Sharpe Ratio

Excess return per unit of total volatility. Computes the mean of the return series, subtracts the risk-free rate, and divides by the sample standard deviation of returns.

When to use: Compare excess return per unit of total volatility using matching return periods and risk-free rates. Compare ratios only on the same frequency and estimation basis.

Calculator

Formula

\text{Sharpe} = \frac{\overline{R_p} - R_f}{\sigma_p}

Variables

Symbol	Name	Description	Unit
Sharpe	Sharpe Ratio	Excess return per unit of total volatility	integer
Returns	Periodic Returns	Sequence of periodic returns as decimals (e.g. 0.05 for 5%)	%
Rf	Risk-Free Rate	Per-period risk-free rate as a decimal (use the same period as the returns)	%

Real-Life Examples

Example 1: Five-Period Portfolio

Periodic returns of 10%, 15%, 5%, 20%, 8%. Per-period risk-free rate is 3%.

Given

Returns = [0.1, 0.15, 0.05, 0.2, 0.08]Rf = 3.0000%

Step-by-Step

1.Mean periodic return = 0.116; target/risk-free rate = 0.03

2.Sum of squared deviations from the mean = 0.01412; divisor = 4

3.Denominator = √(0.01412 / 4) ≈ 0.0594138031101

4.Ratio = (0.116 − 0.03) / denominator (before rounding)

5.Sharpe ≈ 1.447475

Result:1.45

For these inputs, Sharpe Ratio is 1.447475 under the stated payment, compounding and accounting assumptions.

Frequently Asked Questions

No. It is a per-observation-period ratio. Under independent, identically distributed excess returns and consistent rates, multiply by the square root of periods per year to annualize. Serial correlation can invalidate that conversion.

There is no universal cutoff. Frequency, sample length, estimation uncertainty, leverage and return distribution affect interpretation; monthly and annual values are not directly interchangeable.

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