A negative report on the ‘near optimality’ of the max-expected-log policy as applied to bounded utilities for long lived programs

Much controversy surrounds the use of the portfolio investment rules induced by maximizing the expected logarithm of terminal wealth (henceforth referred to as the MEL policy). It has been thought that the MEL policy is a good approximation to the optimal investment program when the utility of terminal wealth function is bounded and when the time horizon is long. However, I exhibit a class of bounded utility of terminal wealth functions for which the MEL policy is a very poor approximation to the optimal program. Hence, the wholesale use of the MEL policy as an approximation to the optimal program is unwarranted.