Sharpe Ratio
The Sharpe ratio is an investment's return in excess of the risk-free rate divided by the volatility of that return — how much reward an investor earned per unit of risk taken, on the assumption that risk is variability. A ratio of 1 means the excess return equalled its standard deviation; above 1 is good, above 2 rare. Robo-advisers and fund selectors use it to compare portfolios and managers; it flatters strategies whose risk arrives all at once.
- Also known as
- Sharpe, Risk-adjusted return, Reward-to-variability ratio
- Used at
- fund and manager comparison, portfolio construction (robo-adviser model portfolios are optimised on it or its cousins), hedge fund marketing, and investment committee papers
- Binding
- no — a statistic, defined by William Sharpe in 1966
- Typical formula
- (portfolio return − risk-free rate) ÷ standard deviation of portfolio returns, usually on monthly returns annualised; the ratio of a broad equity index over long periods is around 0.4–0.5
- Typical failure
- strategies with steady small gains and rare large losses — selling options, some credit strategies, stablecoin yields before 2022 — show high Sharpe ratios until the loss arrives, because standard deviation does not measure what has not happened yet
- Parties
- analysts, fund selectors, robo-advisers' investment teams, and anyone comparing two investments with different risk
How the Sharpe ratio works in practice
Two portfolios returned 8% and 12% last year. The second looks better until the risk is counted: the first had a volatility of 6%, the second 20%. With a risk-free rate of 3%, the first's Sharpe ratio is (8 − 3) ÷ 6 = 0.83 and the second's is (12 − 3) ÷ 20 = 0.45. The first earned more per unit of risk; an investor who wanted the second's return could have levered the first and taken less risk to get it. That is the ratio's argument: return is only meaningful against the risk paid for it.
The ratio's assumptions are its limits. It treats upside and downside variability alike, though investors mind only one. It assumes returns are roughly normally distributed, though many strategies are not: a fund that collects a small premium every month and loses a year's gains in one week has a low measured volatility and a high Sharpe ratio right up to the week. And it depends on the period: a strategy's Sharpe over a calm three years says nothing about the next three. Variants — Sortino (downside deviation only), Calmar (return over maximum drawdown) — address the first problem; judgement addresses the rest.
For a robo-adviser the ratio is the tool for building model portfolios: allocations chosen to maximise expected excess return per unit of volatility, with the customer's risk score deciding which portfolio she gets.
Example
A robo-adviser compares two candidate "balanced" portfolios over ten years of backtested monthly data, with a 2% risk-free rate. Portfolio A (60% global equities, 40% bonds): 7.2% a year, 9.5% volatility — Sharpe 0.55. Portfolio B (50% equities, 30% bonds, 20% a "low-volatility income" strategy that sold volatility): 7.8% a year, 7.1% volatility — Sharpe 0.82. B is chosen. In its third live year a market shock costs the income strategy 35% in a month; B falls 14% against A's 9%, and B's ten-year Sharpe ratio, recomputed, is 0.48. The backtest had measured a decade in which the loss had not occurred, which is the ratio doing exactly what it does.
Common mistakes
- Comparing Sharpe ratios computed over different periods or with different risk-free rates. - Trusting a high Sharpe ratio on a strategy whose returns are not normally distributed. - Reading a backtested ratio as a forecast. - Optimising a portfolio on Sharpe and delivering a client the volatility the optimiser ignored. - Judging a single stock or a private investment on it; the ratio is for diversified, liquid returns.