market timing (part 3)

Market timing rules that rely on quantitative data (stock prices, economic data, etc) to generate a buy/sell decision can generally be classified as momentum strategies or reversion to the mean strategies. The premise of momentum strategies is essentially that whatever is increasing will build on itself in some fashion and continue going up (at least in the short-term). One of the simplest momentum trading rules is a stop-loss, whereby if the price of the stock drops below a certain level, the rule is to sell it at that point rather than continue riding it down. By the same token, one can create a rule whereby if the price of the stock increases above a certain level, the stock is purchased at that point in hopes of riding it upward.

The Test

To test the efficacy of this sort of strategy, I set up a back-test using historical price data for SPY, which is a stock that tracks the S&P 500 index. The rules I used were:

1. If the price of SPY drops to a level that is eight standard deviations (calculated on a daily basis) lower than its most recent highest price, then a stop-loss is triggered and the stock is sold.

2. Then, if the price of SPY increases to a level that is seven standard deviations higher than its most recent lowest price, a 'go-purchase' order is triggered and the stock is bought.

Results

The results of this test are shown in the charts above. Just as with the timing strategy based on retail sales data (a couple posts below), this strategy entails being out of the market a substantial amount of time (37% of the time in this case), which causes the trading portfolio value to be less volatile than the buy&hold portfolio value. As a result, the Beta of the trading portfolio is only 0.3 as calculated against the buy&hold portfolio. However, the return of the trading portfolio is 2.9% (annualized) vs. -3.4% for the buy&hold portfolio, which implies a trading portfolio Alpha of 4.0%.

Next Steps

You may wonder how I came up with the parameters for the test (eight standard deviations, etc). The answer is that I optimized the parameters to provide for the maximum Alpha based on this data set. The resulting Alpha for differing stop-loss and go-purchase rules are shown above in the sensitivity chart. Next week, I'll run this test again using price data from the past year to see how our optimized parameters perform against out of sample data. If the stock prices are truly random, it's not likely that our optimized parameters will result in any meaningful Alpha (but we'll see). I'll also run this test against price data for a different stock as another way to see if our results are at all robust.

Technical Notes

1. The test includes transaction costs of 0.20% for each trade.

2. The trading portfolio earns 0% interest during those times it holds all cash.

Quote for the Week: "No man is crushed by misfortune unless he has first been deceived by prosperity." - Lucius Annaeus Seneca (c. 4 BC-AD 65), Roman Stoic philosopher.