Drawdown Measure in Portfolio Optimization

We propose a new one-parameter family of risk measures called Conditional Drawdown (CDD). 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 α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 − α) ∗ 100 % drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. We studied mathematical properties of the CDD and developed efficient optimization techniques for CDD computation and solving asset allocation problems with CDD measure. 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 CDD family of risk functionals 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 functionals for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed measures.