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7.3.1 Kelly Criterion Portfolio In 1956, a scientist working for Bell Labs, John Larry Kelly, Jr., brought together game theory and information theory (Kelly, Jr., 1956). He showed that in order to achieve maximum growth of wealth, a gambler should place bets that maximize the expected value of the logarithm of the capital, usually referred to as the Kelly criterion. The Kelly criterion was ...
the Kelly criterion derives the optimal fraction of capital to invest in each trade, by maximising the expectation $\mathbb {E} [\log G]$. Why did Kelly choose to maximise $\mathbb {E} [\log G]$ rather than simply maximising $\mathbb {E} [G]$? What is the rationale behind this choice?
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.
The Kell y (-Breiman-Bernoulli-Latan ι o r capita l growth ) criterio n i s to maximize the expected value E log X of the logarithm of the random variabl e X, representin g wealth .
1. Optimal investment strategy – log utility criterion Suppose there is an investment opportunity that the investor will either double her investment or return nothing. The probability of the favorable outcome is p. Suppose the investor has an initial capital of X0, and she can repeat this investment many times. How much should she invest at each time in order to maximize the growth of capital?
Kelly (1956) is given credit for the idea of using log utility in gambling and repeated investment problems and it is known as the Kelly criterion. Kelly’s analyses use Bernoulli trials. Not only does he show that log is the utility function which maximizes the long-run growth rate, but that this utility function is myopic in the sense that period by period maximization based only on current ...
The remaining term approaches log X, thus we wind up losing everything except for what we cannot gamble. Either way, log wealth teaches us going all in is a bad strategy.
We use the logarithmic utility function as the utility function showing risk aversion investors. In this article we also give histograms with respect to ter-minal wealth and fundamental statistics of log-return at the maturity in order to understand features of each strategy.
This chapter focuses on Kelly's capital growth criterion for long-term portfolio growth. The Kelly (–Breiman–Bernoulli–Latané or capital growth) criterion is to maximize the expected value E log X of the logarithm of the random variable X, representing wealth. The chapter presents a treatment of the Kelly criterion and Breiman's results.
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expres-sions of the optimal portfolio weights are obtained for both utility functions. Moreover, we prove that both optimal portfolios belong to the set of mean-variance feasible portfolios and ...
There is a sizable literature reporting the conclusion that expected utility theory cannot provide a coherent positive theory of risk averse behavior. Recently-published articles have sharpened the criticism with calibrations based on assumed concavity and additivity of initial wealth to income. We demonstrate that the negative conclusions in this literature are valid for only one expected ...
The only explaination that I have supposed arises from the fact that the log utiliy is a special case of the power utility when $\eta=1$ , where $\eta$ is a measure of the risk aversion of the investor.