Risk & Performance
Sharpe Ratio
A risk-adjusted return measure showing excess return earned per unit of volatility, comparing investments fairly.
Formula
Variables
Rₚ- Portfolio return
Rf- Risk-free rate
σₚ- Portfolio standard deviation (volatility)
Worked Example
Scenario: Portfolio returning 9% with 10% volatility, risk-free rate 4%, has Sharpe ratio = (9% − 4%) ÷ 10% = 0.50.
- Identify portfolio return: 9%
- Identify risk-free rate: 4%
- Calculate excess return: 9% − 4% = 5%
- Identify portfolio volatility: 10%
- Divide: 5% ÷ 10% = 0.50
When to Use This Formula
- Compare risk-adjusted returns of multiple investments
- Evaluate fund performance fairly
- Account for volatility when comparing strategies
Limitations & Assumptions
- Penalizes upside volatility equally with downside
- Non-normal returns can hide tail risk
- Omits drawdown, leverage, and liquidity considerations
- Choice of risk-free rate affects results
Common Questions
What is a good Sharpe ratio?
No universal cutoff exists. Higher is better, but compare within similar asset classes and time periods. 1.0+ is generally considered strong.
Why does it penalize upside?
Because standard deviation measures total variability; a portfolio with big wins and big losses has high volatility regardless of direction.
Measuring return and risk
- Sortino ratio formulaFormula
- Maximum drawdown formulaFormula
- Profit factor formulaFormula
- Win rate formulaFormula
- Risk-reward ratio formulaFormula
Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.