Construct · 3 fields · 3 citations
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The Kelly criterion is the rule for sizing a sequence of favorable bets so as to maximize the long-run exponential growth rate of capital, which is equivalent to maximizing the expected logarithm of wealth each round. Kelly's 1956 A new interpretation of information rate derived it by analogy with a communication channel, showing that a gambler with private information should stake a fraction of capital equal to the edge divided by the odds, and that this fraction maximizes growth while making eventual ruin impossible. The referent is a growth-optimal proportional betting rule, specified as the optimal fraction of capital to wager, the same construct that recurs in gambling bet sizing and in portfolio choice.[1]
In gambling theory the same construct sets how much of a bankroll to stake on a favorable game such as advantage blackjack or sports betting, balancing fast growth against the risk of deep drawdowns. Thorp's 1969 Optimal gambling systems for favorable games worked out the Kelly strategy for real play, showing it beats any essentially different strategy over the long run while noting that betting more than Kelly ('overbetting') lowers growth and sharply raises risk. It is the identical log-optimal proportional-betting construct as in Kelly's channel analogy, here realized at the table and measured by long-run growth rate and drawdown behavior.[2]
In finance the Kelly criterion reappears as the growth-optimal, or log-optimal, portfolio: the allocation that maximizes the expected logarithm of wealth and so the long-run compound growth rate of an investment. MacLean, Thorp, and Ziemba's The Kelly Capital Growth Investment Criterion: Theory and Practice collects the theory and its use by investors, along with the common 'fractional Kelly' practice of staking a fraction of the full amount to temper volatility. It is the same growth-maximizing proportional construct as in information theory and gambling, transposed to asset allocation and measured by compound growth rate against the volatility an investor will tolerate.[3]
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