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Sharpe ratio calculator

By Jude Wallis

The Sharpe ratio is portfolio return minus a matching risk-free rate, divided by the portfolio's volatility. A 12 percent return, 4 percent risk-free rate and 10 percent volatility produce 0.8.

Sharpe ratio

0.80

8.00 points of excess return per 10.0 points of volatility.

Portfolio return
12.00%
Risk-free rate
4.00%
Excess return
8.00 points
%

The portfolio return over the same window as the risk-free rate.

%

A matching low-risk rate, in the same currency and for the same period.

%

Standard deviation of the portfolio's returns, on the same scale as the two rates.

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On this page

The formula

S=Rp−RfσpS = \dfrac{R_p - R_f}{\sigma_p}

RpR_p is the portfolio return. RfR_f is the matching risk-free rate. σp\sigma_p is the standard deviation of the portfolio's returns, on the same scale.

Excess return per unit of variability

The ratio asks how much return sat above a low-risk alternative for each unit of measured variability. The units cancel when both the numerator and the denominator are rates on the same scale.

A 12 percent return against a 4 percent risk-free rate is 8 points of excess return. At 10 percent volatility that is 8/10=0.88 / 10 = 0.8. The result is a ratio, not a percent.

How the Sharpe ratio works is the explainer. This page is the working identity.

The risk-free rate has to match the window

A monthly portfolio return belongs beside a monthly risk-free return. An annual return belongs beside an annual rate. Mixing those windows makes the numerator meaningless before volatility enters.

Currency matters for the same reason. A portfolio measured in one currency should use a rate in that currency, or the ratio starts to include an unrelated interest-rate gap.

Risk and return is why the excess part is removed. Return available without the portfolio's market risk is not compensation for bearing that risk.

Same excess, a rougher path

Hold excess return at 8 points and raise volatility from 10 percent to 16 percent. The ratio falls from 0.8 to 0.5. The start and the finish can match while the route does not.

Standard deviation of returns treats upside and downside departures from the average alike. That makes comparisons consistent. It does not make volatility identical to the loss an investor felt.

The risk-return explorer holds the same trade still while you move return or volatility.

What this page is not doing

It does not annualise a monthly series, pick a risk-free proxy, or strip fees from a reported return. Those choices belong to the inputs you type.

Use the same window, frequency, currency and fee treatment when you compare two results. This is educational material, not financial advice.

Worked examples

Eight points of excess return at 10 percent volatility

A portfolio returned 12 percent, the matching risk-free rate was 4 percent and annualised volatility was 10 percent. What is its Sharpe ratio?

  1. Excess return is 12−4=812 - 4 = 8 percentage points.
  2. Divide by volatility: 8/10=0.88 / 10 = 0.8.

The Sharpe ratio is 0.8. That is 8 points of excess return per 10 points of volatility.

The same excess return at 16 percent volatility

The portfolio still returned 12 percent against a 4 percent risk-free rate, but volatility was 16 percent. What is the Sharpe ratio now?

  1. Excess return is still 12−4=812 - 4 = 8 percentage points.
  2. Divide by the larger volatility: 8/16=0.58 / 16 = 0.5.

The Sharpe ratio is 0.5. The excess return did not change. The path was rougher.

Dropping a CAGR into a period-by-period denominator

CAGR describes the compound rate between a start value and an end value. The Sharpe denominator is the standard deviation of the period returns in the window.

Putting a CAGR in the numerator while using month-by-month volatility in the denominator mixes two summaries. How CAGR works is the growth-rate object. Keep it off this sheet unless the whole window is being treated as one period on both sides.

Common questions

Is the Sharpe ratio a percentage?

No. It is excess return per unit of volatility. A result of 0.8 is a ratio, not 0.8 percent.

Can a Sharpe ratio be negative?

Yes, when portfolio return sits below the chosen risk-free rate. Ranking negative ratios needs care, because a larger volatility then moves the result toward zero.

What is a good Sharpe ratio?

There is no universal threshold. Compare portfolios over the same window, frequency, currency, risk-free proxy and fee treatment.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.