Maximum Drawdown
Maximum drawdown (MDD) plays a key role in risk management and has been widely studied in the academic literature. Given a price process
where
Maximum drawdown is a simple, yet popular measure of extreme risk which is widely used in adjusted performance measures such as the Calmar, Sterling and Burke ratios. In practice, the drawdown process is often designated as the negative of
A weakness of MDD is that it only uses available historical data. This can be misleading when instruments have different lengths of historical data available. To address this limitation, we use Scientific Portfolio's long-term risk model to simulate systematic returns for periods when observed returns are not available. By combining the observed returns with simulated returns, we calculate a portfolio's historical drawdowns over a rolling 15-year time period. This approach ensures that MDD is comparable across different portfolios, regardless of data availability.
Drawdown from Simulated Returns
Consider one portfolio with a return series , where . Assume that the other portfolio has a return series with a limited history, only covering the interval . Accordingly, to ensure that the maximum drawdown is comparable across the two portfolios, and need to be truncated to the shared history. This truncation severely limits the applicability of drawdown measures for portfolios with varying time periods.
To mitigate this issue, we propose a method that leverages the SP risk model to simulate missing returns, thus allowing for a computation of the drawdown process over a 15 year time period. Rather than coercing the returns of the portfolio to the shared history, we rely on the risk model and systematic returns to compute portfolio returns that cover the whole history. That is, for every portfolio, we compute the systematic return series (simple return) as
where and represent the risk model’s parameters. While the specific return, , is available only for the interval , the systematic return relies merely on characteristics that are, by design, available over the entire interval (see risk model characteristics). Consequently, we define a systematic price process
that is computable for any asset in the universe up to time . To recover the price process for , we use the total return (both the systematic and specific return) where available, and for the rest, we impute the systematic return obtained from the risk model.
Finally, by inputting the imputed price process into , we recover the drawdown process.
Remark
Since only captures the systematic return, we provide confidence bands derived from the empirical distribution of the specific return. Specifically, we bound the drawdown process as
where denotes the empirical quantile function of the portfolio's specific return distribution . Therefore, when the maximum drawdown occurs within the simulated returns data, a confidence band with is included in the drawdown process to ensure a level of conservativeness.