Return per unit of shake
From Track 3 lesson 6: r_f is the anchor. From Track 3 lesson 2: σ measures volatility. Combine them and you get the most-used "risk-adjusted return" measure in finance:
Sharpe ratio = portfolio's excess return over the risk-free rate, divided by the portfolio's σ. It tells you "how much extra return did this portfolio generate per unit of risk it took?" Higher = better.
Named after William Sharpe (1990 Nobel laureate, alongside Markowitz and Merton Miller). It's the most-cited single statistic when comparing investment performance.
Why "excess return" matters
You don't compare portfolios on raw return — you compare on excess return over what you'd have earned doing nothing risky (parking money in T-bills). A 10% return when r_f is 4% gives you 6% of "extra" — that's what risk earned you. The 4% you'd have earned anyway.
So Sharpe ratio asks: "for the σ you took, did you earn enough excess return to be worth it?" The answer depends on what counts as "enough" — usually compared to other portfolios.
Sharpe ratio interpretations
Rough benchmarks (annualized):
- Sharpe < 0.5: not great. The risk wasn't well-rewarded.
- Sharpe 0.5-1.0: acceptable for many real-world portfolios.
- Sharpe 1.0-2.0: good, often excellent.
- Sharpe > 2.0: exceptional. Sometimes too good to be true (overfit, lucky, or fraudulent).
- Sharpe > 3.0 sustained: very rare; treat with skepticism.
Numbers depend on time period and methodology. Bull markets boost Sharpe ratios; bear markets crush them. Strategies that quietly accumulate small gains can show high Sharpe ratios that disappear in tail events (Madoff's fund showed unbelievably high Sharpe — turned out to be fraud).
Why Sharpe is the natural performance measure
From lesson 9-1: the Sharpe ratio is the slope of the Capital Allocation Line. Higher Sharpe portfolio = steeper CAL = better risk-return tradeoff. So Sharpe directly answers "which portfolio is closer to the efficient frontier?"
It's also scale-invariant. A portfolio that returns 6% with σ = 6% has the same Sharpe as one returning 12% with σ = 12% (assuming r_f = 0). Both deliver the same return per unit of σ. Mixing the second with r_f at 50/50 gives the same risk-return as the first.
Limitations
Sharpe assumes σ is the right measure of risk. For some assets and strategies, σ doesn't capture the full picture:
- Skewed returns. Strategies with frequent small gains and rare large losses can have high Sharpe but real tail risk (e.g., selling deep OTM options).
- Non-normal distributions. Real returns aren't normal; Sharpe under-penalizes fat-tail strategies.
- Time-varying risk. Sharpe assumes constant σ; real volatility shifts.
Variants exist — Sortino ratio (only penalizes downside σ), Calmar ratio (uses max drawdown), etc. — but Sharpe is the universal default.
The takeaway
Sharpe ratio = (R − r_f) / σ. Excess return per unit of σ. The slope of the CAL. Higher Sharpe = closer to the efficient frontier. The most-used risk-adjusted performance measure. Limitations: σ doesn't capture all risk, especially for tail-risk strategies. Despite imperfections, it's the universal benchmark for comparing portfolios.