## What Is a Risk-Adjusted Return?

Risk-adjusted return defines an investment's return by measuring how much risk is involved in producing that return, which is generally expressed as a number or rating. Risk-adjusted returns are applied to individual securities, investment funds, and portfolios.

Some common risk measures include alpha, beta, R-squared, standard deviation and the Sharpe ratio. When comparing two or more potential investments, an investor should always compare the same risk measures to each different investment to get a relative performance perspective.

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In its simplest definition, risk-adjusted return is of how much return your investment has made relative to the amount of risk the investment has taken over a given period of time. If two or more investments have the same return over a given time period, the one that has the lowest risk will have the better risk-adjusted return. However, considering that different risk measurements give investors very different analytical results, it is important to be clear on what type of risk-adjusted return is being considered. Below are examples of conflicting risk-adjusted return calculations and their implications.

## Sharpe Ratio Example

The Sharpe ratio is a measure of an investment's excess return, above the risk-free rate, per unit of standard deviation. It is calculated by taking the return of the investment, subtracting the risk-free rate, and dividing this result by the investment's standard deviation. All else equal, a higher Sharpe ratio is better. The standard deviation shows the volatility of an investment's returns relative to its average return. Greater standard deviations reflect wider returns, and narrower standard deviations imply more concentrated returns. The risk-free rate is the yield on a no-risk investment, such as a Treasury bond.

Mutual Fund A returns 12% over the past year and had a standard deviation of 10%. Mutual Fund B returns 10% and had a standard deviation of 7%. The risk-free rate over the time period was 3%. The Sharpe ratios would be calculated as follows:

Mutual Fund A: (12% - 3%) / 10% = 0.9

Mutual Fund B: (10% - 3%) / 7% = 1

Even though Mutual Fund A had a higher return, Mutual Fund B had a higher risk-adjusted return, meaning that it gained more per unit of total risk than Mutual Fund A.

## Treynor Ratio Example

The Treynor ratio is calculated the same way as the Sharpe ratio, but it uses the investment's beta in the denominator. A higher Treynor ratio is better. Using the previous fund example, and assuming that each of the funds has a beta of 0.75, the calculations are as follows:

Mutual Fund A: (12% - 3%) / 0.75 = 0.12

Mutual Fund B: (10% - 3%) / 0.75 = 0.09

Here, Mutual Fund A has a higher Treynor ratio, meaning that the fund is earning more return per unit of systematic risk than Fund B. Given this result and the result of the Sharpe ratio calculation, it can be concluded that Fund B is more efficiently earning returns per unit of unsystematic risk.