Sharpe Ratio Calculator

The Sharpe ratio asks how much excess return a portfolio delivered for each unit of volatility it imposed. The numerator is the return above a risk-free alternative, because an investor can always hold Treasury bills without variance, so only the increment above that rate is compensation for risk. The denominator is the standard deviation of the same return series, annualised by multiplying a monthly figure by the square root of 12 or a daily figure by the square root of 252. Both terms must cover the same period and currency. Conventional readings put a ratio under 0.5 as weak, 0.5 to 1.0 as ordinary and typical of a broad index fund, 1.0 to 2.0 as good, and above 2.0 as rare over long horizons; the S&P 500 has run near 0.4 to 0.5 across multi-decade periods. The related measures on this page vary the denominator. Sortino divides by downside deviation only, on the argument that upside volatility is not a harm; the approximation used here takes downside deviation as about 70 percent of total standard deviation, which suits roughly symmetric distributions but not skewed ones. Treynor divides by beta, isolating market risk and therefore suiting well-diversified portfolios. The Information ratio divides active return by tracking error, measuring skill against a benchmark. M-squared restates the Sharpe ratio as a percentage return by levering the portfolio to benchmark volatility. All of them inherit the same weaknesses: they assume approximately normal returns, they are sensitive to the window chosen, and strategies that sell tail risk can post high ratios for years before a single loss reverses them. Three to five years of monthly data is the usual minimum for a meaningful estimate.

William F. Sharpe introduced the measure in a 1966 article on mutual fund performance in the Journal of Business, where he called it the reward-to-variability ratio and used it to rank 34 funds. It followed directly from his work on the capital asset pricing model, which established that investors should be paid for bearing non-diversifiable risk, and it gave a practical way to score managers on that basis. Sharpe shared the 1990 Nobel prize in economics with Harry Markowitz and Merton Miller. Other names attached to the ratio, and in a 1994 article in the Journal of Portfolio Management Sharpe revisited it, generalising the numerator from an absolute risk-free rate to the return differential against any chosen benchmark and separating ex-ante from ex-post versions. The measure arrived alongside close relatives. Jack Treynor had proposed dividing excess return by beta in 1965, and Michael Jensen introduced his alpha in 1968, so by the end of the decade fund evaluation had a full toolkit. Frank Sortino argued through the 1980s that punishing upside deviation was wrong and popularised the downside-deviation variant that carries his name. Franco Modigliani and his granddaughter Leah Modigliani published the risk-adjusted performance measure now called M-squared in the Journal of Portfolio Management in 1997, expressing the same information in percentage terms for readers who found ratios unintuitive. Sharpe himself later cautioned that the ratio is unreliable for strategies with option-like or highly skewed payoffs.