Significant downside tail-risk for equity markets is another reason Thorp and a co-author estimates Kelly fraction to be 117% for the American stock market SP500 index.

half-Kelly).Ī detailed paper by Edward O. Both of these estimates of Kelly fraction appear quite reasonable, yet a prudent approach suggest a further multiplication of Kelly ratio by 50% (i.e. Where losing the bet involves losing the entire wager, the Kelly bet is:į ∗ = p − q b = p − 1 − p b. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors including Warren Buffett and Bill Gross use Kelly methods. The practical use of the formula has been demonstrated for gambling, and the same idea was used to explain diversification in investment management. Under the stated assumptions, the Kelly criterion leads to higher wealth than any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity). Kelly Jr, a researcher at Bell Labs, described the criterion in 1956. It assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate.

In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. Formula for bet sizing that maximizes the expected logarithmic value Example of the optimal Kelly betting fraction, versus expected return of other fractional bets.

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