January 4, 2011

One needs to do a lot of tests to convince himself of the methodology just as I did in my own process of trying to understand the dynamics of the underlying equations. My strategy does not use fixed-percentage of equity trades; they start at 2% or less and decrease in time from there. In time each trade becomes a smaller percentage of available equity. Each data series was different within each test and from test to test. The initial price was random – then normalize to 20 – all three Gaussian were randomly set in amplitude and drift for each stock. I could not replicate any data series.

Whatever the test run, all stocks simulated would be different from all previous runs. There was nothing from any of the tests that could be used in the next. And there lies the usefulness of the approach: whatever the stock series selected, you could profit from them as a group. You could save yourself some research time by reverse engineering my equations to see how they work.

The basis for the three papers is equation (16) in the first paper (Alpha Power) which led to a second representation in the equation on page 33 of the Jensen Modified Sharpe paper. The latter presents the payoff matrix as a binomial equation and is of significance as it implies that one can extract from the markets what he/she wants, based on a predefined long-term trading procedure (again page 33). The procedure presented is not a unique solution; it is part of a family of such equations which result in position sizing methods whose sole purpose is to improve performance at the portfolio level.

I have a great admiration for the simplicity of the Schachermayer equations (see the Payoff Matrix). There is not much you can do to change what the prices will be in the future; the best you might be able to do is a better selection of long-term up-trending stocks. Notwithstanding, you can design a holding function matrix that can easily outperform the Buy & Hold strategy.

The method is base on averages, scaling in and out of trades and over-diversification. From an initial bet on selected stocks, trades are added as a behavioral reinforcement. It is within your decision surrogate that trades and their size are determined according to their incremental settings.

You are making one bet. It’s like taking the Warren Buffett’s 37 billion long-term put option. What you ask from the markets is that in 20 some years, the market will be higher than it is today. And on this, I agree with Mr. Buffett’s bet: it is more than a reasonable bet that the secular trend should prevail.

In the end, you know, there is only one person that you really need to convince and that is yourself. You will be alone to make your trading decisions and it is the degree of your own convictions, your own beliefs, which will dictate your position sizing method. I had to go through the same process and the result of writing the research papers not only led to a better understanding of the game but also to the belief in my own trading abilities.