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.
Friday, December 19, 2008
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.
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.
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