The Sharpe Ratio is a measure of return-risk for a portfolio or individual investment. Like many concepts that lend themselves to mathematics, it is easier to understand what the Sharpe Ratio means if written in the form of an equation.
S = (R - T)/Sigma (My editor does not have the correct symbol for Sigma.)
Developed by Stanford Professor, William F. Sharpe, the return of the portfolio or investment is represented by R. T is a T-bill (90-Day for example) or risk-free cash investment and Sigma is the uncertainty or volatility of the investment.
To help understand the Sharpe Ratio, Faber and Richardson, in their The Ivy Portfolio book write,
"A good rule of thumb for Sharpe Ratios is that asset classes, over the long term, have Sharpes around 0.2 to 0.3. A "dummy" 60/40 allocation of stocks/bonds is around 0.4. The Ivy Portfolio allocation is around 0.6. However, over shorter periods, the numbers can bounce all over the place. From 1900-2008, the S&P 500 has had Sharpe Ratios per decade ranging from negative 0.8 (-0.8) (the 1970s) to 1.4 (the 1950s)." Keep in mind the current construction of the S&P 500 began around 1957.
The reason for not using the Sharpe Ratio is that it penalizes the money manager for upside volatility. That is the nature of the Sigma calculation. Both the Sortino and Retirement Ratios circumvent this problem as both employ a semi-variance calculation in the denominator. This calculation omits upside volatility.
The reason for using a "downside risk" calculation in the denominator is that the purpose of investing is to make money and this requires volatility to the upside. It makes no sense to downgrade the money manager for gaining an upside advantage.
Both the Sortino and Retirement Ratios are slight modifications of the Sharpe Ratio, and for this reason we need to give Dr. Sharpe credit for his outstanding research.