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Steve Mayo

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Subject : RE: The 90% Hit Rate Experiment
Posted : 5/7/2014 12:42 PM
Post #30415 - In reply to #30408

Craig, your thoughts are on-target. In gambling, there's something called the Martingale strategy, where you essentially increase your "bets" at an exponential rate. IF you have unlimited capital and unlimited time to "ride it out" and the expectancy of return is equal (like a coin toss) it is theoretically a guaranteed winning strategy. (That's why casino's have table limits!).

With stock trading, returns are serially correlated (markets really DO trend/cycle because of the economic cycle, news, crowd psychology, etc.) so, again in theory, you CAN have non-equal expectancy of return (something better than 50/50 odds) and a prolonged 'winning streak' is quite possible. The question, as you pointed out, is what IS the true expectancy of your trading system and how much data do you need to determine it with sufficient accuracy.

In drug trials, we do power calculations to determine how many patients we need to test to get a specified level of confidence in our findings. The statistics looks impressive, but in the end, it's still a guess, and it is often wrong -- that's why so many clinical trials fail to reach statistical significance. If you can't do it for a well-controlled clinical trial, can we really figure it out for something as complex and unpredictable as the stock market?

Likewise, how many trades does a system have to generate before it is considered robust? It's a hard question that gets into statistical things like mean, standard deviation and whether the the return from your trading system follows a normal bell curve. But, rule of hand, I would say at least 20 to 30 trades across your timeframe. (My example had as few as 3 to 5 trades in some strats which is why I expressed caution. However, is the sum of the parts -- 6.5 TPM for the port -- different after you combine 28 strats? Probably yes, but it still seems like too few trades to be robust.)

Hit rate, Profit Factor, and %Allocation are mathematically related: optimum hit rate = 1/(SQRT(1+PF). Thus with a profit factor of 1.2 (gains 120% as much as it loses), you need a hit rate of 66%. Increase your profitability to 2 and the hit rate needed drops to 58%.

There is similar math for the probability of having consecutive losses (at 3 sigma confidence): n=log(0.0027)/log(1-HR). At 70% HR, you can expect about 5 consecutive losses in a row with odds of 1 in 370 or about 1 such run per year (1/370 = .003 = a 3 Sigma tail); at an 80% hit rate, expect about 4 sequential losses, at 90%, expect about 3 in a row once a year. But, as we know, the stock market doesn't always follow the "normal" rules.
Deleting message 30415 : RE: The 90% Hit Rate Experiment


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