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In less-liquid investments, such as hedge funds and private equity, capital may be tied-up for months or years.1 Consequently, monthly risk measures like value at risk (VaR) can understate the potential losses that investors face when they are eligible to redeem their capital-especially if losses in one month increase the risk of losses in future months. A popular multiperiod risk measure for illiquid assets is maximum drawdown, defined as the maximum peak-to-trough decline in the fund's net asset value (NAV).2 A related concept is maximum-drawdownat-risk (MDaR). Similar to VaR, the Gi-percentile MDaR is the maximum drawdown such that a fund recovers its peak NAV OLpercent of the time before reaching it. For example, if a fund's 95%ile MDaR is -15%, only 1-in-20 maximum drawdowns is -15% or worse.
Hedge fund investors often use a fund's historical maximum drawdown as a proxy for its current drawdown risk. Given the short track records and dynamic nature of many hedge funds,3 however, historical maximum drawdown may not accurately estimate future maximum drawdowns. A new hedge fund might never have experienced a drawdown, whereas an older fund could have different risk characteristics than during its prior drawdowns. Also, since drawdowns are relatively infrequent (about one per year in hedge fund indexes see Exhibit i), data on historical drawdowns may be inadequate to characterize drawdown risks, even in longer-lived funds.
We derive formulas for MDaR that do not require a previous drawdown and utilize parameters that can be estimated over relatively brief historical periods. The inputs are mean return, volatility, serial correlation, and current drawdown.4 Three questions we address with the model are
1. For a fund whose current drawdown is D < 0, what is the probability that it recovers before reaching a specified (worse) drawdown, δ < D?
2. For a fund whose current drawdown is D < 0, what is its Cf-percentile MDaR?
3. If a fund begins a drawdown with a onestandard deviation loss, what is its CC-percentile MDaR?
Questions 1 and 2 pertain to funds currently experiencing a drawdown, whereas 3 applies to all funds, not just those in drawdowns. Equation (27), derived to answer 3, could be a useful measure of drawdown risk for hedge fund investors.
Our formulas come from a Markov...