Tuesday, March 31, 2009

The Difficulty of Backtesting

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.

Saturday, March 21, 2009

My Solution to the AIG problem

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?

Wednesday, March 18, 2009

Is the BoE reading the Money Illusion

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.

Tuesday, March 17, 2009

Condor Options

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.

Thursday, March 12, 2009

50 shapers of Finance

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.

Wednesday, March 11, 2009

Greenspan is wrong

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

Sunday, February 8, 2009

Component TAA Update

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.

Wednesday, February 4, 2009

Kaizen ECB quotes

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."

Friday, December 19, 2008

Buy and Hold (Part 2.5)

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.

Sunday, December 14, 2008

Re: Hulbert

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.