Sharpe ratio: the right mathematical answer to the wrong question

The Sharpe ratio is such an intricate part of life in the industry that a mundane greeting such as "how are you?" could easily be interchanged with "how is your Sharpe?" The question the ratio is trying to answer is conceptually simple: for every unit of volatility, how many units of excess returns over a risk-free asset do you receive in return? Now, all the problems derive not from the formula, but from the meaning people have ascribed to volatility. Is volatility bad, risky, or uncertain?

Here is the mathematical formula of the Sharpe ratio, where Rp is equal to asset returns, and Rf is equal to risk-free returns:

This ratio looks at the annualized average excess returns over a risk-free asset divided by the standard deviation of those returns. Standard deviation measures the variance from the median returns. The more volatile the returns, the higher the standard deviation, and the...