Sunday, 21 November 2010

More trading developments

Over the last couple of weeks, I have been reading Poundstone's Fortune's Formula - a book about the Kelly Criterion for position sizing in betting. We watched The Sting the other night and I was struck by the comparison between the situation set up in this movie and the generalised problem of bet-sizing. In The Sting, Robert Shaw's error is to believe something with certainty, which causes him to be willing to bet big. But if you generalise from this movie setting, the issue becomes one of assessing your bet size when you aren't absolutely certain. This leads into information theory, and so on.

And so much of this leads back to Ed Thorp. There were one or two clues in this book about some of the ways that Thorp had applied the Kelly Criterion for trading in the 1970s and 80s in the fund Princeton-Newport. This made in excess of 20% per annum at an SD of about 4% - a most remarkable result. The occasional example has allowed me to ask the question of how to apply this to our trading
Ed Thorp playing blackjack in the 1960s

But the remarkable thing today was that I finally had the necessary insight to work out how to apply the Kelly criterion to our results to date. Our combined trading system has made 17% so far. By calibrating off one day's particular loss, I was able to re-cast the data into other possible results based on different levels of leverage. This allowed me to generate the humped-back curve that characterizes the Kelly Criterion and it revealed that our maximum return would have been made at a leverage of 21x our current position size!
Of course, no one would actually trade full-Kelly in case they were wrong about their so-called edge. So I am looking at various fractional Kelly positions, focusing my current research on 1/10th Kelly. This would have returned 4% a week based on our trading results to date, with a worst drawdown of 10.2%, a perfectly acceptable situation.
Moving on from the overall model, I was able to use the Kelly model to calculate position sizes in the four markets we trade, and also a basis for increasing and decreasing our position size day-to-day.
Jerome and I spoke for a couple of hours about all this and are amazed that yet another possible huge development has arisen from our research. Our goal is to now deliver the core trading result and to increase position sizing slowly to 1/10th Kelly by January and possibly as high as 1/5th Kelly by Easter. If we were really sure of the results, 1/5th Kelly suggests possible returns of 5% a week. The ludicrousness of this figure suggests that we err on the side of caution though. Such a return is not necessary for us!

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