Optimal Portfolio Strategy to Control Maximum Drawdown - The Case of Risk Based Dynamic Asset Allocation

Abstract

Draw-down losses from a previously reached maximum portfolio wealth level, is an important risk measure for investment management. In this study, we present a discrete trading strategy to directly control a portfolio’s maximum percentage of drawdown within a target level while maximizing the portfolio’s long term growth rate.

Modifying the continuously rebalancing models proposed by Grossman and Zhou (1993) and Cvitanic and Karatzas (1995), we define the loss control target as a Rolling Economic Drawdown (REDD) with a constant look-back window progressing in time. Additionally, investor’s risk aversion in the power law wealth utility function is specified as complement of the maximum loss limit to construct a portfolio’s risk-return efficient frontier.

We test the dynamic strategy using data of three broad asset class indexes: S&P 500 Total Return Index (SPTR), Barclays Capital 20 Year US Treasury Bond Index (TLT) and Dow-Jones UBS Commodity Total Return Index (DJUBS), with 3-month U.S. Treasury Bill as the risk-free asset. Over a test period of the past 20 years (1992-2011), a simplified risk-based out-of-sample dynamic asset allocation portfolio is robust against variations in capital market expectation inputs, and out-performs the in-the-sample calibrated model portfolio and traditional asset allocation portfolios significantly.

Keywords: portfolio optimization, risk control, drawdown loss, dynamic asset allocation, discrete trading, efficient frontier, rolling economic drawdown, leverage, risk aversion, power utility function, capital market expectation, Sharpe ratio, volatility, out-of-sample test

JEL Classification: C51, C61