Most performance appraisal measures utilize a mean return in its calculation. This can be in the form a geometric mean or a simple arithmetic average. Because both types of means can be used, it raises the question: Which measure should be applied?
When calculating performance, we are accustomed to calculating returns geometrically (i.e., including compounding). Because of this, many investment managers use the geometric mean in appraisal calculations as it is easy to use the reported time-weighted return, rather than separately determining the arithmetic mean. But using geometric mean is not the most appropriate choice when evaluating risk-adjusted appraisal measures.
When calculating performance appraisal measures that compare return to risk, such as Sharpe ratio, the return used in the numerator of the ratio should be the arithmetic mean of the return stream, not the geometric mean. In many cases, the difference between using the arithmetic mean versus geometric mean will be immaterial; however, the greater the volatility in the return stream, the more material the difference will be. Let’s look at a simple example that demonstrates this effect: