Risk-Adjusted Performance
- Risk Management
The performance notes compare return with the risk taken to earn it. The Sharpe ratio uses excess return divided by volatility, while beta measures sensitivity to a common market factor. The capital asset pricing model summarizes the factor relation as
$$\mathbb E[R_i]-R_f=\beta_i\bigl(\mathbb E[R_m]-R_f\bigr).$$
The class also discusses relative measures and the danger of ranking portfolios without matching their horizons or benchmarks. A high raw return can be a poor outcome if it came from concentrated or illiquid exposure. Risk-adjusted performance is therefore a comparison of both payoff and distribution, not a replacement for understanding the position itself.