A refined measure of conditional maximum drawdown

Risks associated to maximum drawdown have been recently formalized as the tail mean of the maximum drawdown distribution, called Conditional Expected Drawdown (CED). In fact, the special case of average maximum drawdown is widely used in the fund management industry also in association to performance management. It lacks relevant information on worst case scenarios over a fixed horizon. Formulating a refined version of CED, we are able to add this piece of information to the risk measurement of drawdown, and then get a risk measure for processes that preserves all the good properties of CED but following more prudential regulatory and management assessments, also in term of marginal risk contribution attributed to factors. As a special application, we consider the conditioning information given by the all time minimum of cumulative returns.