What is the Risk-Adjusted Measure of Performance?

Does the choice of risk-adjusted performance measure matter? This is the question the current discussion in academic literature revolves around. Risk-adjusted performance measures are an important tool for investment decisions. Whenever an investor evaluates the performance of an investment he will not only be interested in the achieved absolute return but also in the risk-adjusted return – i.e. in the risk which had to be taken to realize the profit.

The first ratio to measure risk-adjusted return was the Sharpe Ratio introduced by William F. Sharpe in 1966. It has been one of the most referenced risk/return measures used in finance, and much of this popularity can be attributed to its simplicity. The ratio’s credibility was boosted further when Professor Sharpe won a Nobel Memorial Prize in Economic Sciences in 1990 for his work on the capital asset pricing model (CAPM).

The Ratio Defined

Most people with a financial background can quickly comprehend how the Sharpe ratio is calculated and what it represents. The ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset. Remember, you always need to be properly compensated for the additional risk you take for not holding a risk-free asset.

Return

The returns measured can be of any frequency (i.e. daily, weekly, monthly, or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio – not all asset returns are normally distributed.

Abnormalities like kurtosis, fatter tails, and higher peaks, or skewness on the distribution can be problematic for the ratio, as standard deviation doesn’t have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed.

Risk-Free Rate of Return

The risk-free rate of return is used to see if you are being properly compensated for the additional risk you are taking on with the risky asset. Traditionally, the risk-free rate of return is the shortest dated government T-bill. While this type of security will have the least volatility, some would argue that the risk-free security used should match the duration of the investment it is being compared against.

For example, equities are the longest duration asset available, so shouldn’t they be compared with the longest duration risk-free asset available – government-issued inflation-protected securities (IPS).

Standard Deviation

Now that we have calculated the excess return from subtracting the return of the risky asset from the risk-free rate of return, we need to divide this by the standard deviation of the risky asset being measured. As mentioned above, the higher the number, the better the investment looks from a risk/return perspective.

Using the Sharpe Ratio

The Sharpe ratio is a risk-adjusted measure of return that is often used to evaluate the performance of a portfolio. The ratio helps to make the performance of one portfolio comparable to that of another portfolio by making an adjustment for risk.

For example, if manager A generates a return of 15% while manager B generates a return of 12%, it would appear that manager A is a better performer. However, if manager A, who produced the 15% return, took much larger risks than manager B, it may actually be the case that manager B has a better risk-adjusted return.

The Sharpe ratio is quite simple, which lends to its popularity. It’s broken down into just three components: asset return, risk-free return, and standard deviation of return. After calculating the excess return, it’s divided by the standard deviation of the risky asset to get its Sharpe ratio. The idea of the ratio is to see how much additional return you are receiving for the additional volatility of holding the risky asset over a risk-free asset – the higher the
better.

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