### What is the Stutzer Index

The Stutzer index is a measure of the variability of returns on a portfolio that penalizes underperformance against a benchmark and rewards portfolios with fewer extreme variations in returns. By rating more highly portfolios that are more likely to have positive returns and fewer large drawdowns, the index aims to capture better-than-average performance.

### BREAKING DOWN Stutzer Index

The Stutzer index is useful for fund managers, like pension funds and hedge funds, that favor portfolios with a low probability of negative returns against a benchmark because it penalizes negative skew and high kurtosis (return distributions that have more positive or negative extreme returns than normally distributed returns with the same mean and variance). Such risk-averse investors are willing to accept lower positive returns in order to avoid negative ones.

The Stutzer index, unlike the Sharpe ratio — the average return earned in excess of the risk-free rate per unit of volatility or total risk — captures this asymmetric preference. Unlike the Sharpe ratio, the Stutzer index does not assume returns are normally distributed — and that the standard deviation of the return distribution fully describes risk. Instead, it takes the shape of the distribution of returns into account. When returns are normally distributed, the Stutzer index and Sharpe ratio are identical.

However, the Stutzer index is more difficult to calculate than the Sharpe ratio, and the results are only robust over longer time periods. Also, the index assumes a constant for risk aversion, which is not necessarily valid, as investors’ risk aversion falls as their wealth increases.

### Calculating the Stutzer Index

The Stutzer index measures the speed at which the probability of negative returns decays to zero. The higher the decay rate, the better the portfolio. The index is defined by the following equations:

• rt are the excess returns
• IP is the information statistic
• θ is a numerically calculated parameter than maximizes IP
• r-bar is the average excess return