March 9, 2013

Maximum Drawdown

There is a new research paper out by Wes Gray and Jack Vogel that is interesting not only to momentum investors, but to all investors and researchers. The paper is "Using Maximum Drawdown to Capture Tail Risk." In it, Wes and Jack show that academic anomalies, identified by linear factor models (alpha), are often not great trading strategies.

Wes and Jack select eleven long/short anomalies from academic literature and show that a number of them, despite positive alphas and attractive Sharpe ratios, show very large drawdowns that would likely trigger margin calls and investor withdrawals at inopportune times. Six of the eleven strategies have drawdowns exceeding 50%, with the three worst being 86.1%, 84.7%, and 83.5%. (Long/short stock momentum is the one with an 86% drawdown. Perhaps QuantShares should reconsider calling their long/short momentum stock ETF, the "US Market Neutral Momentum Fund").

Some researchers look at the Sortino ratio, which divides excess return by downside variability, rather than total variability, like the Sharpe ratio. Incorporating upside variability may be useful, however, especially when evaluating investment opportunities with similar downside volatility.  Neither the Sharpe nor the Sortino ratio considers the full extent of downside exposure in the extreme left tail of a distribution..

Wes and Jack say it is important for researchers and investors to consider tail risk. They suggest looking at the maximum peak-to-valley loss (drawdown) associated with a time series as a relatively easy way to do this. They have an explanatory video on their Turnkey Analyst blog, along with the Excel VBA macro code and a spreadsheet for calculating maximum drawdown. (There are other good videos there as well, showing how to use Excel for mean variance optimization and how to calculate 3 or 4 factor alpha.)

Of course, maximum drawdown is not perfect as a risk measure. It is not amenable to traditional statistical analysis, such as confidence intervals. (Given the stochastic nature of financial markets, traditional statistical analysis may not be so accurate anyway.) Maximum drawdown is time dependent – the longer a track record, the more likely that maximum drawdown will increase. Drawdown frequency, as well as magnitude, is also important. Furthermore, maximum drawdown shows only a single past event that may be a chance occurrence and not be representative of what the future may bring.

Other ways of looking at tail risk attempt to deal with these concerns. Conditional value at risk (CVAR) tries to show what a drawdown will most likely look like given an extreme event. Extreme value theory (EVT) tries to identify large deviations from the medians of probability distributions. Both these approaches are computationally challenging and rarely found in finance literature. (I used to compute CVAR myself, but didn’t find it as intuitively appealing as maximum drawdown.)

Wes and Jack have done a service in showing how the usual ways of evaluating investment opportunities, such as alpha and Sharpe ratios, can be seriously lacking. Neither alpha, nor standard deviation, nor maximum drawdown, represent a complete measure of investment risk.

Maximum drawdown is good in that it gives some indication of extreme tail risk. However, I also look more broadly at strategy drawdown versus benchmarks drawdown under a variety of adverse conditions.

I also examine interquartile ranges and extreme outliers using box plots of the data. You can see all four of these methods at work in my dual momentum paper. I hope other researchers catch on soon and start presenting more than just Sharpe ratio or alpha as their objective function. These often mean little on their own in terms of true risk exposure. Tail risk is important to investors, and it should also matter to researchers.