Modeling Expected Drawdown Risk


There are no silver bullets for profiling risk, but drawdown’s properties arguably give this metric a leg up over most of the competition. The combination of an intuitive framework, simplicity, and sharp focus on how markets actually behave is a tough act to beat.

Perhaps the strongest argument in favor of drawdown can be summed up by recognizing that peak-to-trough declines always resonate with investors. Sharpe ratio, Sortino ratio and the like are too abstract for most folks, but no one’s eyes will glaze over when you’re discussing losses relative to previous peaks.

Drawdown doesn’t replace other risk measures, but any risk analysis that excludes this metric may be overlooking crucial insight. With that in mind, the first order of business is developing robust estimates for assets and investment strategies to answer the question: What should you anticipate for maximum drawdown (MDD)?

The obvious way to begin is looking at the historical record. As an example, let’s review the history of the US stock market by way of the SPDR S&P 500 ETF (SPY), which tracks the S&P 500 Index. The ETF’s MDD since its 1993 launch is a hefty 55%. As such, it’s reasonable to assume that this fund is subject to getting cut in half in the depths of a bear market.

It’s tempting to leave it there, but SPY’s relatively short record inspires more stress testing to consider what might be lurking down the road. There are many possibilities on this front, but let’s start with a simple round of resampling the actual data for additional insight. The technique here is to create new sequences of daily returns from the actual track record to simulate alternative histories that might have occurred.

Let’s fire up R to generate 10,000 resampled variations, with the results shown in the chart below. As you can see the range of MDDs varies widely, from a relatively light 31% loss up to a dramatic 97% crash. Most of the MDD estimates, however, are within 62% to 77% (based on the interquartile range of the data. The median MDD for this simulation is 69%, or moderately deeper than the 55% decline posted in the actual record since 1993. In other words, there’s a case for thinking that SPY’s MDD could be worse in the future, perhaps much worse.

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