Wednesday, November 9, 2011

Diary: Kelly Formula

 A grab-bag of my notes about the KF (Kelly Formula).

My main gripe with the KF you don't know the odds, or the payoffs. If you knew that, then there wouldn't be much to investing.

Motley Fool article 13-Oct-2006

A commenter on a TMF article refuted the notion of applying KF to investing:
Kelly's formula gives the best size of your bet, if you were to SEQUENTIALLY (SERIALLY) bet on the same setup, such as in a casino. In stock market, you bet in PARALLEL on multiple scrips. In such times, Kelly's formula cannot tell you the best size of your bet. After all, Kelly's formula tells you what the best bet size should be to get the most returns after 'N' rounds. And it is to account for the drawdown (losses) that might occur in the process. In stock market, the ratio Edge / Odds is irrelevant. The Edge is the only thing that matter. Go back to the derivation of Kelly's formula. Kelly's formula can help a trader who has to take huge number of punts one after the other based on a trading system but cannot help a fundamental investor.

Value Buddies board

A reader on a discussion board writes:
Standard Kelly results could have you investing a large % of your portfolio in one stock. I'm adjusting Standard Kelly by a diversification formula I found in an Ed Thorp paper. (Ed Thorp popularized the Kelly formula in his book "Beat the Dealer"). The formula ends up close to the % difference between your winning % - losing % based on your historical trades. Using my standard inputs this results in a maximum of 10% in each stock. But a stock would have to be trading at 80% discount to fair value to get 10%. I've read Pabrai's books and much about him and I will go back and learn more of his experience with Kelly. I'm no Pabrai (or Buffet or Gross) but I will comment on my analysis of Pabrai's picks. I used to try to analyze his stock picks but couldn't understand what he saw. He seemed to be buying "cigar butt" stocks (ie. Ben Graham type) that I guess mostly ended up being just 'butts'. I'm looking for stocks with at least 10 years of growing free cash flow, and good profit and ROIC margins.


A non-standard way of calculating the position size, which I happen to prefer, is detailed on a page at Reaper Trades. I reproduce their calculation method below.

The formula is: P_invest = E(r) / M(r)
Proportion of portfolio to invest = P_invest
Expected return= E(r)
Maximum return = M(r)

One thing to consider is that the Kelly formula seeks only to maximize gains. If you wish to minimize portfolio variability as well, you should invest significantly less than the maximum allowed by the Kelly formula. Also, keep in mind that the formula is only as good as your guesses of probability. In order to minimize portfolio volatility and because it is very difficult to accurately estimate the expected return on a trade a priori, many traders stick to using a very small fixed percentage of their portfolio on each trade.

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