Sharpe Ratio Calculator
Sharpe Ratio Calculator
Return earned above a risk-free rate for each unit of volatility: the Sharpe ratio, and the Sortino ratio if you have the downside deviation. Both describe the past, not the future.
Sharpe ratio
A 12% return, 6% risk-free, 15% standard deviation and 10% downside deviation a year
Sharpe and Sortino
- Rp
- the portfolio’s return a year
- Rf
- the risk-free rate a year
- σ
- the standard deviation of returns, a year
- σ down
- the downside deviation: only returns below the target (here the risk-free rate) count
Worked example
A 12% return, 6% risk-free, 15% standard deviation and 10% downside deviation a year
Excess return = 12 − 6 = 6%
Sharpe = 6 ÷ 15 = 0.40
Sortino = 6 ÷ 10 = 0.60
If the 15% were a monthly 4.5%: 4.5 × √12 = 15.59% a year, and Sharpe = 6 ÷ 15.59 = 0.38
What the Sharpe ratio measures, and its limits
William Sharpe proposed the ratio in 1966 as the “reward-to-variability” ratio for comparing mutual funds, and restated it in 1994 as the excess return over a benchmark divided by the standard deviation of that excess. With a risk-free rate as the benchmark it answers: how much return did the portfolio earn above a safe alternative for each unit of volatility it carried? In the example, 6 points of excess return with 15% volatility is 0.40. A fund returning 16% with 25% volatility scores the same 0.40, and one returning 10% with 8% volatility scores 0.50: the higher return is not the better risk-adjusted one.
Volatility is often measured on monthly returns. To turn a monthly standard deviation into an annual one, multiply by the square root of 12, about 3.46, because variances of independent returns add up. A monthly 4.5% becomes 15.59% a year. Andrew Lo showed in 2002 that this is exact only when returns are independent and identically distributed; when good months tend to follow good months, or a fund’s reported prices are smoothed, the √12 rule understates the real annual risk and flatters the ratio. Returns should be annualised on the same basis as the volatility.
The Sharpe ratio treats rises and falls alike. The Sortino ratio, set out by Frank Sortino and Lee Price in 1994, divides by the downside deviation instead, counting only returns below a target; here the target is the risk-free rate. Neither ratio has an official good or bad level, and this page gives none: compare funds of the same kind, over the same period, with the same risk-free rate. Both are backward looking; a fund’s past ratio says little about its next year. To measure the return itself, use the CAGR calculator or the ROI calculator; for the drag of costs, the expense ratio calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How do you calculate the Sharpe ratio?
(Portfolio return − risk-free rate) ÷ standard deviation, all a year. A 12% return with a 6% risk-free rate and 15% volatility gives 6 ÷ 15 = 0.40.
How do I annualise monthly volatility?
Multiply the monthly standard deviation by √12, about 3.46: 4.5% a month is 15.59% a year. It assumes monthly returns are independent; if they are not, the true annual figure differs.
What is a good Sharpe ratio?
There is no official threshold. The ratio depends on the period, the risk-free rate and how volatility was measured, so it is only meaningful when comparing similar funds measured the same way.
What is the difference between Sharpe and Sortino?
Sharpe divides by all volatility; Sortino divides by downside deviation only, so rises in price do not count against a fund. In the example Sortino is 0.60 against a Sharpe of 0.40.
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References
- Sharpe WF. Mutual Fund Performance. Journal of Business. 1966;39(1, Part 2):119–138.
- Sharpe WF. The Sharpe Ratio. Journal of Portfolio Management. 1994;21(1):49–58.
- Lo AW. The Statistics of Sharpe Ratios. Financial Analysts Journal. 2002;58(4):36–52. Annualising by the square root of time is exact only when returns are independent and identically distributed.
- Sortino FA, Price LN. Performance Measurement in a Downside Risk Framework. Journal of Investing. 1994;3(3):59–64.
- Bodie Z, Kane A, Marcus AJ. Investments. McGraw-Hill. Holding-period return, transaction costs, risk-adjusted performance (the Sharpe ratio), dividend reinvestment and total return, and asset allocation.