The Sharpe ratio compares the return achieved by the fund’s manager (Rp) to the return of risk-free instruments (Rf), such as for example government bonds, and with the level of risk that characterizes the composition of the managed portfolio (Sp).

The numerator of the above formula refers to the so-called excess return, i.e. the difference between the return on the portfolio and the return on risk-free assets. The value of said difference must be positive, because a negative value would mean that the investor could have achieved a better return than the one obtained by fund’s manager had he invested in risk-free financial instruments.

The denominator indicates a parameter representative of the degree of risk of the fund’s assets, in other words, the volatility (standard deviation) of the portfolio return. Overall, the Sharpe index measures the increased return obtained by the fund’s manager for each additional unit of risk taken.

Let’s assume that an investor wants to compare two different mutual funds in his portfolio with different risk levels. As already mentioned, the more risky of the two will tend to have higher returns, but which one has a higher return relative to the risk associated with the investment? The Sharpe ratio may show which one is performing better.

**Investment X:**

Portfolio return: 40%

Risk free rate: 20%

Standard deviation: 5

**Investment Y:**

Portfolio return: 60%

Risk free rate: 20%

Standard deviation: 80

**Sharpe ratio results:**

Investment X: 4

Investment Y: 0.5

Investment Y out performed investment X, but this doesn’t necessarily mean that investment Y performed well relative to its risk level. Actually, accordingly to the Sharpe ratio, the investment X performed better relative to the risk involved in the investment.