For example, a recent paper indicates that the returns for currency managers are largely Beta. Those returns could be an additional asset class that could be added with little correlation to the others. Also, there is evidence that investing in commodities based on their term structure (buy most backwardated positive roll-return commodities, short most negative roll-return contango commodities). These two strategies, combined with mean reversion of the five assets used in TAA and the Momentum TAA risk parity weights, could be particularly strong and they could be included in a broader portfolio using the risk parity weights.

Finally, I recently discussed a probit model I use to forecast recessions. I am considering linking that model (and augh converting it to Matlab) to this program so that I choose margin based on the probability of a recession. The returns of this strategy outperform the S&P500 during the bad times, but they still underperform compared to the remainder of the period. I'm going to consider increasing leverage when the probability estimates are low and cut off leverage when the probability begins to increase. I believe this can improve returns.

edit: There was a slight discrepancy with the interest rate data in the original results that has been corrected.

On to Part 3.

Component Tactical Asset Allocation: Part 1

2008-03-27T20:37:00.006-04:00

Mebane Faber published an article in the Journal of Wealth Management in the Spring of 2007 called a Quantitative Approach to Tactical Asset Allocation. The thrust of the paper is that if you invest in U.S. stocks, foreign stocks, bonds, commodities, and REITs when they are above their respective 200 day moving averages and invest in commercial paper otherwise, you can achieve returns similar to equity investments with significantly lower volatility. Mr. Faber has graciously provided the monthly returns from the strategy as well as much more information on his website, World Beta. Based on the data on the website (more up to date than the original paper), the timing model returned 12% since 1972 with a standard deviation of 6.43% (.93 Sharpe) compared to an 11.5% return on the buy and hold asset allocation strategy (20% in each asset mentioned above) with a 9.78% standard deviation (.56 Sharpe). I programmed his strategy into Matlab using the same data and found similar results (slightly different due to the vagaries of Matlab rounding and computing returns statistics based on monthly data instead of yearly data).

Lately I have been interested in how to improve on this concept. First, I would like to discuss two additions I made and I will make an additional post to discuss the results of what I tested.

On his blog, Mr. Faber compares different methods that readers have requested to improve the returns (that he doesn't use). The first is to enter long positions above the 200 day MA and short positions below while the second is to enter each position "all in," equally weighted for each buy signal, no positions in cash . Each of these methods fails to improve the Sharpe ratio. I expect the L/S portfolio fails due to the fact on that most of the top 50 best and worst days are when the market is below the 200 day moving average. It is possible to profit by shorting the worst, but you can get burned on the best.

I believe the "all in" portfolio fails by ignoring the correlations between the assets (and would require more re-balancing costs than the traditional TAA). In order to test this, I followed a white paper by Panagora Research which describes the Risk Parity Portfolio. Their concept is to adjust the weights of a portfolio so that the amount you can risk on each position is equal. The traditional method to do this is to estimate the Value at Risk for a portfolio and break it into the component parts for each security. This method takes into account the correlations among each asset and the Beta. As a technical concern, I waited a year to create the Risk Parity weights (but used the initial 20% allocation during that period to make comparisons to Faber's paper) and brute forced the first weights using the covariance matrix and existed at the time of investment decisions and only changed the weights if the Component Value at Risk of an individual asset went outside predefined bounds. The weights stay relatively constant over time, but I could have created tighter bounds where they would change more often. As of the time of writing, bonds would have 34.8% weight, REITs 15.9%, Commodities 19.3%, Domestic Stocks 15.1%, Foreign Stocks 14.9%. In other words, REITs and Stocks would have their shares reduced and bonds would increase their weights in order to take into account the fact that they are more strongly correlated with each other than Commodities and Bonds and have higher variances. Based on the research provided by Panagora, I expected a slightly lower return, but a substantially reduced standard deviation.

The other method I used was investigating the j-k Momentum strategy proposed by Jegadeesh and Titman. In this paper, J and T investigate ranking stocks based on their returns from j periods ago and holding them for k periods forward. They used this model to show that stocks have a momentum factor like a size or value factor that helps determine their future returns. Within the context of the TAA model, I chose to test this strategy by choosing a proportion of the ETFs for an asset class and then applying the j, k methodology to a proportion of the ETFs with returns. I waited until a certain proportion of the total ETFs (in each classand that I considered representative of the asset class) began to trade to start the momentum strategy for that asset class. I will only report (and compare) the returns since the earliest strategy began to take effect (Select Spiders began trading in December of 1998, but it requires j months before the strategy can work). Since they have uneven start times, I used the returns from the normal TAA strategy when the Momentum strategy cannot work. I should emphasize that I am not using only a Momentum strategy on ETFs, but investing in a j-k Momentum strategy based on a TAA model. Within each Momentum category, the ETFs are equally weighted and I don't think it makes sense to use Risk Parity Portfolios in this context.

Furthermore, if I am not mistaken, Mr. Faber uses a method similar to this in actual practice, however, he does not report his results using this method. The most obvious reason is that he created his model in Excel which is substantially more cumbersome the model gets more complex. Also, ETFs have a short history that may not be indicative of the 35 years of returns where the TAA model has shown considerable strength. There's also no doubt that using ETFs in this strategy would require more trading costs and more taxes (unless in a tax-free account). Even if this strategy is not successful (it is), it is at least interesting to investigate and note the return characteristics for different levels of j and k.

The next post will compare the Equal Allocation (no TAA) model to the TAA and their Risk Parity equivalent portfolios, it will compare the TAA models with the Momentum TAA models (equal allocation and risk weighted), and some discussion about future additions I plan on testing.

On to Part 2.

Probit Models and Crisis

2008-03-26T22:57:00.005-04:00

In a typical linear regression model, you would regress something like yt=b1+b2*xt+e (t is a subscript and e represents error). Many are aware of this concept. However, there are many assumptions that must be made in order to get the math to be correct in OLS. Due to these assumptions, such as constant variance and normality of residual errors, if you yt dependent variable consists of only 0 and 1 or is truncated by any other means, then you will have misspecified your model. Given some series xt and b1 and b2, it is possible to predict yt much larger than 1 or smaller than 0. Two questions arise, how do you correct for this and why does it matter?

The main method to correct for truncated variables is to use a probit or logit model. The concept behind probit and logit is essentially the same except that they use different means to make a correction. In a probit model, instead of estimating the equation above that is yt=b1+b2*xt, you would estimate yt=phi(c1+c2*xt) where phi is the cumulative normal distribution. Since the cumulative normal distribution is bound by 0 to 1, then any values that are chosen within the parentheses can only predict values of y between 0 and 1. The logit model is similar, but instead of weighing by the normal distribution, it uses a calculation based on e^x and natural logs.
And why does it matter? These models are meant to estimate the likelihood that events will take place or not (this is the 0 and 1). The benefit of the normal distribution is that you're actually estimating the probability that a particular event will take place given your independent variables. I can think of two uses of an econometric model, to explain the past and explain the future. Econometric models have their uses in the former, but many times drastically fail in the latter. It is possible that the models are misspecified or that fundamental relationships are not merely absent, but are immeasurable. Furthermore, the models may not be stable which can cause forecasting errors to be too large to be useful. However, I find probit models to be a useful alternative to typical forecasting when events can be categorized as binary.

My primary use of the probit models follows in the footsteps of Wright (06-07) by examining the NBER dataset of business cycle dates. Wright uses a binary variable equal to 1 if there would be a recession within the next x months and 0 otherwise. Originally in my research, I attempted multiple lags forward such as 6,12,16 months ahead, but I eventually focused in on the 12 month as a base to compare alternative models. I continued to investigate additional variables and have settled on a fair group of variables that outperforms Wright's variables while maintaining and important economic significance of each. I continued to use the Fed Funds and the spread of long-term treasuries over the effective fed funds rate. I added the spread of the Fed Funds relative to BAA corporate securities adding a factor that includes the markets tolerance for risky debt (TED isn't as strong as this one) as well as measure of volatility of the S&P500 (% of days in last quarter with a change greater than or less than 1.25%). Finally, I added the most important component which is the money supply measure. Following Paul Kasriel (originally testing Mish's MPrime), I use the long-term change in real monetary base (bank reserves +currency divided by CPI). Positive values of this indicator represent expansionary monetary policy while negative shows that the Fed is tightening the money supply. As Mr. Kasriel notes, this normally happens to curb an expansion and combined with an inverted yield curve represents a particularly powerful indicator of a recession.

Over the 40 years tested (had to exclude the recent ones since no NBER dating exists for the current financial crisis), these variables in a probit model correctly classify 91% of months as whether they are in a recession or not (defined by above 50%). It's recent track record is that the estimated probability of a recession in the next 12 months briefly went above 75% back in 2006 and then came up above 75% again in June of 2007. Nevertheless, I would use a figure above 50% to definitely eliminate any leverage in U.S. equities and possibly cut down size (and an increasing trend in general as a sign to cut down) , above 75% means "Sell Mortimer!" The high values in June 2007 were driven by real monetary base values that were historically low. In previous episodes it barely crosses into negative values, but it has stayed essentially flat since then.

I have been mulling over the implications of this model for several months. In particular, the model estimates the probability of a recession, but the probabilities increase during all financial crises. For example, in times of large volatility or greater credit risk (flight to safety) or future rate cuts, this number increases. I wondered whether it would be appropriate to test times of financial crisis and recession using this model (how to measure, but at least my false positive in 1998 would go away) . However, even if this financial crisis is not called a recession, I wouldn't say this model failed because it was predicting one. A serious financial crisis occurred and a significant stock market correction. Using this model to avoid those situations is much more important than the classification.

Indications and the Visa IPO

2008-03-20T14:13:00.005-04:00

Visa IPOed yesterday at $59.50 after the initial investors paid $44.00 for their initial holdings. While there is a significant amount of coverage following the IPO, there has been little discussion on how to trade in IPO in general. This was the first major IPO that I've had the luxury to trade, but I have followed many in the past and traders at work spent all week talking about the major initial public offerings in the past five years and how they traded them.

An IPO is the primary offering of equity in a company that will be listed on an exchange. The company sells shares in its company in order to raise capital for future expansion. The difficult part of the process is determining the number of shares to offer and the price at which they should be sold. It is the job of investment bankers to determine the interest in the shares and get a sense of how many should be offered and at what price. They also perform due diligence on the company to determine an estimate the company's value. The difficult part is that the company does not trade actively so not only is the valuation subjective, but there is almost no objective way to confirm if the valuation is correct or not until the offering itself. Several methods are used to estimate the value. The IBankers could use a comparable multiples approach which values the company similar to the market valuation of other companies in the same industry. A discounted cash flow model will estimate the value based on forecasts of future earnings. Finally, the IBankers can compare recent IPOs to the present one; if marketwatch.com's IPO does well, you would expect thestreet.com's IPO to do well also.

For the trader who does not have access to the Investment Banker with the original distribution of shares, there is an opportunity to take advantage of a relative difference in the Banker's valuation and the market's valuation. Philosophically, value is only subjective and the value of a company can be considered only subjective. The market price of shares and the market value of a company is determined by the subjective opinions of the marginal investors (who happen to be the largest market participants like institutions and hedge funds). So the question is, how does the trader determine when the marginal beliefs are out of line with valuation provided by the investment bankers?

Before stocks open, they give an indication of interest if there is a significant discontinuity. This indication is in the form of a bid and offer prices based on opening orders already submitted. If there is going to be a gap up or down on an IPO, it will be shown on the indications prior to when the stock opens. Major IPOs typically are underpriced by at least 30-50% according to the traders I work with. To determine if there is going to be a large jump in the IPO price, listen (or watch) for the indications to keep hitting the offer. On the Nymex IPO, the offer kept getting hit many points above the IPO price. This lead traders to put in more orders to bid the price up further. When Nymex opened, it jumped something like 30 points (from the opening price, but significantly more from the IPO price) until the offer was no longer hit by the bidders (the price got too steep and buying interest no longer kept up with the selling interest). A market order at that time would have faced at least a point of slippage, but a substantial gain nonetheless with no down ticks going up 30 points. In other words, each 100 shares earned 3000 dollars.

On the Visa IPO, I looked for indications to drastically increase similar to what I had heard about the Nymex IPO. At 9:45, there was a bid/ask indication of 52.50 to 57.50, up from the IPO price of 44. I considered this a good sign and then saw the next indication of 55-60 at 9:52. I expected another indication at roughly 10. When this indication did not come, I reduced my size and changed my orders to market OPG (at the open). After a significantly longer gap where I was hoping for another indication, the stock eventually opened at 59.50. I considered this a particularly weak opening and exited my position almost instantaneously at the opening price. Visa hovered briefly around the figure and a small number of shares ended up getting bid in the 60s, but over the next hour, the stock went down to 55 (a possible buy point since the bid indication was at 55, but it easily could have sunk further).

Visa rallied later in the day, but the quick profits to be made on IPOs are getting the price the IBankers offer and taking advantage of the mispricing. Even a 400 million float wasn't enough to result in some mispricing, but there was almost no jump after the open which you would have known had you paid careful attention to what the indications were telling.

Minimum Variance Portfolios

2008-03-19T23:22:00.001-04:00

I am interested in the cross-section of stock returns, why some companies with particular characteristics outperform others. According to the conventional Capital Asset Pricing Model, stock returns have a linear relationship with market risk. The model predicts that companies with high sensitivities (Beta) to the market will tend to outperform the market in the future. In practice, many of the greatest long-term investors choose stocks (whether they know it or not) that fluctuate less than the average stock (and have a lower Beta).

Falkenstein Financial Data’s blog, Falkenblog, describes a possible arbitrage of going long stocks with small Betas and shorting stocks with big Betas. The aim is to profit if CAPM is wrong. Since many of the stocks in their universe are small that would be difficult to short, they came up with an alternative on their website. It is called a Minimum Variance Portfolio. In simplest terms, I would say that it is just the portfolio of the stocks with the smallest Betas, but the actual algorithm is a little more complicated. The algorithm chooses the weights of the stocks in order to minimize the variance after taking into account the correlations of each stock (so you can’t take all low Beta stocks that are highly correlated). The minimum variance portfolios have greater returns with lower volatility (though they may under-perform the market during boom times as conservative investors tend to do) than their base indices.

Looking on their website, I noticed that several of the top 50 holdings of the S&P500 minimum variance portfolio contain holdings of Warren Buffett and Berkshire Hathaway. Anheuser-Busch, Coca Cola, Johnson and Johnson, Proctor and Gamble, United Parcel Service, and United Health Group are the overlapping holdings. Almost all of the companies on the list are well-established, well-run companies.

I was curious if the reason for the out-performance of this group was due to any remaining factors that may not have been presented on their website. I performed a multiple regression analysis of the returns of the S&P500 and its accompanying minimum variance portfolio against six technical and fundamental factors available on Kenneth French’s website. The six are the equity risk, size, value, momentum, short-term reversal, and long-term reversal premiums. The equity risk premium is similar to Beta from above, but it is relative to the entire market and not just the S&P500 (so we can assume it won’t equal 1). Size (SMB) and value (HML) premiums are from the Fama-French literature and reflect the risk of small companies and companies with low Price/Book ratios. Momentum is based on the relative performance of portfolios formed based on 2-12 month returns. Short and long term reversal portfolios are similar to momentum except instead of assuming higher momentum leads to higher returns, they assume mean-reversion. All things considered, I wanted to throw as many factors as I had data on out there to see if anything stuck.

The regressions are both highly significant in their F tests. The coefficients and intercepts are all significant at the 1% level except the coefficient on long-term reversal for the S&P500. What I found most interesting is that this model almost perfectly explains the S&P500 with an adjusted R squared of 98.8%, but the adjusted R squared for the minimum variance portfolio is only 60%. In other words, this model does not describe minimum variance portfolios and there could be some other factor out there that might help explain the returns. All things considered, the reversal factors add very little to the analysis. While the S&P500 returns are mostly determined by the market risk premium, less than 50% of the variance of the returns of the minimum variance portfolio is described by the market risk premium alone while the remaining factors add about 15%.

Comparing the coefficients of the full model, I noticed that the minimum variance portfolio has a lower coefficient on the size factor indicating that it holds larger companies. However, these companies are more exposed to growth than value. The momentum effect is virtually identical, but there is a strong long-term reversal tendency of the minimum variance portfolio, but smaller (and negative) short-term reversal relative to the S&P500.

If I have free time, I might create price to cash flow and dividend yield factors from Professor French’s data and combine it with some of the other portfolios on the Falkenstein website. It is likely that the minimum variance portfolios really do have some quality (such as idiosyncratic volatility) that is difficult to model. Nevertheless, I am quite convinced that MV Portfolios will have more promise than building portfolios with CAPM (just buy the market) or Fama-French (buy small-cap value, hold 20-50 years). CAPM is too lazy for the entrepreneur in me and it is hard to buy small-caps as an institutional investor without moving the markets. Building a MVP could be the first step in a screen and then one could shorten that list to 15-25 names based on fundamental information and industry trends. However, it seems like there could be something else that is explaining their returns that is worth investigating.

Agriculture Prices

2008-03-14T15:21:00.006-04:00

For those who have been watching, CPI core and headline came in flat today.


                 Dec. Jan. Feb.
                 2007 2008 2008
                          
Energy............ 1.7   .7  -.5
Food..............    .1   .7   .4
All items less                                                       
 food and energy     .2   .3   .0

I was under the impression that if agriculture prices increased .4% and energy decreased .5%, then a play today would be long DBA (the ag etf) and short USO (the oil etf). Unfortunately, the market seems to have paid more attention to the fact that CPI overall is negative. As of roughly 3:30, DBA is down 2.3% from the open, but USO is only down .15%. In other words, it would have been a horrible trade. On the other hand, DBA has ripped about 2 dollars since a double bottom around 1:30. Crude had a very intense downtick around 2:14, but besides that, it has trended down. It didn't trade this, but for future reference, it might make sense to wait until any craziness in the market dies down before putting on a trade like this.

More on inflation

2008-03-14T00:35:00.003-04:00

I admire Paul Kasriel's forecasting abilities. He has a recent research report (HT: Calculated Risk) where he describes a scenario where inflation can increase. He is more scared of inflation than I am. His scenario is that foreign countries will drop the dollar instead of defending their pegs ending their purchases (to defend). The current defending involves purchasing dollars by printing home country currency which leads to inflation (that will inevitably need to be reined in). Furthermore, these countries have acquired massive dollar holdings and eliminating the buying pressure could further depress the dollar and result in inflation at home.

I think these are all good points (though that were just as true in 2005 as they are now), but he misses one main point. The massive dollar holdings abroad represent significant assets on the balance sheets of central banks. If they drop the dollar, they know it will cause a drop in the value of their assets which will have a competing affect on the value of central bank reserves. I think each central bank is worried that another (major) central bank will unpeg their currency first, not that different than Mutually Assured Destruction. If inflation gets out of control in one of these countries where they have nothing else left to do, then Mr. Kasriel's scenario is a real possibility. However, I would consider this an exogenous shock to react to if it occurs and not something forecastable (unless seen a mile away in import prices or trends in inflation numbers of those countries) than I would actively bet money on.

In other words, I'm still more worried about the monetary base contracting in the U.S. and leading the recession here than I am about Mr. Kasriel's scenario.

Thoughts on inflation

2008-03-07T14:07:00.003-05:00

"Inflation is always and everywhere a monetary phenomenon." - tons of Economists

With equity markets dropping today and a record increase in Non-Farm Payrolls, I thought I would begin a discussion on the determinants of inflation and what it means when there is a recession and what it means for asset allocation.

Inflation really only makes sense when you refer to it as the debasement of a currency. Simply put, governments and central banks print too much money in order to reduce interest rates. Consumers borrow more and drive up the prices of existing goods. The market process contribution to this reasoning is that the changes do not happen instantaneously, but happen over time. This causes real dislocations in the economy which helps bring about the business cycle.

Market process theorists, monetarists, and others have used money supply data to guide them to central banking policies towards the creation of money. I really don't have the answers as to which one to use or not not use. For example, I don't know whether Travelers Checks or TAF should be included. I prefer to stick with monetary base adjusted for inflation (so that I can compare it between periods). Monetary base is cash plus reserves, it's simple and easy to use. The long-term change in this statistic is a good indicator to reflect monetary policy. When it is increasing, it means the Fed is creating money faster than the money is being debased.

This graph is courtesy of Paul Kasriel. Periods of increasing real monetary base are associated with boom times and periods of decreasing RMB typically coincide with recessions or other economic crises (not necessarily a recession defined by NBER). Currently facing a period of declining RMB, we could have expected one or the other. The question to ask is, what now?

To understand the current inflation, it should be clear that agriculture and energy prices are a large component in headline CPI. For example, the energy CPI index was .7% in January compared to .3% for the core number. Looking at the CPI chart below, core commodities, however, are actually relatively flat compared to the last boom. Core commodities (excludes food and energy commodities) also dropped significantly during the last recession as core commodities do. The reason is that as economic and industrial activity slows, metals such as zinc, copper, and aluminum are in less demand. If there is to be a recession, or any further slowing of economic activity, these core commodities will likely enter a bear market over the course of the slowdown.

Several market commentators are still worried about the possibility of inflation despite the fact that RMB is most decreasing. This is mostly due to a long-run bull run in commodities driven by agriculture and energy prices and a weaker dollar. Indeed, if we are entering a recession, industrial minerals should be beat down further than they are.

Above are the graphs for the past two years worth of DBA and DBB (the agricultural and base minerals etfs, respectively). DBA (and GLD and USO) have all been on a run lately. Some of this run is certainly based on fundamental factors (ethanol, the collapse of the financial markets, and market's determined belief in peak oil). However, I would caution anyone looking to put on new positions in these commodity classes to hedge your risk by shorting a value of DBB equal to the whole value of those positions. If the market thinks inflation will be coming down, industrial minerals will decline faster than the others since it fundamentally should do that. The spread will certainly widen though it might make sense to wait to put on the long side of the spread until there is a pullback or a naked position on the short side until the recent trend shows signs of ending. You don't have to think that inflation is going to decrease (which it usually does in recessions, but not always), but just that industrial minerals will decrease more than the rest of commodities.

Warren Buffett's Derivative Positions

2008-03-01T13:05:00.005-05:00

Berkshire Hathaway recently released its chairman's letter to the shareholders. Chairman Warren Buffett, opposed to many of the absurd and overlevered uses of derivatives, has used derivative positions over several years to take large positions. The most recent letter describes their current contracts which are divided among writing credit default swaps and puts on equity indices and leftover currency positions. Since Buffett has written the credit default swaps and sold the puts, he is able to hold all of the premium upfront and has eliminated his counterparty risk (which can be significant since they are all long-term contracts) and he is able to invest that money with returns greater than the likely implied interest rates in the contracts (either buying companies or pieces of companies). If he has an untimely death, I would hope that his successor can allocate capital as efficiently as Buffett can.

Credit Default Swaps
Berkshire-Hathaway (BRK) holds 54 contracts on specific bonds in high-yield indices. These contracts expire between 2009 and 2013 and BRK has received 3.2 billion, with a liability of .47 billion (and a max of 4.2). Professor Ed Altman at NYU has pointed out that there were practically no defaults in 2007 compared to historic averages (source: his Bankruptcy class). In fact, he estimates that the high-yield bonds will go to 4.64% (ht: FinanceProfessor), significantly higher than it is now. Typically when the economy sours, there are waves of defaults. These contracts are a very good investment given the historic lows and the financial trouble that will be coming.

Selling Puts
40 put contracts were written by BRK on the S&P500 and three other foreign indices. These contracts will last 15 to 20 years and were struck at the market. BRK has received premiums of 4.5 billion with a liability of 4.6 billion. However, these are European puts which means that they can only be exercised at expiration, 15-20 years from now. With inflation at 3% over the next 15-20 years, I see almost no possibility that Buffett will have to pay out any money on these contracts. In that time period, he (and his successor) will be able to invest that money generating large profits for shareholders. However, I do see these markets coming down over the next year or two which will require large liabilities and could temporarily hurt earnings. It's such a good investment (when not levered, which I doubt Buffett would do) in the long-term that they will never actually have to pay out any money. I would ignore any profits or losses they generate in the next five years. These won't be real losses by any stretch.

Currency Swaps
BRK held a currency swap in the Brazilian real in 2007 purchased in 2002 and euro-denominated Amazon.com bonds purchased at something like 57% of par during the internet crash. As the dollar fell, the Brazilian real and the euro have increased in value which have yielded very strong profits for Buffett. In fact, almost half of the profit on his Amazon bonds was due to appreciation of the euro and the bonds are now valued at more than par. However, Buffett is no longer exposing himself to bets on the weak dollar as he has in years past. This seems like a smart play. Real monetary base has been essentially flat or negative for the past year now and most inflation that will be coming will be due more to higher commodity prices (which will come down if the overall economy slows and affects all countries) than due to too much real printing of dollars. Core inflation will likely go lower throughout the year which will give some strength back to the dollar. I would wait to put on any positions shorting the dollar until real monetary base starts cranking up and then I would only do it after looking at the relative monetary policies of the opposite country.

Buffett discusses many other interesting topics in his letter than deserve attention (his analysis of accounting assumptions is always written better than anyone else), but I will confine myself with these three topics.

Mark-to-market Accounting and the Credit Bubble

2008-02-29T16:30:00.002-05:00

Naked Capitalism comments on the idea that Mark-to-market accounting contributed to the credit crisis. The argument made is that by marking the money to market they can grow their capital bases which allowed them to use more leverage.

It should be clear to most observers that credit bubbles are created by interest rates below the natural rate. In this case low interest rates drove higher home prices. Obviously this made securitized debt appear less risky than it should have been which kept the equity and mez tranches spectacularly overpriced.

I suppose I should go on to say that mark-to-market still would make sense for things that are actively traded or things that are strongly correlated with things that trade actively. However, the question comes to whether assets that do not trade actively should be marked-to-market?

Most securitized debt does not trade actively by any common-sense way of looking at it. Since they are typically classified as level 3 assets, these securities are actually marked-to-model when there are no market prices. That being said, the problem is too much of a reliance of mark-to-model, not mark-to-market. They couldn't properly value these instruments (ignoring times of declining home prices) and overestimated the fair value of the securities. Mark-to-market was what kept them honest when the securities lost value. I agree with the story that the increase in value due to the securities allowed them to increase their capital base and lend an larger absolute value, but I disagree that mark-to-market was a cause of that.

Update on 1% days

2008-02-29T16:29:00.002-05:00

Obviously today opened more than 1% down and the trade woulnd't have been successful. I suppose an update would be to rate the value of the news. If there is important news, the trade shouldn't be taken.

1% up or down days at the open

2008-02-20T15:24:00.002-05:00

In the past 250 days of trading, there have been 25 days where the market opened up or down by 1% or more. Today and yesterday were two of them and there have been quite a few lately. I have noticed that most of these days, especially lately are a fade (do the opposite, sell when it is higher, buy when it is lower).

To test that strategy, I programmed it in TradeStation to buy when the market is down 1% and sell when the market is up 1% and to enter the position the next minute after it starts to go my way. I used simple position sizing of 1000 shares of SPY with $.007/share commissions each way (what I'm paying now). The cover strategy is simply after 30 minutes to get out of the positions.

Over the past 250 days, excluding interest from not being in the market most of the time, you would have made 7,490 with a profit factor of 3.55(4.35 long, 2.7 short) with 52% profitable (50.00% long, 54.55% short) and the ratio of average profit to average loss would be 3.27 (4.35 long, 2.25 short). In other words, this strategy is right most of the time and the profits are much larger than the losses.

If you wanted to hold positions longer and just sell out some time after holding it thirty minutes when stochastics give an indication to cover, there's a profit factor of 3.68 (3.32 long, 4.91 short), but you are right 68% of the time (71.43% long, 63.64% short) and unfortunately the profit factor decreases to1.73 (1.33 long, 2.8 short). You would be making 11,590 over the entire period which is about 4 grand more for a very simple change.

With the SPY, 1000 shares would require at least probably 35k in margin to be able to trade it and you could get about a 33% return just trading this strategy (not including interest) over the course of a year. A more complex exit strategy could hold longer or start taking profits to reduce the draw down that can occur. Nevertheless, I find it interesting that this strategy (at least for a relatively small amount of money) could be this successful.

Bond Insurers

2008-02-14T12:12:00.003-05:00

It looks like there is a proposal to split up the bond insurers. I'm not particularly surprised by this development. If MBIA and Ambak took Buffett's deal, it would effectively have split them up anyway.f Buffett offered to take the Muni portfolio of the three major bond insurers. By taking that portfolio, they would be left with their CDS and CDO positions that would have likely bankrupted the firms. I would much rather prefer these companies to take Buffett's private offer than to be forced to split up. However, if they do not split up voluntarily, it is fairly clear that they will be forced to split up whether it is part of a bankruptcy agreement or outright. Municipalities won't put up with interest rates that high and not being able to borrow money and will complain up the chain of government until it gets done. The new firms holding the Muni insurance might be worth examination of whether to buy. I'm guessing that the other part will declare bankruptcy, there could be a situation where it would be a VERY distressed play. If it isn't liquidated in bankruptcy it would likely be severely undervalued coming out of bankruptcy.

Societe Generale

2008-02-11T10:47:00.000-05:00

Societe Generale announced a rights offer today almost 40% below the current share price. The current share price is roughly 77.72 euro and the rights offer guarantees the holder of 4 shares of SocGen the right to buy one share at 47.50 euro. The cost of the rights offer is estimated in the article with a theoretical value of 5.90 euro. Current shareholders should be particularly happy with this offer. If you held 4000 shares of SocGen, you could swap out 1000 for 5900 euro for an immediate net profit of 24,320 euro (excluding commissions and slippage) which would be about 7.8% of the current value of your shares while maintaining the same allocation. I should note that I haven't read the document and there might be limits to the offer so that this arbitrage could not happen exactly. I'm just pointing out the theoretical profit.

If you don't hold any of the shares, there could still be a big opportunity here. Many firms, Bearings, LTCM, Amaranth, to name a few, have been destroyed by large unprofitable trades. However, many of these trades would have been profitable had they been able to hold on to them (or at least not nearly as costly). These firms could have continued to exist if they had weathered the storm and mainained their financing. Their problem is the crisis and the sharks moving their positions against them. SocGen doesn't hold any more of their costly positions and have announced the write-off. The problems are over. The stock might continue to go down further in the short-term, but with it makes real sense to take advantage of this offer. I did a few calculations in an excel sheet and found that if you take advantage of this offer the spread between the yield when taking advantage of this offer and just holding shares outright increases substantially as the stock price increases (never going negative, but that makes sense). Selling at the current price would earn almost 7% on this strategy. That seems to be pretty safe and could be levered for a large return. With a longer term outlook on this company, you could earn a very nice return beyond what you could earn otherwise.

Dow 100^100

2008-02-08T19:46:00.000-05:00

During the 90s there were two books predicting the Dow would go to insane levels of valuation. Dow 36000 and Dow 40000. While there certainly is much to criticize in these books, I was thinking about when inflation would make their dreams come true. The Dow Jones Industrial Average closed at 12650 in the end of January. According to Global Financial Data, the DJIA earnings were 260.86 at the end of January implying a PE of roughly 48.49. I suppose this number isn't exactly fair since the number jumped up in July (a nice signal to get out of the market) when GFD has earnings going from like 800 to like 200 or so. It looks like the data is quarterly and they just have the numbers in the months spots multiple times. So, I'll just use the PE and earnings data from before the ratio goes from 20 to 50 since 20 is closer to the historical average. For that quarter GFD has earnings at 824.65 and with 13409.3 as the number for the DJIA. I'll average those two with the most current numbers so that I don't totally throw off my estimates of the growth rate (giving 542.76 and 13029.65). That gives a PE estimate at 24 that I'll assume could be a long-term number.

I'll split the difference of 36k and 40k (38k) and use that a future price target. Since PE=P/E, That leaves 24 on the left side and 38000 in the denominator. The earnings value I want to use is 542.76*(1+r)^n where r is the rate of growth for earnings and n is number of years to achieve 38k in the Dow (what I want to solve for). GFD has the June 2005 earnings number at 571 which would give a 44% increase in earnings to June and a similar negative decrease to use January's number. It would probably be more appropriate to run a Monte Carlo simulation using all of the data and put together a complicated model (since I am at a library with limited user rights I can't do that right now). Another long-term estimate would look at the average growth rate over the paste twenty years (the 1976 number is 95.81) which gives a number of about 9% growth a year. This number includes inflation (which is important) so you could consider the real number at about 5 or 6% a year depending on your estimate of inflation.

Plugging in the numbers and solving for n (ln 2.912/ln 1.09) gives 12.42 years. This would seem like a few number of years. I agree. This number is incredibly sensitive to the PE ratio or the growth rate. A one point change in the PE ratio would change n by (-1/24)/(ln 1.09) or roughly 6 months (granted the effect changes as you change the start date and decreasing the PE means lengthesns the time it takes to reach 36k). However, a one point change in the growth rate has an even larger effect, -ln(2.912)*(1/1.09)/(ln 1.09)^2 or (-132.3/100) or decreasing by 1.3 years for each percentage point increase in the growth rate. Certainly there are huge uncertainties with this analysis and calibrating the proper numbers. If actual earnings growth is comes in at 6% (3% inflation, 3% real GDP growth) with a long-term PE of 15 (not historically uncommon), then it might take (4.5+3.9) or 8.4 longer than originally planned at almost 21 years.

The Dow may reach 36000 (or 38000 or more) with a sound valuation over the next 10-20 years by pretty reasonable assumptions and 20-30 years from when the author's book was published. However, this does not imply anything about what the Dow will do tomorrow, next month, or next year (or even the next five years). It is a simple estimation that anyone who has taken high school math and introductory finance could figure out. I suppose the author's main flaw was not looking at a longer-trend of earnings growth and PE ratios. Saying the Dow will go to whatever 20 years from now doesn't save you from a Standard deviation that's twice as large as the yearly expected return if you're retiring in five years.

Furthermore, when the earnings growth for the Dow is a number as low as 6% or 9%, inflation will destroy half of the increase in value. If you only looked at real earnings, real Dow Prices, and the real PE, it would be unlikely to see real Dow going to 36000 by the end of the 21st century and it is mathematical impossibility with positive inflation for it to double in value when the nominal Dow doubles in value. For the average long-term investor, country and sector analysis combined with tactical rotation can provide much stronger returns in an inflationary environment.

News from the front

2008-02-08T08:53:00.000-05:00

I'm honestly amazed by Hank Paulson. He has been going around to the press since mid-January and has been talking about the risks to the economy. According to the Guardian, Paulson has said, "I still believe that we are going to continue to grow, although at a slower pace for a while, but the risk is very much to the downside and the risks are primarily housing." This would have been something to have said like 8 months ago or maybe a year and a half ago when housing started showing its decline. More than that, though, I'm curious as to how he thinks about risk. He's obviously not thinking about standard deviation, a traditional measure of how risky an asset is. Standard deviation is not biased to one side or another it is a statistical fact (he might have meant that these figures are increasing, but then he should have said risk is increasing). Furthermore, Value at Risk or the size of losses in worst case scenarios could not be what he is thinking of since they are necessarily always concerned with the downside. I guess I use a pretty common-people conception of risk that is different from Paulson's. There's really no one definition of risk, but courtesy of Frank Knight I know that risk is quantifiable. I know that risk is somehow related to the probability of a loss (or downside deviation from the mean) and the size of that loss. But I'm just not sure how risk could ever not be on the downside. I'm pretty sure that he's not talking about risk, but he is talking about where he thinks the economy in general will be going and saying risks are on the downside (repeatedly to the media) for pure rhetorical reasons.

The Economic Stimulus plan passed Congress last night. I'm pretty sure I'm going to receive some money. I'm pretty sure that it's going to be bad for this country. I'm pretty sure I'm still going to cash the check anyway.

Antitrust regulators are also going after the Nymex/CME deal. The Justice Department is opposed to having the financial futures exchanges controlling or owning their own clearing operations. Typically, antitrust regulators are sticking up for the consumers who get fleeced by prices too high. Most futures contracts have notional values in the hundreds of thousands of dollars and a lot of good brokerage firms don't let you open a futures trading account without sufficient experience. These markets have fierce competition and the people who participate in them have ample means to compete with any exchange if they wanted to. There are plenty of markets where they just block trade equities. It is absurd if the market is just defined as the futures exchanges. Any exchange or ECN could compete in this market and any Investment Bank could start their own if the structure were really fleecing them.

Great opinion piece in the WSJ about McCain's VEEP options. I've heard abunch about Mark Sanford from South Carolina (who would be much better for the economy as President than any of the frontrunners) and I'm glad WSJ put him on their short list. I'm just concerned if he might be too principled for McCain. Sanford could at least run in 2012 by himself.

2/4/2008

2008-02-04T16:18:00.000-05:00

The market mostly went down for the day. Downgrades in financials and weakness in the housing sector lead the decrease in the beginning of the day. Oil was up with railroads, autos, and airlines down. Utilities were up on the down market. Gold was getting crushed in the pre-market and as long as you stayed away from the South African miners, you could have done well shorting the miners. It felt like there was little moving the market later in the day. There was little news or releases (except Factory orders). The trends that developed in the beginning of the day were pretty much the trends that drove the market the rest of the day.

Microsoft May Borrow for First Time to Buy Yahoo

Yahoo May Seek Pact With Google to Fend Off Microsoft

I can't help but think the Microsoft bid for Yahoo is an awful idea. As a disclosure, I was a former long-term shareholder of Microsoft (by gift and I think I only made $3/share). Microsoft makes the vast majority of its profit on software and operating systems. Their web business doesn't generate nearly the revenues that other lines of businesses either can generate or are generating. Not only that, but they are bidding up Yahoo to such a high level, beyond any reasonable valuation, that they will likely lose money on it. Microsoft has an incredibly long time horizon and they might have thought that with the lower interest rates it would be worth it. However, I don't see anywhere for rates to go, but down. They could have waited several more months and probably could have saved a lot of money on the interest on the debt. This deal will only benefit Yahoo shareholders, Microsoft shareholders are getting hosed like Time Warner by AOL.

Fed Says U.S. Banks Are Tightening Lending Standards
I consider this good news for economy in general, but it could lead to short-term slowdown (not that there's anything wrong with that).

2/1/2008

2008-02-01T10:47:00.000-05:00

The jobs number was in negative territory. Not one of the 80 economists surveyed by Bloomberg predicted it would be that low. You could have made 140 dollars per 100 shares of SPY shorting in the pre-market and covering before the squeeze.

In other news, the ISM index was slightly better than expected. The initial market reaction was bullish, but I suspect that was hampered by thoughts of a smaller rate cut. Gold has been down, railroads up, mortgages are up (Fannie, Freddie, etc), but what is up has been trending lower and only has relative strength because of a strong open. Everything else I'm looking at is kind of mixed.

Tomorrow's job data

2008-01-31T23:20:00.000-05:00

Payroll and unemployment numbers come out tomorrow. I've been watching the Birth/Death model for months now. This model is meant to adjust employment numbers to take into account the Birth and Death of businesses. The problem is that statistical forecasting is much better at predicting the trend going forward than it is the turning point. If the economy turns south, the BD numbers will make the situation appear rosier than it would be otherwise. Mish, Barry Ritholtz, and John Crudele have all expressed concerns about the numbers. Briefing.com shows the consensus around 70,000-80,000 compared to a prior number of about 18,000. I'm agreeing with Barry and John that the number will probably be significantly lower. Maybe as much as 25-50% lower. The reason, explained by each, is that every year there is an annual rebalancing of the Birth/Death Model to recalibrate their estimations. If there is a significant deviation of the model with reality, the model will be adjusted to take that into account. In a time when advance GDP in Q4 came in at .6% and Q3 was only up due to better than expected inventory numbers, it's likely that there will be a significant adjustment.

From the short-term perspective it will be curious how the market reacts. If they are not aware of this information (traders read the Post for sports not finance), they will think the economy is worse than expected and play up hopes for a rate cut. However, they will have to weight rate cuts with a shitty economy. The person who follows the Birth/Death numbers already knows that the intermediate outlook for the economy is absolutely awful and the numbers have made it appear much better and should already be short (or in bonds) in that time frame. In the shorter-time frame, it will be easier to just take advantage of those who don't read the Birth/Death numbers. For the short-term, Gold will be a buy no matter what the market thinks will happen.

1/30/2008 rate cut

2008-01-30T21:56:00.000-05:00

The Federal Reserve cut interest rates by 50 basis points today. Despite the 10 minute (or so) squeeze, it was a profitable buy until later in the day when the Dow gave back most of its gains. Market commentators claimed this way due to bad news about Ambac and MBIA. Unfortunately for them, the news about Ambac and MBIA was out before the cut and no one reacted to it. I think the likelier explanation is that three days ago the discussion was 75 or 50 basis points and today it was 25 or 50. If the cut were 75 based on the information from 3 days ago (ex GDP-advance numbers at only .6%), then I would have thought the market would behave exactly how it did today. Go up huge and give back its gains when people realize the problems are worse than people realize.

For some time, I have been very bearish on the market. For one of my econometric classes, I developed a statistical model to estimate the probability of a recessions that's very similar to Merrill Lynch's model (I compared indicators from Kasriel and Mish). That model began predicting a recession in the next six months back in June and was giving scary readings as early as April. However, right now there is a competing influence that adds significant uncertainty to how bearish I am for the intermediate term (next 3-6 months). True, the housing crisis is a disaster and the stimulus plan and the rate cuts ultimately will harm the economy much more than it will help it. However, for as many bad numbers that come out, there are good numbers as well. What worries me most right now is inflation. 125 basis points in 8 days is a recipe for disaster if the economy isn't as bad as people think. Inflation is 2.6% right now and if the economy doesn't significantly slow or enter a recession, then inflation will come back with a vengeance, most likely after there has been significant time for the housing crisis to truly be felt. So if I were holding/shorting stocks for the next 3 to 6 months, I would most likely get out into something safer until I could figure out where the general market would stand. The fed might cut one or two more 25 basis point cuts over that period and treasury bonds and tips will likely do well over that period. While I am bullish on commodities, industrial commodities will not do stellar in a slowdown or recession. Gold is still a buy if it pulls back.

Lastly, I've been reading Intermarket Analysis by John Murphy. I have to say it is probably one of the best books out there on technical analysis for the person with longer time horizons. Murphy centers his discussion on interpreting trends among many different markets and it is pretty good. It amazes me when (most?) economists say they put all of their money in index funds. They are trained to study markets and rather than put their money where their mouths are, they give up. Especially when most of the trends can be seen a mile away.

New Blog

2008-01-30T21:34:00.000-05:00

I am a recent graduate of a graduate program in Economics (where Israel Kirzner taught) and thankfully just heard that I passed level 1 of the C.F.A. exam. I mention that only to say I know a little what I'm talking about, but I'm always learning more. I am working in the finance industry trading equities principally on a short-term intraday basis. This blog will reflect my opinions about current short-term market conditions, long-term prospects as well as my thoughts and opinions about Economics in general. I don't mean to comment on politics (about which I tend to be so passionate that I am indifferent between most candidates) except in relation to how policies will affect the market. I'm not sure how long this blog will last or how much I will get out of this or if I will have any readers at all. One thing I know: if there's a time to take risks, it's when you're young.

I will generally try to stay away from discussing set-ups, entries, exits, money-management, or any other specifics about trading strategies. This site is mostly for commentary. That said I might put on different "time horizon" caps when I discuss different subjects. From the short-term perspective (5 to 15 minutes) a Fed rate cut (like today, 1/30/2008) might be a good chance to earn a good return. However, that doesn't imply the same strategy should be adopted by a long-term investor. Given my short-term strategy, I can frequently change from a bullish to bearish perspective and back with little thought or cost. This may not be the case for the person with a longer time horizon and I will do my best to make clear what my thoughts are on the market and the time horizon for those thoughts.