How to Calculate a Risk Adjusted Return

How to Calculate a Risk Adjusted Return
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When investors are evaluating an investment, they typically analyze its return during a specific time period, like one year or five years. In order to gain a true understanding of the risk involved, a calculation can be done that results in a risk adjusted return, allowing an investor to evaluate both the return and risk when comparing investments.

What Is Risk Adjusted Return?

A risk adjusted return applies a measure of risk to an investment's return, resulting in a rating or number that expresses how much an investment returned relative to its risk over a period of time. Many types of investment vehicles can have a risk adjusted return, including securities, funds and portfolios. When two investments with similar returns are compared, the one with the least risk will have the better risk adjusted return, making it a better investment.

Types of Risk Adjusted Returns

There are several common risk adjusted measures used to calculate a risk adjusted return, including standard deviation, alpha, beta and the Sharpe ratio. When calculating risk adjusted returns for comparison of different investments, it's important to use the same risk measurement and the same period of time. Otherwise, it's like comparing apples and oranges.

Sharpe Ratio and Standard Deviation

The Sharpe ratio is a popular risk-adjusted measure developed by William Sharpe, a Stanford professor of finance and Nobel Laureate. The ratio is also referred to as the Sharpe measure or Sharpe index. It measures the excess return per unit of deviation in an investment to determine the reward per unit of risk. A higher Sharpe ratio indicates better risk-adjusted performance during the designated period of time.

The Sharpe ratio uses standard deviation, which is a mathematical measure of the dispersion of values within a range. To calculate standard deviation, first find the mean by adding all values and dividing by the number of values in the dataset. Then calculate the variance for each value by subtracting it from the mean and squaring the result. Add all the variances and then divide by the number of values minus 1.

The square root of this result is the standard deviation. A higher standard deviation indicates more variation among values in the dataset.

Sharpe Ratio Calculation Example

The Sharpe ratio for an investment is calculated by taking the average return for the time period and subtracting the risk-free rate, then dividing by the standard deviation for the period. The number that results is the Sharpe ratio. It can be used for comparison with the ratio for another investment to determine relative risk.

If Fund A has a return of 10 percent and a standard deviation of 8 percent, and the risk-free rate is 4 percent, then the Sharpe ratio is (10 – 4) / 8 or 0.75. If Fund B's return is 20 percent and its standard deviation is 16 percent, its Sharpe ratio is (20 – 4) / 16 or 1.0. Fund B has a higher Sharpe ratio and was the better investment for the time period.

Using Risk Adjusted Returns

Investors can measure the performance of their portfolio by comparing their risk adjusted return to the return for the benchmark for their fund or investment. Having investments with lower risk in a strong market can limit returns. On the other hand, having higher risk investments when the market is volatile can result in higher losses.

Risk Adjusted Return on Capital

Risk adjusted return on capital (RAROC) is another type of economic measure that's used to evaluate the risk level in projects and investments that are being considered for acquisition. It's based on an assumption the projects and investments with the greatest risk offer higher levels of return. RAROC is calculated by subtracting expenses and expected losses from revenue, then adding income from capital. The result is divided by total capital.

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