Sharpe ratio
Return per unit of volatility: how much you were paid for the swings you put up with.
How it is computed here
The annualised excess return over the risk-free rate, divided by the annualised volatility of the same series.
Worked example
- Annual return +10.4% ÷ annual volatility 25.5%.
- 0.1038 ÷ 0.2549 = 0.41 (with a zero risk-free rate).
- The return here counts trading sessions, 252 a year, to match the volatility; that is why it reads +10.4% and not the calendar +10.8% of the annual return. Both are right; they count years differently.
Demo portfolio: four invented companies, generated prices, measured by the real engine. Past returns do not predict future ones.
Where it misleads
It treats upside volatility as risk, and it assumes a bell curve. A strategy that wins a little every day and loses everything once in a while scores beautifully here right up until it does not.
The formula
- Rp — the portfolio's annualised return.
- Rf — the annual risk-free rate (here, converted to its daily equivalent and subtracted day by day before annualising).
- σp — the annualised volatility of the portfolio's daily returns: their standard deviation times √252.
- SR — return in excess of the risk-free rate, per unit of volatility.
How to read it
The Sharpe ratio asks whether the swings were paid for. Two portfolios that both returned 8% are not equally good if one got there with half the volatility: that one delivered more return per unit of the discomfort that makes people sell.
It is most useful to compare portfolios over the same dates. Across different periods it mostly measures the market each one lived through.
Where the number comes from, and how noisy it is
A Sharpe ratio is an estimate, and a noisy one. With returns that behave roughly independently, its standard error is about √((1 + SR² ⁄ 2) ⁄ T), with T in years (Lo, 2002): for a ratio of 1 measured over three years, about 0.7. Two portfolios with ratios of 0.7 and 1.2 over that window may not be distinguishable at all. The longer the history, the more the figure means.
Compared with
- Sortino ratio — the same idea, but only downside volatility counts as risk
- Calmar ratio — return per unit of the worst fall instead of per unit of volatility
- M² — the Sharpe ratio turned back into a return, comparable with a benchmark's
Questions people ask
What is a good Sharpe ratio?
There is no universal threshold, because it depends on the period measured. As a reference, a broad stock index has had a long-run Sharpe ratio of roughly 0.3 to 0.5; sustained values above 1 for a long-only stock portfolio are unusual and usually mean the window was short or unusually kind.
Can the Sharpe ratio be negative?
Yes. When the portfolio returned less than the risk-free rate, the excess return is negative and so is the ratio. Between two negative Sharpe ratios the comparison stops meaning much, because more volatility makes a negative ratio look better.
Why subtract the risk-free rate?
Because that part of the return was available without taking any risk. The ratio only credits the portfolio for what it earned above a Treasury bill.
Sources
- Sharpe, W. F. (1966), Mutual fund performance, The Journal of Business 39(1)
- Sharpe, W. F. (1994), The Sharpe ratio, The Journal of Portfolio Management 21(1)
- Lo, A. W. (2002), The statistics of Sharpe ratios, Financial Analysts Journal 58(4)
Last reviewed 2026-09-27 by Sphinx Risk.