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Comment by anonu

4 years ago

This has been posted 5 other times on HN with no real discussion [1].

I'll add my 2 cents: I used to use the principles of kelly betting back when I designed systematic HFT strategies. It gives you a good framework to think about how much to bet based on the batting average of a particular pattern you recognize in the market...

[1] https://hn.algolia.com/?q=https%3A%2F%2Fen.wikipedia.org%2Fw...

You may be interested to know that Kelly's work was instrumental in a company called Axcom in the 60s. Elwyn Berlekamp, previously an assistant to Kelly at Bell Labs, implemented Kelly et al's work in early financial trading at Axcom, which was later turned into the Medallion Fund at Renaissance Technologies. Wikipedia [1] has some info on this, but I also highly recommend "The Man Who Solved The Market" (Zuckerman, 2019) for more history.

[1] https://en.wikipedia.org/wiki/John_Larry_Kelly_Jr.

  • You may be interested to know that Ed Thorps - Princeton Newport Partners/ the Santa Fe school work lives on at an even better performing fund called TGS Management based in Irvine.

> I used to use the principles of kelly betting back when I designed systematic HFT strategies.

possibly a dumb question, but how did this work exactly? the kelly criterion assumes you know the amount by which the coin is weighted, how would you know the equivalent for the stock market in the very near term?

  • You make a conservative guess. The Kelly criterion is somewhat forgiving about guessing it wrong.

    Your question is not dumb: you figured out exactly what's hard about this stuff.

How did you apply Kelly to a HFT strategy? Usually those strats don't have a binary outcome so standard Kelly wouldn't fit.

  • Kelly goes beyond binary outcomes. The underlying principle is the same, though: you maximise expected logarithmic wealth.

    To do that you need the joint distribution of outcomes (what are the possible future scenarios and how likely are they?) Estimating this well is the trick to successful application of the Kelly criterion.

  • the binary outcome formulation you see everywhere is just "real" kelly boiled down. the real thing, which is contained fully in the first paragraph ("The Kelly bet size is found by maximizing the expected value of the logarithm of wealth"), has no such restrictions.

    • How do you maximize the E(log(wealth)) when applied to a HFT strategy? In such a strategy we have N sequential bets, each bet has a roughly normal distribution outcome with mean just above zero.

      The example on Wikipedia supposes we are investing in a geometric Brownian motion and a risk free asset.

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Hi I work at a small hft firm and would love to discuss this more in detail, please contact me if you have the time.

Thank you