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📊 Risk Metrics

Risk metrics provide quantitative measures of portfolio risk. Each metric captures a different aspect of uncertainty, and no single metric tells the whole story. Using multiple metrics together gives a comprehensive view of portfolio risk.

📋 Comparative Overview

Metric What It Measures Formula Range Details
Sharpe Ratio Risk-adjusted return (total vol) \(\frac{R_p - R_f}{\sigma_p}\) \((-\infty, +\infty)\) 📖
Sortino Ratio Risk-adjusted return (downside only) \(\frac{R_p - R_f}{\sigma_d}\) \((-\infty, +\infty)\) 📖
Max Drawdown Worst peak-to-trough decline \(\frac{Trough - Peak}{Peak}\) \([-100\%, 0\%]\) 📖
Volatility Dispersion of returns \(\sigma = \sqrt{\text{Var}(R)}\) \([0, +\infty)\) 📖

🔑 When to Use Each Metric

Scenario Best Metric Why
Comparing two funds Sharpe Ratio Normalizes return by total risk
Asymmetric return distributions Sortino Ratio Only penalizes downside volatility
Worst-case scenario planning Max Drawdown Shows the maximum pain point
General risk assessment Volatility Foundation for all other metrics
Portfolio optimization All four Each captures a different dimension

⚠️ Common Pitfalls

Limitations

  • Historical metrics ≠ future risk: Past volatility may not predict future volatility
  • Normal distribution assumption: Sharpe and Sortino assume returns are roughly normal; financial returns have fat tails
  • Lookback sensitivity: Metrics change significantly depending on the time window
  • Benchmark dependency: Sharpe and Sortino depend on the risk-free rate, which changes over time