Andrew Lo’s book, “In Pursuit of the Perfect Portfolio,” delves into the history of academic thought in finance, with a particular focus on the work of Bill Sharpe. Sharpe, known for the Sharpe ratio which measures risk-adjusted return, is portrayed as humble and slightly surprised by his widespread recognition in the finance world. Lo also mentions mathematician Benoit Mandelbrot, who challenged some of the ideas underlying Sharpe’s work.
The Sharpe ratio, calculated by dividing the average return of an investment by its volatility, is commonly used as a measure of risk. However, critics like Mandelbrot argue that the assumption of a normal distribution of returns is flawed, as returns in the real world do not follow a normal distribution. This discrepancy is illustrated by comparing two portfolios with the same Sharpe ratio, one following a normal distribution and the other a real-world distribution with heavier tails and negative skew.
The issue of drawdown experience further demonstrates the limitations of using the Sharpe ratio alone to measure risk. Even two funds with the same Sharpe ratio can have vastly different drawdown profiles, highlighting the importance of considering factors beyond volatility. Upside volatility, which is included in the standard deviation used in the Sharpe ratio, may not be as concerning to investors as drawdowns.
Alternative measures like the Sortino ratio, which considers only downside volatility, address some of the limitations of the Sharpe ratio but still rely on the assumption of a normal distribution. Other measures such as Expected Tail Loss and Stress Loss attempt to capture skewness and the shape of tails in return distributions, but they too have limitations in predicting future losses accurately.
Despite the shortcomings of the Sharpe ratio and the availability of alternative risk measures, Sharpe ratios remain widely used as a universal language for comparing investments. While it is important to consider other metrics and not rely solely on the Sharpe ratio, it is also essential to recognize the value of having a common tool for evaluating investments in a complex financial landscape. The search for the perfect risk measure should not overshadow the importance of practicality and efficiency in decision-making.
