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:

Formula for calculating the Stutzer index.

  • 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
  1. Modified Sharpe Ratio

    The modified Sharpe ratio is a version of the original Sharpe ...
  2. Mean Return

    1. In securities analysis, it is the expected value, or mean, ...
  3. Risk-Adjusted Return

    A risk-adjusted return takes into account the amount of risk ...
  4. Probability Distribution

    A probability distribution is a statistical function that describes ...
  5. Return

    A return, in finance, is the profit or loss derived from investing ...
  6. Abnormal Return

    A term used to describe the returns generated by a given security ...
Related Articles
  1. Investing

    Understanding Quantitative Analysis Of Hedge Funds

    Learn how hedge fund performance quantitatively requires metrics such as absolute and relative returns, risk measurement, and benchmark performance ratios.
  2. Investing

    5 Ways to Rate Your Portfolio Manager

    These five performance ratios will help you measure how good your money manager is at increasing the value of your portfolio.
  3. Investing

    How to Use a Benchmark to Evaluate a Portfolio

    What is an investment benchmark and how is it used to evaluate the risk and return in a portfolio.
  4. Financial Advisor

    Measure Your Portfolio's Performance

    Measuring the success of your investment solely on the portfolio return may leave you blindsided to risk. Learn how to evaluate your investment return.
  5. Investing

    Mitigating Downside With the Sortino Ratio

    Differentiate between good and bad volatility with the Sortino ratio.
  6. Investing

    PRHSX: Risk Statistics of Health Sciences Mutual Fund

    Examine the risk metric of the T. Rowe Price Health Sciences Fund. Analyze beta, capture ratios and standard deviation to assess volatility and systematic risk.
  7. Investing

    3 Investments With the Best Long Term Track Records

    Take a look at the three asset classes with the best risk-adjusted performance since 1990, and find out why the Sharpe ratio can help you make better decisions.
  8. Investing

    Explaining Expected Return

    The expected return is a tool used to determine whether or not an investment has a positive or negative average net outcome.
  9. Financial Advisor

    Does Your Investment Manager Measure Up?

    These key stats will reveal whether your advisor is a league leader or a benchwarmer.
  10. Investing

    Most Common Probability Distributions

    In this article, we'll go over a few of the most popular probability distributions and show you how to calculate them.
  1. What is the difference between a sharpe ratio and an information ratio?

    Understand the meaning of the Sharpe ratio and the information ratio, and understand how they differ as tools for evaluating ... Read Answer >>
  2. Use market risk premium for expected market return

    Find out how the expected market return rate is determined when calculating market risk premium – and how to estimate investment ... Read Answer >>
  3. What is the difference between the Sharpe ratio and alpha?

    Use alpha and the Sharpe ratio to evaluate mutual funds by comparing their risk-adjusted returns. Learn what modern portfolio ... Read Answer >>
  4. What's the difference between absolute and relative return?

    Knowing whether a fund manager or broker is doing a good job can be a challenge for some investors. It's difficult to define ... Read Answer >>
Trading Center