Risk-Adjusted Return: Definition & Formula

Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

This lesson will introduce you to the concept of risk adjusted return. The most widely used formula for measuring risk adjusted return is the Sharpe Ratio which will be introduced and illustrated with examples.

Mark likes to invest in mutual funds. He is always evaluating the thousands of funds that are out there trying to figure out the best ones to put his money into. Like all investors, Mark thinks a lot about the returns he can get from fund investments. Returns are the money he can make. Investing in funds with a good return can cover college expenses for Mark's kids, or provide for his own retirement. But he also has to consider the risk that his funds might lose money.

He knows funds that invest in big U.S. companies will be a lot less risky than funds that invest in emerging market countries in various parts of the world. Those funds may have large swings in value because their economies are fragile and not very well diversified.

Risk and Return

So why would any investor in his or her right mind put hard earned money into unstable emerging market funds when they could invest it in a big stable market like the U.S. instead? The answer is that the emerging market fund might offer a higher return! Mark will accept a lower return on the big U.S. company fund because it is more of a sure thing. He knows that the big U.S. companies the fund manager selects are well managed and have established brand names that are a good bet to have continued success. His risk of losing serious money in that fund are much lower than the emerging market fund. The emerging market fund will need to produce better returns to get investors interested in taking on the greater risk.

A Measure for Risk Adjusted Return

So Mark wonders, just how much extra return he should get from that emerging market fund to justify taking on the greater risk that he might lose his shirt! He wants to determine the risk adjusted return for these funds. The risk adjusted return is the return on an investment adjusted for the risk taken in generating that return. And for that we have the most widely used measure of risk adjusted returns, the Sharpe Ratio. The Sharpe Ratio divides the excess returns from risky investments by the amount of risk taken to achieve them.

The Sharpe Ratio explained

The Sharpe Ratio was developed by Nobel prizewinning economist William Sharpe.

William F Sharpe
Creator of the Sharpe Ratio

It is widely used because of its simplicity. The formula is:

Sharpe Ratio for security x = (returns on security x - returns on a risk free security) / standard deviation of returns for x.

The returns are described in the numerator of the formula and the risk in the denominator. A critical assumption is that the returns for the security in question be normally distributed. The returns on a risk free security are typically the returns on U.S. Treasury securities. The United States Government has not defaulted on its debt repayments in its entire 240 year history! So the financial community uses U.S.Treasury Bills as a risk free security.

The risk in a security is measured by the standard deviation of its returns. Returns that are more volatile will have a greater standard deviation than returns that are stable and don't fluctuate by large amounts. The standard deviation of returns is easily calculated by anyone with an Excel spreadsheet or financial calculator. The higher the Sharpe Ratio the better the risk adjusted returns are. This makes the Sharpe Ratio a great tool for doing comparisons!

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