Sharpe Ratio Calculator

What the Sharpe ratio measures

The Sharpe ratio is return above the risk-free rate divided by the volatility that came with it. The formula is S = (Rp - Rf) / sigma, where Rp is the mean return of the strategy, Rf is the return on cash and sigma is the standard deviation of the returns. It answers a question that raw performance cannot: how much movement did you have to accept for every unit of return you earned?

Because volatility grows with the square root of time while returns grow roughly in proportion to it, the ratio is annualized by multiplying the per period figure by the square root of the number of periods in a year. Monthly data is scaled by the square root of 12, daily data by the square root of 252. That scaling is why the frequency selector changes the answer even though the numbers you pasted are identical.

A worked example from the sample series

The box is prefilled with 24 monthly returns and a 4% annual risk-free rate. Running the arithmetic on that series:

• Mean monthly return is 0.9125%, and the sample standard deviation is 2.6224%.
• The risk-free rate per month is 1.04 ^ (1 / 12) - 1 = 0.32737%.
• Excess return per month is 0.9125% - 0.32737% = 0.58513%.
• Per month the ratio is 0.58513 / 2.6224 = 0.2231.
• Annualized: 0.2231 x sqrt(12) = 0.77.

The same series compounds to 23.39% over the two years, an 11.08% annual rate, with annualized volatility of 9.08% and a worst month of minus 4.5%. Sortino comes out at 1.24 because the downside deviation, at 5.68% annualized, is well below total volatility: most of the movement in this series was upward.

Sortino, downside deviation and drawdown

Standard deviation punishes a 6% month up and a 6% month down equally, which few investors experience as equally unpleasant. Sortino replaces the denominator with downside deviation, the root mean square of the shortfalls below a minimum acceptable return. Leave the field blank and the calculator uses the risk-free rate as that threshold. Set it to zero and only losing periods count as risk.

Neither ratio knows anything about order. A series that alternates gains and losses and a series that delivers every loss in a single stretch produce the same Sharpe ratio and completely different experiences, which is why the maximum drawdown of the compounded series sits alongside them here. Work out what any drawdown costs you in recovery time with the drawdown recovery calculator.

Using the output honestly

Enter returns after every cost you actually pay, including spread and borrow, since gross returns flatter high turnover strategies. Compare the result against a passive benchmark computed the same way before you conclude anything: a Sharpe ratio of 0.8 is only impressive if the index over the same window did worse. The full set of risk measures, and what each one hides, is in measuring portfolio risk, and the correlation question that decides whether your positions are separate bets is covered in diversification explained.

Once you trust the return stream, the sizing question follows. The Kelly criterion calculator turns an edge into a fraction of capital, and risk management for traders covers the rules that keep the fraction sane. For a single holding rather than a series, the stock return and CAGR calculator is the simpler tool.