Don't draw the downs apart: How to best simulate asset price drawdowns

Abstract

This paper evaluates bootstrap simulation techniques for calculating the distribution of the maximum drawdown (MDD), an important risk indicator. Using stochastic dominance tests, we examine the complete distribution properties of the MDD in both the stock and cryptocurrency markets. The standard Efron (1979) bootstrap method, which assumes that the random variables are independent and identically distributed, systematically underestimates the true MDD. While the moving block bootstrap provides reasonable estimates, it is subject to non-stationarity bias, particularly when large drawdowns occur at the boundaries of a return series. The stationary bootstrap of Politis and Romano (1994) produces the most accurate and robust results, especially for longer block lengths. Alternative procedures, such as the block-block bootstrap, the tapered bootstrap and robust resampling, do not lead to better results.