The Sharpe ratio: formula, example, and what counts as good

By Daniel Tolenaar · Updated 1 November 2026

The Sharpe ratio measures how much return an investment earned for each unit of risk it took. It is the average return above the risk-free rate divided by the standard deviation of returns, so a higher Sharpe ratio means more reward for the same volatility.

William F. Sharpe introduced it in 1966 as the “reward-to-variability ratio”. He later shared the 1990 Nobel Memorial Prize in Economic Sciences with Harry Markowitz and Merton Miller. It remains the most quoted single number for comparing funds and strategies.

The Sharpe ratio formula

• R_p is the portfolio’s average return.
• R_f is the risk-free rate, usually a short-term government bill yield, over the same period.
• σ_p is the standard deviation of the portfolio’s returns (strictly, of its excess returns).

Returns, rate and standard deviation must all cover the same period. To turn a Sharpe ratio from monthly returns into an annual one, multiply by √12; from daily returns, by √252. That scaling assumes returns are independent from one period to the next.

Worked example

A fund returned the following over twelve months, while the risk-free rate was 4% a year (0.333% a month). The code subtracts the monthly risk-free rate, divides the mean excess return by its standard deviation, and annualises:

import numpy as np

# Twelve monthly returns of a fund, and a 4% a year risk-free rate.
monthly = np.array([0.021, -0.013, 0.034, 0.008, -0.022, 0.017,
                    0.029, -0.006, 0.012, 0.025, -0.031, 0.019])
rf_monthly = 0.04 / 12

excess = monthly - rf_monthly
sharpe_monthly = excess.mean() / excess.std(ddof=1)
sharpe_annual = sharpe_monthly * np.sqrt(12)

print(f"mean monthly return  = {monthly.mean():.4%}")
print(f"monthly volatility   = {monthly.std(ddof=1):.4%}")
print(f"monthly Sharpe ratio = {sharpe_monthly:.3f}")
print(f"annualised Sharpe    = {sharpe_annual:.3f}")

mean monthly return  = 0.7750%
monthly volatility   = 2.0998%
monthly Sharpe ratio = 0.210
annualised Sharpe    = 0.729

The fund averaged 0.78% a month with 2.1% monthly volatility. Its annualised Sharpe ratio is 0.73: it earned 0.73 percentage points of return above cash for every percentage point of annual volatility.

Sharpe ratio calculator

Paste your own returns (it starts with the example above):

What is a good Sharpe ratio?

A common rule of thumb reads an annualised Sharpe ratio below 1 as modest, 1 to 2 as good, 2 to 3 as very good and above 3 as exceptional. Treat that loosely. A broad stock index held for decades has typically scored well below 1, and a backtest scoring above 3 is more often overfitted than brilliant.

The ratio is most useful for comparison, and only fair when the comparison is like for like:

• the same time period, since every asset looks better in a bull market;
• the same return frequency, since daily and monthly data give different volatility estimates;
• the same kind of strategy, since a hedge fund and a bond fund face different risks.

Limits of the Sharpe ratio

• It punishes good surprises. Standard deviation counts big gains as risk. The Sortino ratio divides by downside deviation only.
• It assumes normal returns. Strategies that sell options or insurance earn small steady gains and rare large losses; they show high Sharpe ratios until the loss arrives. Pair it with a tail measure such as Value at Risk or expected shortfall.
• Smoothed prices flatter it. Assets that are valued rarely (private equity, property) look less volatile than they are.

In portfolio theory, the Sharpe ratio has a geometric meaning: it is the slope of the line from the risk-free rate to a portfolio. The portfolio with the steepest such line is the tangency portfolio on the efficient frontier.