The 10% drift as presented in my first paper was only a $0.02 per day of upward movement on average for the total portfolio. This signal was drowned in the noise of random fluctuations (the error term). Taking away the drift part would leave you with totally unpredictable price variations where no tools could help you predict a future outcome. There would be no optimized 39 period moving average that could be applied to any of the data series. No technical indicator that would have any predictive value. You could make the assumption of the 10% drift based on the fact that it has been the average for the US market for at least the past 100 years. Thereby your tests would not be that far from reality over a 20 year period.
But as already known, the market price distribution has “fat tails” as well as more price variations close to zero (the Paretian distribution). To simulate this, I used the sum of three Gaussian distribution with increasing standard deviation and decreasing probability; thereby introducing random price jumps of unpredictable random magnitude in the price variations. So you could have at random a 6 sigma move with a probability of say 1 / 1000 on a particular stock. Each stock in each test had its own random drift, with its own sum of 3 randomly generated distributions.
The data generated at the time was tested for randomness by Twiga (he was very good at those things). And if I remember correctly; his conclusions were that 25% of the data series could be considered not random. But as you also know, the sum of any random data series also produces a random data series. The “fat tails” or outliers have to be included in any back test you do; otherwise you are over optimizing and developing a trading strategy that will produce a lot less than expected.
In Fig. 7 (see Alpha Power), what you see is the drift part (linear regression) of each of the stocks in that particular test with the average drift in red. Each test provided unique unpredictable data series which when averaged were close to the 10% drift. You’ll notice in Fig. 7 that some of the series go below zero and in the stock market that translate to you lose your bet.
A 7.5 failure rate on an average test is high. On a 50 stock test, selected at random there should be maybe 1 to 3 at most. But I suggest you keep your failure rate at the current level; it will force you to design more robust trading strategies.
What my research revealed me was that instead of trying to find which combination of indicators would turn a back test into a profitable strategy; that it might be better off designing trading procedures which followed preset profit equations. The emphasis is put on position sizing procedures.
Created on ... December 17, 2010 © Guy R. Fleury. All rights reserved.