Portfolio Management with Drawdown Constraint: An Analysis of Optimal Investment

We analyze optimal investment strategies under the drawdown constraint that the wealth process never falls below a fixed fraction of its running maximum. We derive optimal allocation programs by solving numerically the Hamilton-Jacobi-Bellman equation that characterizes the finite horizon expected utility maximization problem, for investors with power utility as well as S-shaped utility. Using stochastic simulations, we find that, according to utility maximization, implementing the drawdown constraint can be gainful in optimal portfolios for the power utility, for some market configurations and investment horizons. However, our study reveals that the optimal strategy with drawdown constraint is not the preferred investment for the S-shaped utility investor, who rather prefers the equivalent optimal strategy without constraint. Indeed, the latter investment being similar to a partial portfolio insurance, the additional drawdown constraint does not appear valuable for this investor in optimal portfolios. Bonelli, Maxime and Bossy, Mireille, Portfolio Management with Drawdown Constraint: An Analysis of Optimal Investment (March 21, 2017). Available at SSRN: https://ssrn.com/abstract=2959955 or http://dx.doi.org/10.2139/ssrn.295995