Quantitative Analysis · Data Science · Machine Learning

# Evaluation Metrics: Gain-to-Pain Ratio

The Gain to Pain ratio (also known as the RPR – Reward to Pain ratio) is a risk-adjusted performance measure that evaluates the return of a portfolio relative to the drawdown or “pain” experienced by the portfolio. It is used to evaluate the performance of an investment by adjusting for the risk taken to generate the return. A higher Gain to Pain ratio indicates that the portfolio has generated more return relative to the drawdown experienced.

The Gain to Pain ratio is calculated by dividing the total return of the portfolio by the maximum drawdown experienced over a given period of time. The maximum drawdown is the largest percentage decline from a peak to a trough during the time period.

The formula for the Gain to Pain ratio is:

### Gain to Pain ratio = Total return / Maximum Drawdown

For example, let’s say a portfolio has a total return of 20% and a maximum drawdown of -10%. The Gain to Pain ratio would be:

### (20 / -10) = -2

A Gain to Pain ratio of -2 indicates that the portfolio has generated -2 units of return for each unit of drawdown. A Gain to Pain ratio greater than 1 indicates that the portfolio has generated more return than the drawdown experienced, while a Gain to Pain ratio less than 1 indicates that the portfolio has generated less return than the drawdown experienced.

The Gain to Pain ratio is useful for evaluating the risk-adjusted performance of a portfolio, particularly for those that are sensitive to drawdown. It can be used to compare the risk-adjusted performance of different portfolios and to identify portfolios that have generated more return relative to the drawdown experienced.

It’s important to consider that the Gain to Pain ratio does not account for the volatility of the returns and it is only based on the drawdown. Additionally, it is also important to consider the Gain to Pain ratio in the context of the investor’s risk tolerance and investment goals.