What Is the Difference Between a Sharpe Ratio and a Treynor Ratio? 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. How the Sharpe Ratio Works 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.1
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.
Expected or actual return on investmentR
=Risk-free investment’s returnSD
=Standard deviation of r
The expected or actual rate of return can be measured in any frequency, as long as the measurement is consistent. Once the expected or actual rate of return is subtracted from the risk-free investment return, it can then be divided by the standard deviation. The higher 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. How the Treynor Ratio Works 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.2 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 LineThe 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.
Excess returns are returns achieved above and beyond the return of a proxy. Excess returns will depend on a designated investment return comparison for analysis. more
Sharpe Ratio Definition
The Sharpe ratio is used to help investors understand the return of an investment compared to its risk.more
What Is the Treynor-Black Model?
The Treynor-Black model is a portfolio optimization model that consists of an active portfolio and a passively managed market portfolio. more
Inside the Treynor Ratio
The Treynor ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio. more
Risk-Adjusted Return Definition
A risk-adjusted return accounts for the riskiness of an investment compared to the risk-free rate of return.more
Capital Market Line (CML) Definition
The capital market line (CML) represents portfolios that optimally combine risk and return. more
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