Bet sizing formula for long-term growth
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets.
In probability theory , the Kelly criterion (or Kelly strategy or Kelly bet ) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate . John Larry Kelly Jr. , a researcher at Bell Labs , described the criterion in 1956.[ 1]
The practical use of the formula has been demonstrated for gambling ,[ 2] [ 3] and the same idea was used to explain diversification in investment management .[ 4] In the 2000s, Kelly-style analysis became a part of mainstream investment theory[ 5] and the claim has been made that well-known successful investors including Warren Buffett [ 6] and Bill Gross [ 7] use Kelly methods.[ 8] Also see intertemporal portfolio choice . It is also the standard replacement of statistical power in anytime-valid statistical tests and confidence intervals, based on e-values and e-processes .
^ Kelly, J. L. (1956). "A New Interpretation of Information Rate" (PDF) . Bell System Technical Journal . 35 (4): 917–926. doi :10.1002/j.1538-7305.1956.tb03809.x .
^ Thorp, E. O. (January 1961), "Fortune's Formula: The Game of Blackjack", American Mathematical Society
^ Thorp, Edward O. (1966). Beat the dealer: a winning strategy for the game of twenty-one: a scientific analysis of the world-wide game known variously as blackjack, twenty-one, vingt-et-un, pontoon, or van-john . New York: Random House. ISBN 0-394-70310-3 . OCLC 655875 .
^ Thorp, Edward O.; Kassouf, Sheen T. (1967), Beat the Market: A Scientific Stock Market System (PDF) , Random House, ISBN 0-394-42439-5 , archived from the original (PDF) on 2009-10-07 , page 184f.
^ Zenios, S. A.; Ziemba, W. T. (2006), Handbook of Asset and Liability Management , North Holland, ISBN 978-0-444-50875-1
^ Pabrai, Mohnish (2007), The Dhandho Investor: The Low-Risk Value Method to High Returns , Wiley, ISBN 978-0-470-04389-9
^ Thorp, E. O. (September 2008), "The Kelly Criterion: Part II", Wilmott Magazine
^ Cite error: The named reference Poundstone book article
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