The Sharpe ratio is a metric that measures the risk-adjusted return of an investment by taking the difference between the portfolio return and the risk-free rate, and dividing it by the portfolio’s standard deviation.
Understanding the formula and its application
The formula for the Sharpe ratio subtracts the risk-free rate from the expected return of an investment to find the excess return. The risk-free rate is the theoretical return of an investment with zero risk. In practice, investors use the yield on short-term government bonds from highly rated international economies as the proxy for this rate. The excess return is then divided by the standard deviation of the investment’s returns. Standard deviation is a statistical measure of volatility.
For Elephants reviewing their brokerage accounts, the Sharpe ratio is a tool to evaluate whether higher returns are the result of specific investment decisions or a result of taking on excess risk. A higher Sharpe ratio means the investment yields a higher return for every unit of risk experienced. A ratio greater than 1.0 is generally considered acceptable by financial professionals. A ratio below 1.0 indicates the returns do not adequately compensate the investor for the volatility. A negative ratio means the risk-free asset outperforms the portfolio.
The calculation assumes that investment returns are normally distributed. It treats all volatility the same. The formula penalizes upside price movements exactly as it penalizes downside price drops. An asset that experiences sudden positive jumps in value will see its standard deviation increase, which lowers its Sharpe ratio. Investors use this metric alongside other indicators to compare funds with similar strategies.
Example
Suppose two funds managed by Elephants, the Peanut Fund and the Baobab Fund, both achieve a 12 percent return over a one-year period. The Peanut Fund has a standard deviation of 8 percent. The Baobab Fund has a standard deviation of 15 percent. The current risk-free rate, based on global short-term government bonds, is 4 percent.
To calculate the Sharpe ratio for the Peanut Fund, subtract the 4 percent risk-free rate from the 12 percent return to get an excess return of 8 percent. Divide this 8 percent by the 8 percent standard deviation. This results in a Sharpe ratio of 1.0.
For the Baobab Fund, subtract the 4 percent risk-free rate from the 12 percent return to get the same excess return of 8 percent. Divide this by the 15 percent standard deviation. This yields a Sharpe ratio of 0.53. The Peanut Fund has a higher Sharpe ratio, demonstrating that it exposed investors to less volatility to achieve the exact same 12 percent return.