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.

## Thursday, May 22, 2008

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## 2 comments:

Great analysis - clearly the strategy ran out of steam. I'm thinking of posting a bunch about "failed strategies."

Interesting. Bill Rempel published a study of RSI(2). If one goes back 70 years or so, when RSI(2) > 90, it was a buy signal (for the S&P I believe). However, around 1970, this changed. Since 1970, when RSI(2) is low, say < 10, that is now the buy signal.

It seems to me the market participants have slowly switched from buying strength to buying weakness.

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