Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria

The main advantage of the Kelly criterion, which maximizes the expected value of the logarithm of wealth period by period, is that it maximizes the limiting exponential growth rate of wealth. The main disadvantage of the Kelly criterion is that its suggested wagers may be very large because the Arrow–Pratt risk aversion, the reciprocal of current wealth, is small compared with other commonly chosen utility functions. Hence, the Kelly criterion is relatively risky in the short term. And although most of the time Kelly bettors will have a lot of final wealth after a long sequence of favorable bets, it is possible, through bad scenarios, to lose most of one’s wealth. Hence, care in the use of Kelly and fractional Kelly strategies is crucial. In the one asset two valued payoff case, the optimal Kelly wager is the edge (expected return) divided by the odds. If there are multiple assets in a continuous time model with a lognormal distribution for returns, the .