Sharpe Ratio: Definition, Formula, and Use

What the Sharpe ratio measures

The Sharpe ratio quantifies risk-adjusted return. It shows how much excess return an investment generates per unit of total volatility. A higher Sharpe indicates better risk-adjusted performance; a negative Sharpe means the risk-free rate exceeds the investment’s return (or the investment has a negative return).

Formula

Sharpe Ratio = (Rp − Rf) / σp

Where:
* Rp = portfolio (or asset) return
* Rf = risk-free rate (e.g., Treasury yield)
* σp = standard deviation of the portfolio’s excess returns

How to calculate

1. Choose a return series and consistent interval (daily, monthly, yearly).
2. For each period, compute excess return = Rp_period − Rf_period.
3. Average the excess returns to get the numerator.
4. Compute the standard deviation of the excess-return series for the denominator.
5. Divide the average excess return by that standard deviation.

Practically, analysts often use monthly returns to balance noise and data length. Be consistent in the chosen look-back period and in the risk-free rate used.

What the ratio tells you

• Compares performance while accounting for volatility: two funds with the same return but different volatility will have different Sharpe ratios.
• Helps distinguish returns driven by skill versus those resulting from taking more risk.
• Useful for comparing similar investment strategies, funds, or portfolios.

Interpretation guidelines

• Sharpe > 1: generally considered good.
• Sharpe ≈ 0–1: modest risk-adjusted returns.
• Sharpe < 0: underperforms the risk-free asset.
  Context matters: compare Sharpe ratios to peers and strategy benchmarks rather than relying on absolute thresholds alone.

Example

Initial portfolio:
* Return = 18%, risk-free rate = 3%, annualized σ = 12%
* Sharpe = (18% − 3%) / 12% = 1.25

After adding an investment:
* Projected return = 15%, projected σ = 8%
* Projected Sharpe = (15% − 3%) / 8% = 1.50

Even though absolute return falls, the risk-adjusted performance improves because volatility drops.

Limitations and pitfalls

• Measurement choices can distort results: interval length (daily vs. monthly vs. annual) and look-back period affect σ.
• Cherry-picking favorable time windows inflates Sharpe.
• Assumes returns are symmetrically distributed and volatility captures risk—this understates tail risk from skewed or fat-tailed distributions.
• Serial correlation (autocorrelation) in returns can lower measured volatility and produce misleadingly high Sharpe ratios.
• Strategies that generate steady small gains with rare large losses (the “nickels in front of a steamroller” pattern) can exhibit high Sharpe ratios until a catastrophic loss occurs.

Alternatives and complements

• Sortino ratio — replaces total standard deviation with downside deviation to focus on harmful volatility (negative returns).
• Treynor ratio — divides excess return by beta (systematic risk) rather than total volatility; suited for evaluating compensation for market-related risk.

Practical tips

• Compare Sharpe ratios only among similar strategies or asset classes.
• Use consistent intervals and risk-free rates when comparing funds.
• Combine Sharpe with other metrics (Sortino, max drawdown, stress tests) to assess tail risk and strategy robustness.
• Be wary of unusually high Sharpe values; investigate return sources and exposure to rare events.

Bottom line

The Sharpe ratio is a simple, widely used measure of risk-adjusted return. It’s most useful for comparing similar investments when calculated consistently. However, it has important limitations—particularly around tail risk and serial correlation—so it should be used alongside other risk measures and qualitative analysis.