I believe the best method for determining optimal leverage involves maximizing the median ending wealth. Harry Markowitz (1959) showed that maximizing median wealth is equivalent to maximizing the mean logarithmic return, and he developed a good approximation for calculating the mean logarithmic return based on the arithmetic mean and variance of returns: Expected log return = expected return – 1⁄2 variance of returns Using an amount of leverage, M, the log return equation becomes: Expected leveraged log return = M expected return – 1⁄2 M2 variance of returns In order to maximize expected log return, we take the derivative of the expected leveraged log return with respect to M. Setting the derivative to zero, we solve for M. It happens that the optimal leverage—the optimal value of M—for use in a trading strategy is calculated by: Optimal leverage = return / variance = μ/σ2 Using the optimal leverage calculated from the above formula, we will be maximizing our median ending wealth, the benefits of which were seen earlier in this chapter. If our strategy is expected to return 5 percent per year over the riskfree rate, with annual standard deviation of 20 percent, then our optimal leverage is (0.05)/(0.20)2 = 125%. We would actually borrow 25 percent of our capital to plow back into our trading strategy.