What Is the Sharpe Ratio? Formula and Examples

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The Sharpe ratio measures how much return an investment earned above a risk-free rate for each unit of volatility it carried. You take the portfolio’s return, subtract the return on a near-riskless asset such as a Treasury bill, and divide the result by the standard deviation of the portfolio’s returns. A higher number means more excess return per unit of total risk. A lower number means the investor absorbed more ups and downs for each point of reward.

The ratio grades return relative to the bumpiness of the ride, not the size of the gain. That makes it useful for comparing two funds with different return and risk profiles, and much less useful as a standalone verdict on a single holding.

How the Sharpe Ratio Works

The Sharpe ratio formula

Sharpe ratio = (Rp − Rf) ÷ σp

where:

• Rp = the portfolio’s return (realized or expected)
• Rf = the risk-free rate, usually proxied by U.S. Treasury bill or bond yields
• σp = the standard deviation of the portfolio’s returns (more precisely, of its excess returns)

The numerator, Rp − Rf, is the risk premium: what the investor earned for not simply parking money in a safe asset. In Sharpe’s original framing, the risk-free rate stood in for an investor’s minimal borrowing cost. Some analysts replace Rf with a benchmark, such as an index or the average return of a fund category, so the ratio measures performance relative to that benchmark rather than to cash.

The denominator is a measure of volatility: how widely individual period returns scatter around their average. A fund that swings from large gains to large losses has a big σ, even if its average matches a fund whose monthly returns cluster tightly.

How to calculate the Sharpe ratio step by step

In practice, the ratio is built from a series of shorter periods, commonly monthly, rather than one total return. A 10-year Sharpe ratio, for instance, might use 120 monthly figures.

1. Collect periodic returns. Record the portfolio’s return for each period (say, each month).
2. Compute excess returns. Subtract the risk-free rate for the same period from each return.
3. Average the excess returns. This average is the numerator.
4. Measure their dispersion. Square each period’s deviation from the average, add up the squares, divide by the number of periods (or by the number of periods minus one, the sample version most software uses), and take the square root. This is the standard deviation.
5. Divide the average excess return by the standard deviation.
6. Annualize if needed. A ratio built from monthly data is usually multiplied by √12 (about 3.46), which assumes monthly returns are independent of one another.

Hypothetical example (monthly data). Suppose a portfolio’s excess returns over six months were 2%, −1%, 3%, 1%, 0% and 1%.

• Average excess return: (2 − 1 + 3 + 1 + 0 + 1) ÷ 6 = 1.0% per month
• Deviations from the average: 1, −2, 2, 0, −1, 0
• Squared deviations: 1, 4, 4, 0, 1, 0, summing to 10
• Sample variance: 10 ÷ 5 = 2; standard deviation = √2 ≈ 1.41%
• Monthly Sharpe ratio: 1.0 ÷ 1.41 ≈ 0.71
• Annualized: 0.71 × 3.46 ≈ 2.45

Six months is far too short a sample to trust, which partly explains the impressive annualized figure. The arithmetic is the same with 60 or 120 observations.

Hypothetical example (annual figures). A mutual fund is expected to return 25% with a standard deviation of 20%, and the risk-free rate is 2.7%. The Sharpe ratio is (25 − 2.7) ÷ 20 ≈ 1.11.

Interpreting the Sharpe Ratio

What is a good Sharpe ratio?

Widely cited rules of thumb grade the ratio this way:

• Below 1.0: sub-optimal; the return has not compensated well for the volatility
• 1.0 to 2.0: acceptable to good
• 2.0 to 3.0: very good
• 3.0 or higher: excellent

By that scale, a ratio of 2.25 falls in the “very good” band, but these bands are conventions, not laws. A fund with a Sharpe ratio of 1.0 can look weak if most rivals in its category score above 1.2 over the same window. A long, calm bull market lifts the ratios of almost every equity fund, while a period that includes a crash drags them down. The meaningful comparison is between similar investments, such as two ETFs tracking the same index, measured over the same period with the same return frequency and risk-free rate. Change any of those inputs and the same fund produces a different number.

Very high figures do occur in specialized settings. The U.S. Commodity Futures Trading Commission estimated a Sharpe ratio of 4.3 for firms specializing in high-frequency trading, a strategy that trades at enormous frequency with tiny per-trade risk. That is not a target for an ordinary diversified portfolio.

Negative and zero values

A Sharpe ratio of zero means the portfolio earned exactly the risk-free rate. A negative ratio means it earned less than the risk-free rate (or the benchmark), or that its expected return is negative. Ranking negative ratios is tricky: when excess returns are negative, a more volatile fund can show a less negative ratio, which would wrongly suggest it performed better.

Ex-post vs. ex-ante

An ex-post Sharpe ratio uses realized returns and their historical volatility. An ex-ante ratio uses a return objective or forecast and an expected volatility. Both use the same formula, but one grades the past and the other tests a plan. Using either for decisions assumes risk-adjusted performance persists, which history does not guarantee.

How Investors Use the Sharpe Ratio

Comparing investments with different risk levels. Raw returns reward whoever took the most risk. The Sharpe ratio corrects for that. Consider two hypothetical funds with a 4% risk-free rate:

Fund A earned more, but Fund B delivered more excess return per unit of risk. The difference matters when leverage enters. If an investor could borrow at the risk-free rate and hold Fund B at two times exposure, the return would be 2 × 9% − 4% = 14% with a standard deviation of 10%, beating Fund A’s 12% at the same volatility. The levered position’s Sharpe ratio stays 1.0, because borrowing at the risk-free rate scales excess return and standard deviation by the same factor. In practice borrowing costs exceed the risk-free rate, so the real-world result is somewhat worse.

Separating skill from luck and risk. A manager riding speculative, low-quality stocks, as during the dot-com bubble or the meme-stock episode, can outperform a disciplined value investor for long stretches while carrying far more volatility. Adjusting both records for volatility shows who earned the better risk-adjusted result.

Testing a change to a portfolio. Suppose (hypothetically) a portfolio returned 18% last year with a 3% risk-free rate and an annualized standard deviation of 12%, for a Sharpe ratio of (18 − 3) ÷ 12 = 1.25. The investor expects that adding a hedge fund allocation would cut next year’s expected return to 15% but lower volatility to 8%, for a projected ratio of (15 − 3) ÷ 8 = 1.5. The addition reduces absolute return while improving return per unit of risk. Comparing a historical figure with a forecast is only fair if the forecast assumptions are realistic.

Portfolio construction. Diversifying across assets that do not move in lockstep can lower total volatility without an equal cut in return, which raises the Sharpe ratio. In modern portfolio theory, the mix of risky assets with the highest Sharpe ratio is the tangency portfolio, the point where a line from the risk-free rate touches the efficient frontier. Finding it requires estimates of expected returns, volatilities and correlations, and small errors in those inputs can produce very different allocations.

Limitations of the Sharpe Ratio

Returns are not normally distributed. Standard deviation is most informative when returns follow a symmetrical, bell-shaped curve. Financial markets, prone to herding and panics, reach extremes more often than a normal distribution predicts (fat tails), and many return series are skewed. The denominator can therefore understate tail risk.

Strategies with hidden crash risk score well until they don’t. Selling deep out-of-the-money options collects small premiums month after month and pays nothing out until a large market move hits. Until then, returns are steady and volatility is low, so the Sharpe ratio looks excellent. Even after a blowup, a long enough history of small gains can leave the long-term ratio looking respectable.

Upside and downside count equally. A sudden large gain raises standard deviation just as a large loss does, so a fund can be penalized for positive surprises. Most investors do not regard an unexpectedly high return as risk.

Serial correlation lowers measured volatility. When returns in neighboring periods move together, because of trends, momentum, mean reversion or smoothed valuations of illiquid assets such as private holdings, the measured standard deviation is lower than the true risk. Strategies that depend on these effects can show misleadingly high ratios, and the √12 annualization step overstates the ratio further.

The ratio can be engineered. Measuring volatility over longer intervals tends to produce lower figures: annual returns generally look less volatile than monthly returns, and monthly less than daily. Choosing a favorable measurement window rather than an objective look-back period is another way to make the history look better.

It ignores the absolute level of risk. A high-Sharpe investment can still be more volatile than one with a lower ratio. The ratio says nothing about whether the drawdowns fit a particular investor’s tolerance or time horizon.

Sharpe Ratio vs. Related Measures

Sortino ratio. Replaces total standard deviation with downside deviation, counting only returns below a chosen target or the risk-free rate. It addresses the complaint that the Sharpe ratio penalizes upside volatility. Some practitioners use the label “modified Sharpe ratio” for similar downside-focused versions.

Treynor ratio. Divides excess return by beta instead of standard deviation. Beta measures how much an investment moves with the overall market, so the Treynor ratio asks whether the investor was paid for systematic, market-related risk. It suits a holding that sits inside a well-diversified portfolio, where diversifiable risk has largely been removed. The Sharpe ratio uses total risk and suits a portfolio held on its own.

Alpha. Alpha is expressed in percentage points: the return above what a model such as CAPM predicts given the investment’s beta. The Sharpe ratio is a ratio, not a return, so a fund can have positive alpha and a mediocre Sharpe ratio if its total volatility is high.

Information ratio. Uses the return above a benchmark divided by tracking error, the standard deviation of that difference. It is effectively the Sharpe ratio with a benchmark replacing the risk-free rate and is the standard tool for judging active managers against an index.

M² (Modigliani risk-adjusted performance). Rescales a portfolio to match the benchmark’s volatility and reports the resulting return in percentage terms, which makes the Sharpe comparison easier to read. Some versions add a risk-aversion parameter.

Return measures. ROI and CAGR describe how much an investment returned, with no adjustment for volatility. The Sharpe ratio starts from a return figure and asks what it cost in risk to get there.

FAQs

The Bottom Line

Investors comparing funds with different risk profiles can use the Sharpe ratio to see which delivered more excess return per unit of volatility. The comparison only holds for similar investments measured over the same period, return frequency and risk-free rate. Fat tails, serial correlation and selective measurement windows can inflate the figure, so the ratio works best alongside measures like the Sortino ratio and a check of absolute risk.