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Pain Index vs. Pain Ratio

Feb 12, 2013 Marc Odo

Although people have found Zephyr’s pain index and pain ratio to be very useful in their understanding of capital preservation risk, there remains some confusion between the two.  Hopefully this blog post will clear up any lingering ambiguity.

While the two are closely related, the pain index should be thought of purely as a risk metric.  The type of risk being measured is drawdown or capital preservation risk.  The pain index measures the depth, duration, and frequency of losses.  Like most of the other risk measures, you want the values to be low, the lower the better.  A value of 0.0% would be the lowest possible value and would indicate the investment never lost money.  However, in order to get a true understanding whether or not a pain index is good or bad it should be compared against the pain indexes for the benchmark and the universe of like investments.

The pain ratio, on the other hand, is a return-verus-risk measure. The pain ratio measures the trade-off between an investment’s excess return over the risk free rate and its capital preservation risk.  The higher the ratio the better, which indicates 1) a lot of return in excess of the risk-free rate, 2) fewer losses, or 3) a combination of both.  The risk metric used within the pain ratio is the pain index. 

A helpful analogy is to think of the widely used standard deviation and Sharpe ratio.  Standard deviation is used to measure risk as well, but a different type of risk.  Standard deviation measures risk in terms of volatility.  Most investors would prefer lower standard deviations, just as most would also prefer low pain indexes.  Similarly, the lowest values for each would be 0.0%, as a negative number for either is impossible. And in both cases one should use a benchmark and a universe as a reference point to know whether the risk measure is good or bad.

Extending the analogy, the pain ratio is quite like the Sharpe ratio.  Both seek to quantify the trade-off between return and risk.  As a matter of fact, they both measure return in the exact same way- the excess return versus the risk-free rate.  The only difference between the two is how they measure risk.  The pain ratio uses the pain index as its definition of risk; the Sharpe ratio uses standard deviation as its measure of risk.  In both cases the investor hopes the value of the ratio is high; the higher the better.  The two ratios are kissing cousins.

For a more in-depth discussion, we have white papers available, as well as StatFACT sheets.

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