Quote from gbos:
Proportional betting (Kelly) makes sense because compared to all strategies with the same risk it maximizes the median of the wealth. So it is an optimality criterion. Risk aversion is controlled by the proportion you are willing to bet in each trade (fraction Kelly).
Good and Bad properties of the Kelly criterion
(+) Asymptotically maximizes the growth rate of our wealth.
(+) Asymptotically minimizes the time we need to reach a goal.
(+) Maximizes median logarithmic wealth.
(+) We don¢t risk ruin.
(+) On average we are never behind in wealth level after n=1,2,…. repetitions of the bet from anyone following a different strategy.
(+) We follow an optimal ¡myopic¢ policy (we only need to consider in every step what kind of bet is available).
(+) If we want to achieve lower drawdown risk, at the expense of greater time to reach our goal, then all we have to do is bet fractional Kelly. That is equivalent to having a negative exponential utility function d*omega^d with d<0. The relation between d and Kelly fraction k is k = 1/(1–d).
(-) Equal number of wins and losses gives us lower wealth than the initial. That¢s because (1+f)(1-f)*W = (1-f^2)*W ≤ W.
(-) When the expectancy of a bet is high and the observed risk is very low, the optimal betting fraction may become unrealistically high.
(-) If there is uncertainty or erroneous estimation about how high our advantage is then it may be possible that we will over bet.
(-) Over betting will lead to ruin. In the fixed coin flip case, betting double Kelly will make our logarithmic growth rate of wealth zero, and betting even more will make it negative.
(-) It can take a long time for a Kelly bettor to dominate an essentially different strategy.
(-) It is possible to have very poor return outcome if a bad scenario is realized.
(-) If we win the expected number of bets then our average rate of return converges to half the arithmetic rate of return. In other words we do not seem to win as much as we expect.
