What Is the Sharpe Ratio? Formula, Worked Example and What It Leaves Out

The Sharpe ratio divides an investment's return above a risk-free rate by the volatility of its return, giving the excess return earned per unit of risk taken.

Fund reports and screeners quote it constantly, often without the inputs needed to compare two of them. This page covers where the ratio comes from, the formula, a worked example that shows how the choice of risk-free rate moves it, how it is annualised, what it leaves out, and where Kresmion shows it. It is descriptive throughout.

Where it comes from

William Sharpe introduced the measure in 1966 to compare mutual fund performance and called it the reward-to-variability ratio. In a 1994 article in The Journal of Portfolio Management he noted that the measure had become popular while his name for it had not, and that other authors called it the Sharpe Index, the Sharpe Measure or the Sharpe Ratio. Sharpe shared the 1990 Nobel Prize in Economic Sciences for the Capital Asset Pricing Model, the theory behind beta.

The formula

Sharpe ratio = (return of the investment minus the risk-free rate) / standard deviation of the investment's return

• The numerator is the excess return: what the investment earned beyond a rate that carries almost no risk, usually a short-term government bill yield.
• The denominator is volatility, the standard deviation of returns over the same period.

Sharpe's 1994 article frames it in more general terms as the average of a differential return, the investment's return minus a benchmark's, divided by that differential's standard deviation. The original benchmark was a riskless security, which gives the everyday version above. The result is a pure number with no units: two investments can be compared on it even when one swings far more than the other.

A worked example

Two hypothetical funds over the same year, with a risk-free rate of 4 percent:

Fund A earned more. Fund B earned more per unit of volatility, so it has the higher Sharpe ratio under either convention. The last column shows how much the risk-free rate matters: setting it to zero raised A's ratio by two thirds and more than doubled B's, because the same 4 points are a bigger share of B's smaller return. Two Sharpe ratios computed with different risk-free rates are not comparable.

Annualising

Most Sharpe ratios are quoted on an annual basis but computed from daily or monthly returns. The usual conversion multiplies the average excess return by the number of periods in a year and the standard deviation by the square root of that number, so the ratio itself scales by the square root. With 252 trading days, a daily average excess return of 0.04 percent and a daily standard deviation of 1 percent give a daily ratio of 0.04 and an annualised ratio of 0.04 x 15.87 = 0.63.

Sharpe's article calls annualising common practice and says it can give at least reasonably meaningful comparisons, while noting that returns may be serially correlated. The square-root rule assumes each period's return is independent of the last. When returns are positively correlated from one period to the next, as can happen with assets priced from appraisals or traded thinly, volatility over a year is larger than the square-root rule implies, and the annualised ratio comes out too high.

What the ratio leaves out

• The shape of losses. Standard deviation counts gains and losses alike. Two return streams with the same volatility can have very different worst periods, which is what drawdown measures. The Sortino ratio is a variant that divides by a target semideviation, a measure that counts only shortfalls below a chosen target return.
• Rare large losses. A strategy that earns a small steady return and occasionally loses heavily can show a high Sharpe ratio for years before the loss arrives.
• The window. The ratio describes one sample period. The same investment can show very different ratios over different years.
• Leverage. Borrowing to scale up an investment multiplies its excess return and its volatility by about the same factor, leaving the ratio roughly unchanged, so the ratio alone does not show how much risk was taken in money terms.

Where Kresmion shows the Sharpe ratio

The Risk section of Kresmion's portfolio analytics reports a Sharpe ratio for the holdings you enter, next to annualised volatility, maximum drawdown and beta. It computes the ratio on the portfolio's daily time-weighted returns, annualises with 252 trading days, and sets the risk-free rate to zero, which the section header states. That makes it the annualised average return divided by the annualised volatility. Read it on that basis: a ratio quoted elsewhere with a positive risk-free rate is lower for the same portfolio. The figure appears once the selected window holds at least 20 daily returns. The portfolio needs a Kresmion account, is stored encrypted, and its analytics are computed in your browser.

Honest limitations

A Sharpe ratio is a ratio of two estimates, each measured over a past window, so it inherits the noise of both: a few years of data can produce a high or low figure by chance. It assumes volatility is the right measure of risk, which is a weaker assumption for returns with fat tails or skew. It depends on the risk-free rate, the period, the return frequency and the annualising rule, so comparisons are only meaningful when all four match. The funds and daily figures on this page are hypothetical, chosen to show the arithmetic.

Key takeaways

Frequently asked questions

What is a good Sharpe ratio?

There is no official threshold. A ratio is only meaningful against others computed the same way, over the same period, with the same risk-free rate and frequency. A higher ratio means more excess return per unit of volatility over that window; it does not describe the size of the worst losses.

What does a negative Sharpe ratio mean?

That the investment returned less than the risk-free rate over the period measured. The size of a negative ratio is hard to interpret, because a more volatile investment with the same shortfall shows a ratio closer to zero.

What is the difference between the Sharpe and Sortino ratios?

The Sharpe ratio uses return above the risk-free rate and divides by the standard deviation of all returns. The Sortino ratio uses return above a chosen target and divides by the variability of shortfalls below that target only, so swings above the target do not count against it.

Which risk-free rate is used?

Usually the yield on a short-term government bill in the same currency, such as a 3-month US Treasury bill for a dollar portfolio, measured over the same period. Some calculators use a fixed rate and some use zero, which is why the convention has to be stated next to the number.

Does a high Sharpe ratio predict future returns?

No. It describes the relationship between return and volatility in a past sample. It does not forecast either one.

This page is information, not investment advice.

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Source: William F. Sharpe, The Sharpe Ratio, The Journal of Portfolio Management (Fall 1994), reprinted at https://web.stanford.edu/~wfsharpe/art/sr/sr.htm ; William F. Sharpe, Mutual Fund Performance, Journal of Business (1966) ; The Royal Swedish Academy of Sciences, press release for the 1990 Prize in Economic Sciences, https://www.nobelprize.org/prizes/economic-sciences/1990/press-release/ ; ratios computed by Kresmion for hypothetical funds ; Kresmion portfolio analytics.

Kresmion Research.