Quantitative Methods & RiskExpectancy, Edge & Sample Size
Sharpe, Sortino & Risk-Adjusted Return
Return per unit of risk, not return alone
Two strategies that both return 15% a year are not equally good if one did it smoothly and the other rode a roller-coaster. Risk-adjusted return metrics divide excess return by some measure of the risk taken to earn it. The Sharpe ratio is the canonical example, and understanding both what it measures and what it hides is essential — a high Sharpe is genuinely attractive, but it can be manufactured and it can conceal a fat left tail.
Sharpe ratio
Sharpe = (R_p − R_f) / σ_p
Sharpe punishes upside volatility too
Sharpe uses total volatility in the denominator, so it penalizes big winning days exactly as much as big losing days. A strategy that occasionally jumps higher looks 'riskier' to Sharpe than one that grinds along and then quietly collapses. That is backwards for most investors, who fear losses far more than they fear gains.
Sortino ratio (downside deviation only)
Sortino = (R_p − R_f) / σ_down, σ_down = √(E[min(r − τ, 0)²])
SHARPE
Excess return / total vol
Simple, universal, comparable across strategies. Penalizes all volatility equally and assumes a roughly symmetric, normal return distribution.
>1 good, >2 excellent, >3 suspect
SORTINO
Excess return / downside dev
Only counts harmful (below-target) volatility. Better for skewed strategies, but the downside-deviation estimate is noisier because it uses fewer data points.
rewards positive skew
CALMAR
Return / max drawdown
Return divided by the worst peak-to-trough loss. Speaks directly to the pain an investor must survive. Very sensitive to the single worst event in the sample.
drawdown-anchored
A Sharpe above 3 should make you suspicious, not excited
Sustained Sharpe ratios above ~2–3 are extraordinarily rare in liquid markets after costs. When a backtest shows a Sharpe of 4 or 5, the overwhelmingly likely explanation is a bug, lookahead bias, or overfitting — not a discovered money machine. Treat an implausibly high Sharpe as a red flag to investigate, never as a reason to deploy capital.
Risk-adjusted return
Return expressed per unit of risk taken to achieve it, so that strategies with different volatilities can be compared fairly. Sharpe (total vol), Sortino (downside vol), and Calmar (max drawdown) are the three you will see most. Each is only as honest as its risk denominator.
Knowledge check
A strategy returns 18%, the risk-free rate is 3%, and its volatility is 30%. What is its Sharpe ratio?