May 27, 2011

I am always looking for reasonable explanations for my trading scripts. What makes them work, what are the principles at play, and what is the main reason for their high or low performance? Are the improvements really real, operating at the portfolio level, or are they just curve-fitting on a single stock? These are all legitimate questions, and if I can’t provide a reasonable answer, a common sense answer, then it should be back to the drawing board.


I need to know where are the strengths and if I can get more out of them. I also need to know where are the weaknesses and if I can get less of those. Naturally, all I do must fit within my global vision of the game, or/and until such time as I find something better.

In the Alpha Power Overview article, I presented my latest Alpha wealth-generation formula. It is repeated here for convenience.

spacerNew Alpha wealth generation formula

A Buy & Hold strategy is implemented with the added twist that the inventory on hand (Q) is put on an exponential growth function (g) to which can be added a short-term trading algorithm (T), a covered call program (C) and an exponential bet sizing function (B). A leverage factor (L) can also be added to push performance higher. All contribute to portfolio performance. Removing all the control variables would reduce the wealth equation to a simple Buy & Hold:

spacerBuy & Hold formula

A Total Trading Solution

In my previous article - Looking for a Total Solution (2009) - it was expressed that a trading component can improve overall performance. It is worth noting the portfolio value formulation at the very beginning of the paper. Three items can have significance at the portfolio level. First, increasing the inventory growth rate on the opened long positions will increase performance. Second, on the closed long positions, it is preferable to seek higher profits on an increasing number of trades before they are sold. And third, increasing the number of such trades can have a major impact on portfolio performance.

Based on recent test results, I tried to explain the achieved performance in light of the Alpha wealth formulation. Whatever the performance achieved, you need a reasonable explanation for the results. It is easy to find explanations when your script loses, but when your performance exceeds the seemingly reasonable, what then?

Alpha Wealth Generation Formula

This is my attempt at providing an answer in light of my trading philosophy and its mathematical framework. The chart below starts with the same initial capital as in the three tested data sets. My methods are scalable up or down, so view the initial capital just as a comparison point.

The objective is to set the value of some of the variables in such a way that the performance result can be reached and that they can provide a reasonable explanation for these same results.

Alpha Power Math Example

(click to enlarge)

First, since no leverage was used and no covered call program was in force, both these controlling variables are set to zero (no influence on the outcome of the aforementioned tests).

The inventory growth rate variable (g) was set to 1, meaning full utilization of the excess equity buildup. The bet sizing variable has for mission to increase bet size as portfolio value grows. It was set to a reasonable value since, after all, the primary objective of the method is to accumulate shares for the long term when feasible. This accumulation only occurs if there is a sufficient equity reserve to add to the existing inventory buildup.

Equity Infusion Trading Method

There is only one variable left: the trading method equity infusion. For the numbers to approach test values, it was required to set that the short-term trading method was providing the equivalent of a 110% increase in the inventory accumulation formula. The short-term trading method alone was generating enough cash to acquire more shares, practically feeding the inventory accumulation process to a large extent.

A Reasonable View of the Numbers

These are the most reasonable numbers and explanations I have that can explain the results of the three separate tests provided (over 120 stocks in all). Note that I have set the rate of return at 20% even if the long-term market average is closer to 10% than anything else; therefore, the Buy & Hold column may be divided by two. Why I used a 20% return was simply that the stocks that were included in these tests were all survivors, and I thought that it would more than reflect the inherent upside bias. Setting a lower value for the rate of return would force to increase the bet sizing algorithm or/and the trading component contribution rate to overall performance (see figure below).·

Alpha Power 10% Return

 (click to enlarge)

To obtain almost the same result as the first table, it was required to increase the Bet Sizing rate to 0.55 and the Trading component to 2.5. This means that the trading algorithm would have to have been more efficient at extracting profits from market swings than first presented.

Increasing the trading algorithm, the bet sizing function, implementing a covered call program, or adding leverage would all have an effect on increasing performance. Another way to increase performance would be to have a better stock selection process.

It was shown in the Control Settings article that increasing the number of profitable trades over the trading interval leads to increased overall performance. The reasoning is understandable in light of the preceding explanations for the overperformance.

The Alpha Power trading methodology presets mathematically the trader’s desired behavior to future market fluctuations. As a method, it allocates more funds to the higher performers while at the same time reducing and starving non-performers. The method ends up making big bets on big winners and small bets on losers. It really is a Darwinian approach to playing the game.

Created on ...·May 27, 2011,    © Guy R. Fleury. All rights reserved.