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.
2 comments:
Excellent post Kirnzer - one question - what is the multiplier? I see that you specify it, but it's not clear to me why you're using a multiplier or how you determine the value.
Thanks!
damian,
The multipliers are just arbitrary. The formula is the base+mult*(the signal). So if the base is .6 and my signal is telling me 1, then the multiplier of 0, says keep it at .6, .1 multiplier says increase to .7, and a multiplier of .5 says 1.1 (but since I truncate, it becomes 1).
I tried to do the same methodology with three assets, but it just gets confusing and the result isn't as pretty. I think another thing to look at would be how would an investors risk aversion need to change over time in order to get a result like this. In other words, could I use the signal in the same way for risk aversion in a Mean-Variance Markowitz optimization framework to replicate the same kind of results. I might have to extend the series if I try this.
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