Sharpe Ratio Calculator

Overview

The Sharpe ratio, introduced by William F. Sharpe in 1966, measures the excess return of an investment per unit of risk taken. Two portfolios with the same return are not equally good if one was wilder along the way — the Sharpe ratio penalises that volatility. Higher is better: a Sharpe of 1.0 is generally considered acceptable, 2.0 strong, and 3.0 exceptional. Most equity index funds historically deliver a Sharpe between 0.4 and 0.7 over long periods.

The calculation is intuitive: excess return divided by the standard deviation of returns. The subtlety lies in periodicity. Monthly returns produce a monthly Sharpe, which must be annualized by multiplying by √12 to match the conventional yearly figure. Daily Sharpe annualizes with √252 (trading days). Using the wrong annualization factor is the most common mistake when comparing strategies. The ratio also assumes returns are reasonably normally distributed — fat-tailed strategies (options, illiquid credit) can flatter their Sharpe by understating tail risk.

How it works

Given a series of periodic returns r_1 … r_n, the average return is μ = Σ r_i / n. The standard deviation is σ = sqrt(Σ (r_i − μ)^2 / (n − 1)). With a periodic risk-free rate r_f, the periodic Sharpe is (μ − r_f) / σ. To annualize, multiply by √(periods_per_year). For monthly data that is √12 ≈ 3.46; for daily trading-day data it is √252 ≈ 15.87. The risk-free rate is typically a short Treasury yield expressed in the same period as the returns.

Examples

• Monthly returns averaging 1% with standard deviation 4% and a 0.2% monthly risk-free rate: monthly Sharpe = (1 − 0.2) / 4 = 0.20; annualized = 0.20 × √12 ≈ 0.69.
• An equity strategy with 12% annual return and 18% annual volatility versus a 4% risk-free: Sharpe = (12 − 4) / 18 ≈ 0.44 — slightly below the broad market average.
• A market-neutral fund returning 8% with 5% volatility: Sharpe = (8 − 4) / 5 = 0.80 — comfortably above passive equity.
• A leveraged strategy producing 30% with 40% volatility: Sharpe = (30 − 4) / 40 = 0.65 — high return but no better risk-adjusted than the broad market.

FAQ

Why subtract the risk-free rate?
To isolate the reward for taking risk. Returns that merely match Treasuries are not earning a risk premium.

Is a higher Sharpe always better?
Subject to the assumption of normal returns. Strategies that sell tail risk can post high Sharpes until a fat-tail event.

How is the Sharpe different from the Sortino ratio?
Sharpe uses total standard deviation. Sortino divides only by downside deviation, ignoring upside volatility.

What period length should I use?
Match it to the strategy's actual decision frequency. Monthly is the most common reporting unit.

Can the Sharpe ratio be negative?
Yes — it goes negative when returns are below the risk-free rate, indicating the investment underperformed cash.

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