# Sharpe Ratio vs. Treynor Ratio: What's the Difference?

## Sharpe Ratio vs. Treynor Ratio: An Overview

The Sharpe ratio and the Treynor ratio are two ratios used to measure the risk-adjusted rate of return. Both are named for their creators, Nobel Prize winner William Sharpe and American economist Jack Treynor, respectively. While they may help investors understand investments and risk, they offer different approaches to evaluating investment performance. The Sharpe ratio helps investors understand an investment's return compared to its risk while the Treynor ratio explores the excess return generated for each unit of risk in a portfolio.

This short article explores how each ratio works and how they differ.

### Key Takeaways

• Both the Sharpe and Treynor Ratios are used to understand an investment's risk-adjusted return.
• The Sharpe Ratio divides the excess return by the investment's standard deviation.
• The Treynor Ratio instead divides excess returns by the investment's Beta.

## Sharpe Ratio

First developed in 1966 and revised in 1994, the Sharpe ratio aims to reveal how well an asset performs compared to a risk-free investment. The common benchmark used to represent that risk-free investment is U.S. Treasury bills or bonds, especially the 90-day Treasury bill. The Sharpe ratio calculates either the expected or actual return on investment for an investment portfolio (or even an individual equity investment), subtracts the risk-free investment's return, then divides that number by the standard deviation for the investment portfolio. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.

\begin{aligned} &\textnormal {SR} = \frac {(r_{x} - R _{F})}{SD}\\ &\textbf{where:}\\ &\begin{aligned} r_{x} = &\text{ Expected or actual return on investment}\\ &\text{ of investment} \end{aligned}\\ &R_{F} = \text{Risk-free investment's return}\\ &SD = \text{Standard deviation of }r_{x}\\ \end{aligned}

The expected or actual rate of return can be measured in any time frame, as long as the measurement is consistent. Once the risk-free rate is subtracted from the expected or actual rate of return it would then be divided by the standard deviation. The lower the deviation, the better the return.

The primary purpose of the Sharpe ratio is to determine whether you are making a significantly greater return on your investment in exchange for accepting the additional risk inherent in equity investing as compared to investing in risk-free instruments.

## Treynor Ratio

Developed around the same time as the Sharpe ratio, the Treynor ratio also seeks to evaluate the risk-adjusted return of an investment portfolio, but it measures the portfolio's performance against a different benchmark.

Rather than measuring a portfolio's return only against the rate of return for a risk-free investment, the Treynor ratio looks to examine how well a portfolio outperforms the equity market as a whole. It does this by substituting beta for standard deviation in the Sharpe ratio equation, with beta defined as the rate of return due to overall market performance.

For example, if a standard stock market index shows a 10% rate of return—that constitutes beta. An investment portfolio showing a 13% rate of return is then, by the Treynor ratio, only given credit for the extra 3% return that it generated over and above the market's overall performance. The Treynor ratio can be viewed as determining whether your investment portfolio is significantly outperforming the market's average gains.

## Limitations of Each Ratio

There are certain drawbacks to each of these ratios. Where the Sharpe ratio fails is that it is accentuated by investments that don't have a normal distribution of returns like hedge funds. Many of them use dynamic trading strategies and options that can skew their returns.

The main disadvantage of the Treynor ratio is that it is backward-looking and that it relies on using a specific benchmark to measure beta. Most investments, though, don't necessarily perform the same way in the future that they did in the past.

## The Bottom Line

The difference between the two metrics is that the Treynor ratio utilizes beta, or market risk, to measure volatility instead of using total risk (standard deviation) like the Sharpe ratio.

Article Sources
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1. Stanford University. "The Sharpe Ratio."

2. Andrew W. Lo Massachusetts Institute of Technology School Of Management. "The Statistics of Sharpe Ratios," Page 45.

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