## When Is Sharpe Ratio Negative?

It is very simple when you look at the Sharpe ratio formula:

\[{Sharpe\:Ratio}={{\bar{r}_p\:-\:r_f}\over\sigma_p}\]

(Here you can find detailed explanation of Sharpe ratio formula.)

Sharpe ratio equals portfolio excess return divided by standard deviation of portfolio returns.

Standard deviation, which in this case can be interpreted as volatility, of course can’t be negative.

(Here you can see why volatility can’t be negative.)

Therefore, Sharpe ratio is negative when excess return is negative.

Excess return is the return on the portfolio less risk-free rate.

Therefore, excess return is negative when the (realized or expected) return on the portfolio (or fund, trading strategy, or investment) is lower than the risk-free interest rate (typically a money market rate or treasury yield).

**Sharpe ratio is negative when the investment return is lower than the risk-free rate.**