Portfolio optimization with drawdown constraints

We propose a new one-parameter family of risk measures, which is called Conditional Draw-down-at-Risk (CDaR). 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 β, the CDaR is defined as the mean of the worst (1 - β) 100% drawdowns. The CDaR risk measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. For a particular example, we find the optimal portfolios for a case of Maximal Drawdown, a case of Average Drawdown, and several intermediate cases between these two. 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. We solved a real life portfolio allocation problem using the proposed measures.