Formula, in Risk & Portfolio Construction
Sharpe Ratio Formula
The Sharpe ratio is the mean excess return of a strategy divided by the standard deviation of its returns. Annualize a periodic Sharpe by multiplying by the square root of the number of periods per year.
4 variables. Published May 26, 2026. By AI Fin Hub Research.
Sharpe = (E[R_p] - R_f) / sigma_p
Annualized: SR_annual = SR_period x sqrt(N)
where N = periods per year (252 daily, 52 weekly, 12 monthly) Variables
E[R_p]
Mean portfolio return
Arithmetic mean of the strategy's return over each period in the sample, expressed per period (per day, week, or month).
R_f
Risk-free rate
Return on a near-riskless asset over the same period, typically a short Treasury bill. Use the per-period rate, not the annual rate, so it matches the return frequency.
sigma_p
Return standard deviation
Standard deviation of per-period returns. This is the denominator that turns raw return into risk-adjusted return, and the term that makes the ratio sensitive to fat tails and autocorrelation.
N
Periods per year
Annualization factor. 252 for daily returns, 52 for weekly, 12 for monthly. The square root applies because variance scales linearly with time under the i.i.d. assumption while the mean scales linearly, so the ratio scales by sqrt(N).
Step by step
- 1
Compute the per-period excess return for each observation: subtract the per-period risk-free rate from each return.
Monthly returns of 0.8% with a 0.3% monthly risk-free rate give an excess return of 0.5% per month.
- 2
Take the mean of the per-period excess returns and the standard deviation of the per-period returns.
Mean excess = 0.5%, standard deviation = 2.1% over 60 monthly observations.
- 3
Divide the mean excess return by the standard deviation to get the per-period Sharpe ratio.
0.5% / 2.1% = 0.238 per month.
- 4
Annualize by multiplying the per-period Sharpe by the square root of the number of periods per year.
0.238 x sqrt(12) = 0.82 annualized.
- 5
Report the standard error alongside the point estimate. For an annualized Sharpe SR over T periods, a first-order standard error is approximately sqrt((1 + 0.5 x SR_period^2) / T).
Over 60 monthly observations a Sharpe near 0.8 carries a standard error wide enough that the interval can include values well below 0.5.
Worked example
Long-short equity strategy, 60 monthly observations
Mean monthly excess return
0.5%
Monthly return standard deviation
2.1%
Periods per year
12
Monthly Sharpe = 0.005 / 0.021 = 0.238. Annualized = 0.238 x sqrt(12) = 0.238 x 3.464 = 0.825.
Annualized Sharpe of about 0.82. Over only 60 months the estimate is noisy, so treat it as a range rather than a single number and confirm with an out-of-sample window before allocating.
Common variations
Run the numbers next
- Calculators Sharpe Ratio Calculator
Paste daily returns; get Sharpe, Sortino, Calmar, and Omega side-by-side with a recommendation on which ratio fits your distribution.
- Calculators Deflated Sharpe Ratio Calculator
Bailey & López de Prado deflated Sharpe — corrects observed Sharpe for selection bias across K trials. Reports deflated Sharpe, PSR (probability of skill).
Sources
- The Sharpe Ratio , William F. Sharpe, Journal of Portfolio Management (1994)
- The Statistics of Sharpe Ratios , Andrew W. Lo, Financial Analysts Journal (2002)
Keep the topic connected
- Learn Sharpe Ratio
Sharpe ratio defined, when it lies (skew, fat tails, autocorrelation), and how to read a Sharpe number you didn't compute yourself.
- Learn Sortino Ratio
Sortino ratio: same numerator as Sharpe, denominator only counts downside volatility. When it's the right number to look at.
- Formula Deflated Sharpe Ratio Formula
The deflated Sharpe ratio formula: the probability a strategy's Sharpe is real after correcting for the number of trials, return skew, kurtosis, and sample length.