Measuring Portfolio Performance: Sharpe, Alpha, or the Geometric Mean?

Moshe Levy
Vol. 15, No. 3, 2017

The most popular portfolio performance measures are the Sharpe ratio and alpha. While the Sharpe ratio is optimal under the capital asset pricing model (CAPM) assumptions of normal return distributions and unlimited borrowing at the risk-free rate, we find that it is not well aligned with investors’ preferences in more realistic settings. Alpha is a poor measure under both the theoretical and the realistic settings. For investors with typical borrowing constraints, the geometric mean provides an alternative measure that is much better than both the Sharpe ratio and alpha. It may very well be the most important single number to consider in portfolio selection.