Pain Ratio

A proprietary return-versus-risk trade-off metric, the pain ratio compares the added value over the risk-free rate against the depth, duration, and frequency of losses.
PDF version: StatFACTs PainRatio

How Is it Useful?

While one certainly wants to minimize losses, it is also important to make money. The pain ratio quantifies this trade-off into a single number. The pain ratio compares the gains over the risk-free investment against the losses that were suffered to obtain that return.

What Is a Good Number?

The pain ratio is similar to the Sharpe ratio, but with a different definition of risk. The Sharpe ratio measures volatility risk as standard deviation. The pain ratio uses the pain index as the key element in measuring capital preservation risk.

With both ratios, the higher the number the better. However, there is no hard-and-fast breakpoint above which one can say the ratios are good or bad. One must compare the pain ratio of a manager to the pain ratios of peers or an index to ascertain whether it is relatively better or worse than the alternatives.

What Are the Limitations?

Like the Sharpe ratio, the pain ratio can exhibit negative values. If the time period analyzed represents a bear market when the investment underperformed the risk-free rate, the pain ratio will be negative. Therefore one shouldn’t set hard-target screens that eliminate managers with a negative pain ratio.

What Do the Graphs Show Me?

The upper graph shows the return metric, the added value above and beyond the risk-free rate in red. One hopes to outperform the risk-free rate, and by a large margin. However, there will be times when risky investments fall short of the risk-free rate.

The lower graph shows the risk metric of the pain ratio. The risk quantified by the pain ratio is capital preservation risk. The metric used in the denominator is the pain index. The pain index represents the depth, duration, and frequency of losses and is measured in the area seen below. One would hope that this area would be as small as possible. These two graphs depict the pain ratio’s numerator and denominator, respectively.



What Are Typical Values?

There is no single value that could be described as “typical” when understanding the pain ratio. The values for the pain ratio will be heavily influenced by the asset class and the time frame under consideration. With the pain ratio, both the numerator and denominator will be impacted by the general market environment. In the 1980s and 1990s, excess returns were high and losses were low, leading to high (i.e. good) pain ratios. In the 2000s, excess returns were lower and losses more frequent, so pain ratios were much lower.



Math Corner: 

The return element of the pain ratio is the annualized return of the investment in excess of the risk-free investment. Typically a short-term cash investment is used as the risk-free investment. The denominator of the pain ratio is the pain index, an integral measuring the depth, duration, and frequency of losses.

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