acalculator

What is my Sharpe ratio?

Enter a portfolio's return, the risk-free rate and the standard deviation of the return. Or paste the return for each month (or week, or day) and the yearly risk-free rate. The calculator gives the Sharpe ratio, the extra return earned per unit of risk, and annualizes it from a list of returns.

Your numbers

Data
Sharpe ratio
0.65

The Sharpe ratio is 0.65.

Excess return
17%

Sharpe ratio: 0.65. The Sharpe ratio is 0.65.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

Computes the Sharpe ratio of a portfolio, its return above the risk-free rate per unit of standard deviation, from summary figures or from a list of period returns, with the annualized ratio.

Example with the default inputs (Data Return and standard deviation, Portfolio return 20%, Risk-free rate 3%, Standard deviation of the return 26%): The Sharpe ratio is 0.65.

Method: S = (Rp − Rf) ÷ σp. From returns: Dₜ = Rₜ − Rf ÷ m, S = D̄ ÷ σ_D with σ_D = √(Σ (Dₜ − D̄)² ÷ (n − 1)), annual S = √m × S, where m is the periods per year.

  • Returns and the risk-free rate are for the same period; a yearly risk-free rate is divided evenly over the periods of a year.
  • Annualizing by √(periods per year) assumes the excess returns of different periods are not correlated.
  • Arithmetic is exact on the typed decimals; the standard deviation uses a floating-point square root.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Data Return and standard deviation, Portfolio return 20%, Risk-free rate 3%, Standard deviation of the return 26% gives Sharpe ratio 0.653846, Excess return 17%.Source: OpenStax, Principles of Finance, 15.4 Applications in Performance Measurement (Sharpe ratio = (R_P − R_f) ÷ σ_P; McKinley: 17% ÷ 26% = 0.65; Mr. Wong 1.5, Ms. Petrov 1.4). https://openstax.org/books/principles-finance/pages/15-4-applications-in-performance-measurement: 17% ÷ 26% = 0.65
  2. Data Return and standard deviation, Portfolio return 14%, Risk-free rate 2%, Standard deviation of the return 8% gives Sharpe ratio 1.5.Source: OpenStax, Principles of Finance, 15.4 Applications in Performance Measurement (Sharpe ratio = (R_P − R_f) ÷ σ_P; McKinley: 17% ÷ 26% = 0.65; Mr. Wong 1.5, Ms. Petrov 1.4). https://openstax.org/books/principles-finance/pages/15-4-applications-in-performance-measurement: (14% − 2%) ÷ 8% = 1.5
  3. Data Return and standard deviation, Portfolio return 16%, Risk-free rate 2%, Standard deviation of the return 10% gives Sharpe ratio 1.4.Source: OpenStax, Principles of Finance, 15.4 Applications in Performance Measurement (Sharpe ratio = (R_P − R_f) ÷ σ_P; McKinley: 17% ÷ 26% = 0.65; Mr. Wong 1.5, Ms. Petrov 1.4). https://openstax.org/books/principles-finance/pages/15-4-applications-in-performance-measurement: (16% − 2%) ÷ 10% = 1.4
  4. Data Return and standard deviation, Portfolio return 6%, Risk-free rate 0%, Standard deviation of the return 15% gives Sharpe ratio 0.4.Source: William F. Sharpe, "The Sharpe Ratio", The Journal of Portfolio Management, Fall 1994: Dₜ = R_Ft − R_Bt (3), D̄ = Σ Dₜ ÷ T (4), σ_D = √(Σ (Dₜ − D̄)² ÷ (T − 1)) (5), S_h = D̄ ÷ σ_D (6), and over T periods σ grows as √T (9), so the ratio does too; an annual excess return of 6% with a 15% standard deviation gives about 0.40. https://web.stanford.edu/~wfsharpe/art/sr/sr.htm: about 0.40
  5. Data List of returns, Returns for each period (%) 2, -1, 3, 1.5, -0.5, 2, Risk-free rate per year 2.4%, Periods per year 12 gives Sharpe ratio per period 0.615491, Sharpe ratio 2.132122, Excess return 0.966667%, Standard deviation of excess returns 1.570563%, Periods 6.Source: William F. Sharpe, "The Sharpe Ratio", The Journal of Portfolio Management, Fall 1994: Dₜ = R_Ft − R_Bt (3), D̄ = Σ Dₜ ÷ T (4), σ_D = √(Σ (Dₜ − D̄)² ÷ (T − 1)) (5), S_h = D̄ ÷ σ_D (6), and over T periods σ grows as √T (9), so the ratio does too; an annual excess return of 6% with a 15% standard deviation gives about 0.40. https://web.stanford.edu/~wfsharpe/art/sr/sr.htm

How it works

From a return and a standard deviation. With the portfolio's return Rp, the risk-free rate Rf and the standard deviation σp, all in percent for the same period:

  • Excess return = Rp − Rf
  • Sharpe ratio S = (Rp − Rf) ÷ σp

From a list of returns. With returns R₁ … Rₙ for n periods (in percent), a yearly risk-free rate Rf and m periods per year:

  • Excess return each period Dₜ = Rₜ − Rf ÷ m
  • Mean excess return D̄ = (D₁ + … + Dₙ) ÷ n
  • Standard deviation σ_D = √(Σ (Dₜ − D̄)² ÷ (n − 1)), the sample standard deviation
  • Sharpe ratio per period = D̄ ÷ σ_D
  • Sharpe ratio (annual) = √m × D̄ ÷ σ_D, the headline in this mode

Rules:

  • Returns and rates are from −100% to 1,000%; the standard deviation is more than 0%. A list holds 2 to 1,000 returns.
  • Periods per year are whole numbers from 1 to 366.
  • If every return in the list is the same, the standard deviation is 0 and there is no ratio.
  • The arithmetic is exact on the decimals you type; only the standard deviation's square root and what follows from it are floating point. Each square root is of an exact value, never of one first rounded to a float: σ_D = √(Σ (Dₜ − D̄)² ÷ (n − 1)), the ratio per period ±√(D̄² ÷ σ_D²) and the annual ratio ±√(m × D̄² ÷ σ_D²), with the sign of D̄. So the square of a fraction has an exact root. Ratios show to 2 decimals and percents to 3, with halves rounded up (away from 0).
  • A result too large for a 64-bit floating-point number gives no answer and a message. So does a result that is not 0 but too close to 0 for one (about 2.5 × 10⁻³²⁴ or less), so no output is ever a silent 0.

Assumptions

  • The risk-free rate is spread evenly over the year (a 2.4% yearly rate is 0.2% a month).
  • Annualizing by √m assumes the excess returns of different periods are not correlated.

Worked examples by hand

McKinley Investment Management (OpenStax). Rp = 20%, Rf = 3%, σp = 26%: S = 17 ÷ 26 = 0.65.

Mr. Wong and Ms. Petrov (OpenStax). At a 2% risk-free rate: (14 − 2) ÷ 8 = 1.50 and (16 − 2) ÷ 10 = 1.40.

Sharpe's market example. A 6% excess return with a 15% standard deviation: 6 ÷ 15 = 0.40.

Six monthly returns. 2, −1, 3, 1.5, −0.5 and 2 percent, with a 2.4% yearly risk-free rate, so 0.2% a month. The excess returns are 1.8, −1.2, 2.8, 1.3, −0.7 and 1.8, with mean D̄ = 5.8 ÷ 6 = 0.967%. The squared differences from the mean add up to 12.3333, so σ_D = √(12.3333 ÷ 5) = 1.571%. Per month: 0.9667 ÷ 1.5706 = 0.62. Annual: 0.6155 × √12 = 2.13.

Other questions people ask

What is the Sharpe ratio?

The Sharpe ratio is the return a portfolio earns above the risk-free rate, divided by the standard deviation of its return. It says how much extra return each unit of risk brought. William Sharpe introduced it in 1966 as the reward-to-variability ratio.

How do I calculate the Sharpe ratio?

Subtract the risk-free rate from the portfolio’s return and divide by the standard deviation of the return. A portfolio that returned 20% with a 26% standard deviation, when Treasury bills paid 3%, has a Sharpe ratio of (20 − 3) ÷ 26 = 0.65.

What is a good Sharpe ratio?

Higher is better, when you compare portfolios over the same period with the same risk-free rate. A portfolio with 14% return and an 8% standard deviation (1.5) did better per unit of risk than one with 16% and 10% (1.4), at a 2% risk-free rate, even though its return was lower.

How do I annualize a Sharpe ratio?

Multiply the ratio for one period by the square root of the number of periods in a year: √12 for monthly returns, √52 for weekly, √252 for trading days. This assumes the returns of different periods are not correlated with each other; if they are, the result is only an estimate.

Why does the standard deviation divide by n − 1?

Sharpe’s 1994 definition of the ex post ratio uses the sample standard deviation: the sum of squared differences from the mean, divided by the number of periods minus 1. This page does the same, so its results match a spreadsheet’s STDEV.S.

What is the difference between the Sharpe ratio and the Treynor ratio?

Both divide the excess return by a measure of risk. The Sharpe ratio uses the standard deviation, which counts all ups and downs; the Treynor ratio uses beta, which counts only market risk.