What Is the Sharpe Ratio?

The Sharpe ratio was developed by economist 澳洲幸运5官方开奖结果体彩网:William F. Sharpe in 1966. It compares the return of an investme⛦n💮t with its risk.

The ratio's numerator is the difference between realized, or expected, returns and a benchmark such as the 澳洲幸运5官方开奖结果体彩网:risk-free rate of return or the performance of a particular investment category over time. Its denominator is the standard deviation of returns over the same period, a measure of volatility and risk.

Formula and Calculation of the Sharpe Ratio

Economist William F. Sharpe proposed the Sharpe ratio in 1966 as an outgrowth of his work on the capital asset pricing model (CAPM), calling it the reward-to-variability ratio. Sharpe won the Nobel Prize in economics for his work on CAPM in 1990.

$\begin{aligned} &\textit{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}\\ &\textbf{where:}\\ &R_{p}=\text{return of portfolio}\\ &R_{f} = \text{risk-free rate}\\ &\sigma_p = \text{standard deviation of the portfolio's excess return}\\ \end{aligned}$​Sharpe Ratio=σp​Rp​−Rf​​where:Rp​=return of portfolioRf​=risk-free rateσp​=standꦅard devꦅiation of the portfolio’s excess return​

澳洲幸运5官方开奖结果体彩网:Standard deviation is derived from the variability of returns for a series of time intervaꩵls, adding up to the total performance sample under consideration.

The numerator's total return differential versus a benchmark (Rp - Rf) is calculated as the average of the return differentials in each of the inꦕcremental periods making up the total. For example, the numerator of a 10-year Sharpe ratio might be the average of 120 monthly return differentials for a fund versus an industry benchmark.

The Sharpe ratio's denomi༺nator in that example will be those monthly returns standard deviation, 🗹calculated as follows:

1. Take the return variance from the average return in each of the incremental periods, square it, and sum the squares from all of the incremental periods.
2. Divide the sum by the number of incremental periods.
3. Take the square root of the quotient.

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 澳洲幸运5官方开奖结果体彩网:variability of such returns.

The risk-free rate was initially used in the formula to denote an investor's hypothetical minimal borrowing costs. More generally, it represents the 澳洲幸运5官方开奖结果体彩网:risk premium of an investment versus a safe asset such as a Treasury bill or bond.

When benchmarked against the returns o💝f an industry sector or investing strategy, the Sharpe ratio provides a measure of risk-adjusted performance not attributable to such affiliations.

The ratio is useful in determining to what degree excess historical returns were accompanied by excess volatility. While excess returns are measured in comparison with an investing benchmark, t🌃he standard deviatiꩲon formula gauges volatility based on the variance of returns from their mean.

The ratio's utility relies on the assumption that the historical record of relative risk-adjusted returns has at least some predictive value.

Important

Generally, the higher the Sharpe ratio, the more attractive the risk-adjusted return.


The Sharpe ratio can be used to evaluate a portfolio’s risk-adjusted performance. Alternatively, an investor could use a fund's return objective to estimate its projected Sharpe ratio ex-ante.

The Sharpe ratio can help explain whether a portfolio's excess returns are attributable to smart investment decisions or simply luck and risk.

For example, low-quality, highly speculative stocks can outperform blue chip shares for considerable periods, as during the 澳洲幸运5官方开奖结果体彩网:Dot-Com Bubble or, more recently, the 澳洲幸运5官方开奖结果体彩网:meme stocks frenzy. If a YouTuber happens to beat Warren Buffett in the market for a while as a re🌼sult, theꦛ Sharpe ratio will provide a quick reality check by adjusting each manager's performance for their portfolio's volatility.

The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance. A negative Sharpe ratio means the risk-free or benchmark rate is greater than the portfolio’s historical or projected return, or else the portfolio's return is expected to be negative.

Sharpe Ratio Pitfalls

The Sharpe ratio can be manipulated by portfolio managers seeking to boost their 澳洲幸运5官方开奖结果体彩网:apparent risk-adjusted returns history. This 𝐆can be done by lengthening the return measurement intervals, which results in a lower estimate of v🍸olatility.

For example, the standard deviation (volatility) of annual returns is generally lower than that of monthly returns, which are in turn less volatile than daily returns. Financial analysts typic🐈ally consider the volatility of monthly returns when using the Sharpe ratio.

Calculating the Sharpe ratio for the most favorable stretch of performance rather than an objectively chosen look-back period is another way to cherry-pick the data that will distort the r🐲isk-adjusted returns.

The Sharpe ratio also has some inherent limitations. The standard deviation calculation in the ratio's denominator, which serves as its proxy for portfolio risk, calculates volatility based on a 澳洲幸运5官方开奖结果体彩网:normal distribution and is most useful in evaluating symmetrical 澳洲幸运5官方开奖结果体彩网:probability distribution curves.

In contrast, financial markets subject to 澳洲幸运5官方开奖结果体彩网:herding behavior can go to extremes much more often than a normal distribution would suggest is possible. As a result, the standard deviation used to calculate the Sharpe ratio may understate 澳洲幸运5官方开奖结果体彩网:tail risk.


Market returns are also subject to 澳洲幸运5官方开奖结果体彩网:serial correlation. The simplest example is that returns in adjacent time intervals may be correlated because they were influenced by the same market trend. But 澳洲幸运5官方开奖结果体彩网:mean reversion also depends on serial correlation, just like 澳洲幸运5官方开奖结果体彩网:market momentum.

The upshot is that serial correlation tends to lower volatility, and as a result, investment strategies dependent on serial correlation factors may exhibit misleadingly high Sharpe ratios.


One way to visualize these criticisms is to consider the investment strategy of picking up nickels in front of a steamroller that moves slowly and predictably nearly all the time, except for the 👍few rare occasions when it suddenly an🎶d fatally accelerates.

Because such unfortunate events are extremely uncommon, those picking u🎃p nickels would, ꦍmost of the time, deliver positive returns with minimal volatility, earning high Sharpe ratios as a result.

And if a fund picking up the proverbial nickels in front of a steamroller got flattened on one of those extremely rare and unfortunate occasions, its long-term Sharpe might still look good: just one bad month, after all. Unfortunately, that would bring little comfort to the fund's investors.

Sharpe Alternatives: The Sortin♕o and the Treynor

The standard deviation in the Sharpe ratio's formula assumes that price movements in either direction are equally risky. The risk of an abnormally low return is very different from the possibility of an abnormally high one for most investors and analysts.

A variation of the Sharpe called the 澳洲幸运5官方开奖结果体彩网:Sortino ratio ignores the above-average returns to focus solely on 澳洲幸运5官方开奖结果体彩网:downside deviation as a better proxy for ꦐthe risk of a fund or portfolio.

𝐆 The standard deviation in the denominator of a Sortino ratio measures the variance of negative returns or those below a chosen benchmark relative to the average of such returns.

Another variation of the Sharpe is the 澳洲幸运5官方开奖结果体彩网:Treynor ratio, which divides excess return over a risk-free rate or benchmark by the beta of a security, fund, or portfolio as a measure of its 澳洲幸运5官方开奖结果体彩网:systematic risk exposure.

Beta measures the degree to which the volatility of a stock or fund correlates with that of the market as a whole. The goal of the Treynor ratio is to determine whether an investor is being compensated for extra risk above that posed by the market.


Example of How to Use the Sharpe Ratio

The Sharpe r🐎atio is sometimes used in assessing how adding an investment might affect the 🀅risk-adjusted returns of the portfolio.

For example, an investor is considering adding a hedge fund allocation to a portfolio that has returned 18% over the last year. The current risk-free rate is 3%, and the annualized standard deviation of the portfolio’s monthly returns was 12%, which gives it a one-year Sharpe ratio of 1.25, or (18% -🐽 3%) / 12%.

The investor believes that adding the hedge fund to the portfolio will lower the expected return to 15% f꧅or the coming year, but also expectꦕs the portfolio’s volatility to drop to 8% as a result. The risk-free rate is expected to remain the same over the coming year.

Using the s🍷ame formula with the estimated future numbers, the investor finds the portfolio would have a projected Sharpe ratio of 1.5, or (15% - 3%) divided by 8%.

In this case, while the hedge fund investment is expected to reduce the absolute return of the portfolio, based on its projected lower volatility, it would improve the portfolio's performance on a risk-adjusted basis.

If the new investment lowered the Sharpe ratio,o it would be assumed to be detrimental to risk-adjusted returns, based on forecasts. This example assumes that the Sharpe ratio based on the portfolio's historical performance can be fairly compared to that using the investor's return and volatility assumptions.

What Is a Good Sharpe Ratio?

Sharpe ratios above 1 are generally considered “good," offering excess returns relative to volatility. However, investors often compare the Sharpe ratio of a portfolio or fund with those of its peers or market sector. So a portfolio with a Sharpe ratio of 1 might be found lacking if most rivals have ratios above 1.2, for example. 澳洲幸运5官方开奖结果体彩网:A good Sharpe ratio in one conteಞxt might be just a so෴-so one, or worse, in another.

How Is the Sharpe Ratio Calculated?

To calculate the Sharpe ratio, investors first subtract the r꧅isk-free rate from the portfolio’s rate of return, often us🌳ing U.S. Treasury bond yields as a proxy for the risk-free rate of return. Then, they divide the result by the standard deviation of the portfolio’s excess return.

What Is the Sharpe Ratio of the S&P 500?

As of Sept. 28, 2024, the S&P 500 Portfolio Sharpe ratio is 2.91.

The Bottom Line

The Sharpe ratio, named after its creator, William F. Sharpe, is a mathematical expression that helps investors compare the return of an investment with its risk. To calculate the Sharpe ratio, investors can subtract the risk-free rate of return from the expected rate of return, and then divide that result by the standard deviation (the asset's volatility).

The Sharpe rat❀io can be helpful only when used to compare very similar investments, like mutual funds and ETFs that track the same underlying index. Still, investors should keep in mind that those investments with a higher Sharpe ratio ♎can be more volatile than those with a lower rate.