The Pain Index

The Pain Index is a measure that computes the drawdown (the decline rate from the peak) at every point across the whole investment period and then averages those values.

The maximum drawdown (MDD) looks only at 'the single deepest time.' The Pain Index, by contrast, looks at 'on average, how deep underwater you were over the entire period.'

For example, even if two assets have the same MDD of -30%, if one briefly touched -30% and quickly recovered while the other stayed at -20 to -30% for years, the latter's Pain Index is far larger. It better reflects the cumulative pain an actual investor feels.

The Pain Index is a very close relative of the Ulcer Index you've already learned about.

- Pain Index: the 'average' of the drawdown at each point - Ulcer Index: the drawdown at each point is 'squared,' then averaged and square-rooted (root mean square, RMS)

Both summarize 'how deep and how long the drawdown normally lasted' as a single number. The difference is that because the Ulcer Index uses squaring, it gives a heavier penalty to 'deep drawdowns.' The Pain Index, being a simple average, is a bit more intuitive.

Using the Pain Index as a risk measure, you can create a 'return relative to risk' measure. This is called the Pain Ratio.

The Pain Ratio is roughly of the form '(return - risk-free return) ÷ Pain Index.' Where the Sharpe ratio uses standard deviation in the denominator, the Pain Index is put in.

For the same return, the smaller the Pain Index (= the less it hurt in normal times), the higher the Pain Ratio. It's the idea of evaluating not only 'return matters, but how long you hurt while earning that return.' Measures like these help prevent the mistake of forgetting drawdowns and loss duration while looking only at returns.