The zero drift scenario was requested by a university professor on this site who knew quite well, as I do, that you can not profit from random data series and therefore this test should have blown me away just like a house of cards. But it wasn’t the case. The test itself was a long process. The first spreadsheet had some 400,000 cells filled mostly with elaborate conditional inter-related formulas and some 150,000 calls to the random function to set price variations. The latest spreadsheet has some 3,000,000 cells and over 600,000 calls to the random function, all to, in the end, execute Schachermayer’s equation: (H.*dS). 100 tests were ran and after each test I recorded the results; then averaged everything and posted the results as the zero drift chart.
The results of the zero drift scenario are outstanding. It showed that using position sizing procedures based on self-directed binomial equations one could not only outperform the Buy & Hold but do it on a grand scale. It also showed that position sizing procedures could help in the trading game where a zero drift scenario should have had an expected value of zero. You won even with an average 72% failure rate! Imagine what would have been the results with only a 3% failure rate.
Each test run was unique and could not be duplicated. Even with the same set of parameters, the answer would be different each time you ran a test. You should not be surprised if I said that when I set all parameter levels to have zero effect, the results were the same as the Buy & Hold. You wanted performance; then you increased the levels within specific constraints to generate some alpha.
So the point being made is that each and every test had totally different data series with no predictive powers that could be applied. You should look at the Alpha Power paper with a sense of “on average” as I selected figures mostly from one test as representative of hundreds being done, all of which responded to particular controlling parameter settings. Figure 14 was generated to show scalability and is a test in itself, different from the one used for the other charts as it had its own higher parameter settings.
What was done for Figure 14 was to increase some parameters within the constraint of self-financing (like pressing on the gas pedal). The main objective was to show scalability. I remember putting my own constraints (so as not to show the pedal to the metal since you could push performance even higher). I could not use the parameter settings for the Figure 14 test as the basis for the paper and then go from there to show scalability without the risk of being considered a crackpot. My goal was to remain reasonable while showing the principles at work, and elaborate the mathematical framework which would explain the results.
It is by controlling equation 16 that you determine equation 33 of the Modified Jensen paper. You want more performance; then you press on the gas, so to speak. This may require additional cash, a higher initial position in each stock, a higher and/or incremental trade basis, a higher leveraging factor, a higher level of equity buildup re-investment, a higher reinforcement feedback or a combination of these. All of which are under your control (see the stuff on the decision surrogate). You can also modulate these settings to your own liking. There are definitely many solutions similar to equation 16 that can be applied.
You play the game and you set your own trading rules (that in essence is equation 16). You may not be able to control the price, but you certainly can control what, when and how much you buy or sell. It is your decision process, your position sizing method that will generate your alpha. In your search for your own total solution, you will notice as you add accelerators, enhancers and scaling factors (all within your constraints naturally), that your CAGR will keep going up.
Created on ... January 19, 2011 © Guy R. Fleury. All rights reserved.