Portfolio Optimization with Drawdown Constraints

Abstract

A new one-parameter family of risk measures, which is called Conditional Drawdown-at-Risk (CDaR), is proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in an active portfolio management. For some value of the tolerance parameter beta, the CDaR is defined as the mean of the worst (1-beta)*100% drawdowns. The CDaR risk measure contains the Maximal Drawdown and Average Drawdown as its limiting cases. For a particular example, the optimal portfolios for a case of Maximal Drawdown, a case of Average Drawdown, and several intermediate cases between these two were found. The CDaR family of risk measures is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Access loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. A real life portfolio allocation problem using the proposed measures was solved.