How do you calculate the Sharpe ratio?

The formula

Sharpe = (R_p − R_f) / σ_p

Where:

• R_p = portfolio return (annualized)
• R_f = risk-free rate (typically 3-month Treasury)
• σ_p = portfolio standard deviation (annualized)

Worked example

A portfolio returns 12% per year with 15% volatility. Risk-free rate is 4%.

Sharpe = (0.12 − 0.04) / 0.15 = 0.08 / 0.15 = 0.53

That's mediocre. The portfolio earned only 53 cents of excess return for every dollar of risk taken.

Interpretation

• Below 0: worse than risk-free assets (cash)
• 0, 1: sub-par, you weren't compensated for the risk
• 1, 2: good
• 2, 3: very good
• 3+: exceptional (and usually unsustainable)

Historical Sharpe ratios (annualized, long-term)

• S&P 500 index: ~0.4-0.5
• Global 60/40 portfolio: ~0.4
• Top-tier hedge funds: 0.8-1.5
• Renaissance Medallion Fund: reportedly ~2.5+

Why it matters

Sharpe ratio lets you compare portfolios with different risk profiles. A 15% return with 30% volatility is worse than a 10% return with 8% volatility, Sharpe makes this explicit.

Limitations

• Assumes returns are normally distributed (they aren't, fat tails matter)
• Penalizes upside volatility the same as downside
• Use Sortino ratio if you only care about downside risk
• Use Calmar ratio if you care about max drawdown
• Short periods give unstable Sharpe estimates, require 5+ years of data