Formula for Sharpe Ratio

The Sharpe Ratio, named after its founder and American economist William Sharpe, is a metric used by investors to find the relationship between the risks and returns of their investment. It is also known as the Sharpe Index or the Modified Sharpe Ratio. The relationship between the risks and returns of investment has always been a crucial deciding factor for investors. The Sharpe Ratio helps investors quantify this relationship.

What is the formula for Sharpe Ratio?

The formula to calculate the Sharpe Ratio of a portfolio is as below.

Sharpe Ratio = (Expected return from an investment - Risk-free rate of return) / Standard deviation of portfolio return

The expected return from an investment is often a forecasted number, which can represent any return from the portfolio. Investors can use different tools to calculate it. Similarly, the risk-free rate of return is the return from a risk-free investment. The difference between these two represents the excess returns investors get from the portfolio. Usually, investors use the return from government treasury bills for the calculation.

Lastly, the standard deviation of portfolio return denotes the volatility of an investment. Usually, a higher deviation represents a more volatile stock or investment.

The higher the Sharpe Ratio of an investment is, the better it is in terms of returns against risk. Conversely, a lower ratio represents a worse risk-adjusted performance. Investors prefer stocks with a higher Sharpe Ratio because it signifies better returns for the risks they are taking. Mostly, investors don't have to calculate the Sharpe Ratio of investments as it is widely available for almost all stocks, especially publicly-listed ones.

Example

An investor is considering a stock that has an expected rate of return of 12%. At the same time, the risk-free rate of return in the market is 4%. Similarly, the stock's standard deviation is 10%. To calculate the relationship between the risks and returns on the investment, the investor must use the Sharpe Ratio. Below is the Sharpe Ratio for the stock.

Sharpe Ratio = (Expected return from an investment - Risk-free rate of return) / Standard deviation of portfolio return

Sharpe Ratio = (12% - 4%) / 10%

Sharpe Ratio = 0.8

What is a good Sharpe Ratio?

There are certain thresholds that investors can use when evaluating investments based on Sharpe Ratio. Usually, a Sharpe Ratio of less than one is considered bad. 1-2 represents a decent or adequate investment. An investment with a Sharpe Ratio between 2-3 is considered very good. Lastly, a ratio of 3.0 or higher is deemed excellent.

Usually, any investment with a Sharpe Ratio of greater than 1.0 is preferable for investors. However, investors can also use the ratio as a comparison tool between different options. As stated above, the higher the Sharpe Ratio is, the more preferable the investment it represents. Therefore, when comparing investors must always select the investment with the highest Sharpe Ratio.

Conclusion

The relationship between the risks and rewards of an investment is always a concern for investors. However, they can use a metric known as the Sharpe Ratio to quantify the relationship. The higher the ratio is, the more preferable the investment it is for investors. Usually, investors consider investments with a Sharpe Ratio of greater than 1.0 as good.

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