The Problem With Raw Returns
Comparing investment returns without accounting for risk is misleading. A fund returning 20% per year sounds impressive — but if it achieves that by taking twice the market's volatility, it may actually be delivering inferior performance on a risk-adjusted basis. A more cautious fund returning 10% with half the volatility might be generating exactly the same quality of return while exposing its investors to far less risk.
William Sharpe addressed this directly in his 1966 paper "Mutual Fund Performance," published in the Journal of Business. Sharpe wanted a single number that could rank mutual funds on the quality of their returns, not just their magnitude. The ratio he proposed has borne his name ever since.
The Sharpe Ratio Formula
The Sharpe ratio is:
Sharpe = (Portfolio Return − Risk-Free Rate) / Standard Deviation of Portfolio Returns
The numerator is the excess return — the return above what you could have earned with no risk at all (proxied by the short-term government bill rate). The denominator is the standard deviation of portfolio returns, measuring how much the portfolio's returns vary from period to period.
A worked example: Fund A returns 12% per year with a standard deviation of 20%, and the risk-free rate is 4%. Sharpe = (12 − 4) / 20 = 0.40. Fund B returns 8% per year with a standard deviation of 7%. Sharpe = (8 − 4) / 7 = 0.57. Despite Fund B's lower absolute return, it delivers better risk-adjusted performance: it earns more excess return per unit of volatility accepted.
The Sharpe ratio can be negative when the portfolio return falls below the risk-free rate — a fund that returns 3% when bills yield 4% has a negative Sharpe ratio, meaning the investor would have been better off holding cash.
Historical Benchmarks
Understanding whether a Sharpe ratio is "good" requires context. Over long historical periods, broad equity market indices have produced Sharpe ratios of roughly 0.3 to 0.5. The US stock market over the 20th century produced a Sharpe ratio of approximately 0.4. A fund producing a Sharpe ratio of 0.7 or above consistently over many years would be considered an exceptional performer.
Hedge funds often advertise high Sharpe ratios, but these figures can be misleading. Some strategies mechanically inflate the Sharpe ratio by generating steady small gains while hiding large tail risks that have not yet materialised in the measurement period. Bernie Madoff's fabricated returns, for instance, showed an implausibly smooth and high Sharpe ratio — one that should have raised suspicion rather than confidence.
Using the Sharpe Ratio in Practice
The Sharpe ratio is most useful for comparing similar strategies over the same time period, using the same risk-free rate and the same return measurement frequency. It is commonly calculated using monthly returns (annualised by multiplying the monthly Sharpe by √12) or daily returns. The choice of measurement frequency can meaningfully affect the result, particularly for strategies with autocorrelated returns.
Sharpe ratios should be compared only between strategies with broadly similar return distributions. For strategies that use options, leverage, or complex derivatives, the standard deviation in the denominator may substantially understate the true risk — the Sharpe ratio will look better than the strategy's actual risk profile warrants.