November 06, 2011

Using Schachermayer's equation: Σ(Q.*ΔP) to express all the generated profits by a trading strategy; what would be the solution to double the profits? Since you cannot change the series of price differentials, you would need to double the quantity of all the trades. This is the same as saying you need to double the bet size Σ(2Q.*ΔP).

To do so, you could simply double the initial capital which in turn would let you double the bet size. It is here that it gets interesting as it places a value on your ability to find extra capital before you start the implementation of your trading strategy.

To answer the question, and therefore show its validity, there is only one way to do that and that is another test. I chose to use the same data set otherwise on what would I compare the results. Therefore, I re-used data set 2, the same as the last test. It is already at a very high level but based on the equation the profits should double by doubling the initial capital and therefore allow doubling the bet size.

After some napkin calculations, the expected results would fall just a little short of the figure I had in mind. So I decided to put just a little extra to be sure that I reached my objectives. I raised the initial capital for all 43 stocks from 100k to 250k. I would have needed a little less, more like 230-235k, but I wanted to reach my magic number. So the little extra was there to push me over. All this is being decided before undergoing the test which I intended to run only once.

## The Test

Since over 95% of the trades will remain random (with no choking), the trading procedures will still compete for their place in the sun with the result that most of the trades will be for different reasons and at different prices. But that is alright, you are not in the business of assuring that a trading procedure will always get its trade at a specific time and price. In fact, every test would be different due to the high degree of randomness.

One thing was for sure, the exercise would help put a value on the extra effort needed to raise more capital before starting to trade and secondly it would also show that indeed the Schachermayer equation is scalable.

I have kept a copy, as usual, of all the charts generated. And I must say that all the objectives were met. I think I should reiterate that no transaction can occur if there is no cash in the account. No margin is being used; the simulator does not allow it. It is a cash and carry kind of thing. So here are the results:

RS Script Nov 5  -  Double Bet Size

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And here are all the charts generated using the old Wealth-Lab 4 website simulator:

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