Pospisil and Vecer derived probabilistic representations of portfolio sensitivity to maximum drawdown and formulated the investment strategy by taking the forward price of the maximum drawdown into account. Sekine further extended the research to an upside-chance maximization problem of a large deviation probability called dual optimization problem, which links the optimization problem with the drawdown constraint in to the standard risk-sensitive-type portfolio optimization problem in Nagai and Kaise and Sheu. formulated the conditional drawdown-at-risk (CDaR) as the mean of the worse drawdowns and provided the practically stable portfolio using the CDaR measure. Besides traditional drawdown, Chekhlov et al. Specially, the risk-free interest rate is deterministic in the work of Cvitanic and Karatzas. Later, Cvitanic and Karatzas generalized this research in a situation in which the multidimensional risky asset price processes are defined by an -dimensional lognormal stochastic differential equation with -dimensional Brownian motion and deterministic coefficients. In a Black-Scholes economy with two securities (one risky and one risk-free), they studied the optimal portfolio problem of a power utility investor, who faces the constraint of losing no more than a fixed fraction of the maximum wealth achieved at any point in time up to that date, by maximizing the long term (asymptotic) growth rate of the expected utility of wealth. The problem of portfolio optimization subject to drawdown constraints was originally introduced by Grossman and Zhou. An important direction of the MVO research is portfolio optimization with risk control. During the recent years, the so-called mean-variance optimization (MVO) problem has advanced much, such as incorporating transaction costs into MVO, multiperiod portfolio selection, fuzzy investment portfolio selection, and extreme value approach in portfolio selection. Therefore, controlling the drawdown is crucial for the fund manager.Īfter Markowitz initiated the study of mean-variance approach on portfolio selection, expected value and variance are widely accepted as the measures of portfolio return and investment risk. pointed out that a 50% drawdown in an account is highly intolerable, and an account will be shut down if it suffers from drawdown for more than two years. Large drawdown usually leads to fund redemptions. It also challenges the clients’ financial tolerance. Maximum drawdown is an important risk measurement for money management professionals. The rolling economic maximum drawdown is more reasonable considering the risk-free return after the past maximum. Maximum drawdown refers to the maximum cumulative loss from a peak to a following bottom. We study the optimal portfolio strategy under rolling economic maximum drawdown ( ) constraints. Empirical results indicate that the REDP strategy successfully controls the maximum drawdown within the given limit and performs best in both return and risk. The investment cases of single risky asset and two risky assets are both studied in this paper. An empirical comparison research on the performances of different strategies is carried out by using the 23-year monthly data of SPTR, DJUBS, and 3-month T-bill. The simulation tests prove that REDP strategy can ensure the portfolio to satisfy the drawdown constraint and outperforms other strategies significantly. Besides, another novel strategy named “ REDP strategy” is further proposed, which replaces the rolling economic drawdown of the portfolio with the rolling economic drawdown of the risky asset. A more practical strategy is developed by using rolling Sharpe ratio in computing the allocation proportion in contrast to existing models. This paper deals with the problem of optimal portfolio strategy under the constraints of rolling economic maximum drawdown.
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