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
Monday, November 24, 2008
Wednesday, November 19, 2008
Kaizen Fed Quotes
"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"
Tuesday, November 18, 2008
AQR and Leverage
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.
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.
Sunday, November 9, 2008
Buy and Hold (Part 2)
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.
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)
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.
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.
Saturday, November 8, 2008
Presidential Inaugurals
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.
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.
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