What Is the Sharpe Ratio?

The Sharpe ratio compares the return of an investment with its risk. It's a mathematical expression of the insight that excess returns over a period of time may signify more volatility and risk, rather than investing skill.

The Sharpe ratio was developed by Nobel laureate William F. Sharpe and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk.

Volatility is a measure of the price fluctuations of an asset or portfolio. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities.

Formula and Calculation

The Sharpe ratio is calculated as follows:

$$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$

Where:

• $R_p$ = Return of portfolio
• $R_f$ = Risk-free rate
• $\sigma_p$ = Standard deviation of the portfolio's excess return

The numerator is the difference between the portfolio's actual return and the risk-free rate (typically the return on government bonds). The denominator is the standard deviation of the portfolio's returns, which measures its volatility.

What the Sharpe Ratio Can Tell You

The Sharpe ratio is one of the most widely used methods for measuring risk-adjusted relative returns. It compares a fund's historical or projected returns relative to an investment benchmark with the historical or expected variability of such returns.

Interpreting the Sharpe Ratio

Generally speaking, Sharpe ratios can be interpreted as follows:

A higher Sharpe ratio is better when comparing similar portfolios or funds. A Sharpe ratio of 1.0 is considered acceptable. A Sharpe ratio of 2.0 is considered very good. A Sharpe ratio of 3.0 or higher is considered excellent.

Negative Sharpe Ratio

A negative Sharpe ratio means that the risk-free rate is greater than the portfolio's return, or the portfolio's return is expected to be negative. In either case, a negative Sharpe ratio does not convey any useful meaning.

Sharpe Ratio Pitfalls

The Sharpe ratio can be manipulated by portfolio managers seeking to boost their apparent risk-adjusted returns history. This can be done by lengthening the measurement interval, which results in a lower estimate of volatility.

Limitations

1. Assumes normal distribution: The Sharpe ratio assumes that returns are normally distributed, which may not always be the case in real markets.

2. Backward-looking: It uses historical data, which may not predict future performance.

3. Can be manipulated: By choosing specific time periods or using smoothed returns.

4. Doesn't distinguish between upside and downside volatility: All volatility is treated the same, even though investors typically only dislike downside volatility.

The Sortino and the Treynor Ratios

Two variations of the Sharpe ratio are the Sortino ratio and the Treynor ratio.

Sortino Ratio

The Sortino ratio removes the effects of upward price movements on standard deviation to focus on the distribution of returns that are below the target or required return. It uses downside deviation instead of standard deviation in the denominator.

$$\text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d}$$

Where $\sigma_d$ is the standard deviation of negative asset returns (downside deviation).

Treynor Ratio

The Treynor ratio uses a portfolio's beta, rather than its standard deviation, to measure volatility. Beta measures how much a portfolio's returns change in response to market changes.

$$\text{Treynor Ratio} = \frac{R_p - R_f}{\beta}$$

Example

Consider two portfolios:

Portfolio A:

• Annual return: 15%
• Standard deviation: 10%
• Risk-free rate: 3%
• Sharpe Ratio = $\frac{15\% - 3\%}{10\%} = 1.2$

Portfolio B:

• Annual return: 12%
• Standard deviation: 5%
• Risk-free rate: 3%
• Sharpe Ratio = $\frac{12\% - 3\%}{5\%} = 1.8$

Even though Portfolio A has a higher absolute return, Portfolio B has a better risk-adjusted return as indicated by its higher Sharpe ratio.

FAQs

What is a good Sharpe ratio?

A Sharpe ratio above 1.0 is generally considered acceptable to good by investors. A ratio higher than 2.0 is considered very good, and a ratio of 3.0 or higher is considered excellent.

How is the Sharpe ratio calculated?

The Sharpe ratio is calculated by subtracting the risk-free rate from the portfolio's return and then dividing by the standard deviation of the portfolio's excess returns.

Can the Sharpe ratio be negative?

Yes, if the portfolio's return is less than the risk-free rate, the Sharpe ratio will be negative. This indicates that the investment underperformed compared to a risk-free investment.

The Bottom Line

The Sharpe ratio is a useful tool for understanding the risk-adjusted return of an investment. It helps investors compare the performance of different investments by accounting for both return and risk. However, it should be used alongside other metrics and analysis tools for a complete picture of an investment's performance.