An Economic Approach to Optimize Capital Allocation

Abstract

A central problem that investors face is how to manage risk on transactions with positive expectation of profit while maximizing the rate of growth of capital. One way to define the problem is given a transaction with a positive expectation of profit, how much risk should the investor take on the transaction to maximize long term growth of its capital base by maximizing risk adjusted return while minimizing ruin. In this paper we explore the use of Kelly Criterion, which is to maximize the expected value of the logarithm of Insurers capital (“maximize expected logarithmic utility”) to find solutions to the problem. The criterion is known to economists and financial theorists by names such as the “geometric mean maximizing portfolio strategy”, maximizing logarithmic utility, the growth-optimal strategy, including the capital growth criterion. We prove these concepts using a hypothetical investor with a fixed probability of total loss. This approach can be generally utilized in allocating capital for investments. Keywords: Kelly criterion, Betting, Long run investing, Portfolio allocation, Logarithmic utility, Capital growth