Abstract
Bernard et al. [(2019) Optimal strategies under omega ratio, European Journal of Operational Research 275 (2), 755–767] use convex ordering arguments to determine the bounded payoff for maximizing the omega ratio. However, it appears difficult to apply such reasoning to estimate the bounded payoff for maximizing the Sharpe ratio. As a proposed solution, this paper uses a Lagrange multiplier method to derive the bounded payoff for maximizing the Sharpe ratio. In contrast to the optimal strategy in Bernard & Vanduffel [(2014) Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection, European Journal of Operational Research 234 (2), 469–480], the optimal strategy in this paper is bounded from below. It can protect investors from substantial losses when they invest in payoffs with a maximized Sharpe ratio.
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