Portfolio Management and Investment Analysis
Risk, return and diversification
Expected return is probability-weighted; risk is variance or standard deviation. Combining assets with correlation below +1 lowers portfolio volatility without necessarily lowering expected return. The efficient frontier shows the best return for each risk level; adding a risk-free asset produces the capital market line and the Sharpe ratio (excess return per unit of total risk).
CAPM and performance
CAPM: E(R) = Rf + beta x (Rm - Rf). Beta captures systematic risk; idiosyncratic risk is diversifiable. Performance measures: Sharpe (total risk), Treynor (beta), Jensen's alpha, and information ratio (active return divided by tracking error). Attribution splits return into allocation and selection effects.
Worked example
Fund A returns 12% with volatility 15%; Fund B returns 9% with volatility 8%; risk-free rate 3%. Sharpe A = (12 - 3) / 15 = 0.60; Sharpe B = (9 - 3) / 8 = 0.75. B ranks higher per unit of risk despite the lower raw return.
Traps
Ranking funds on raw return without risk adjustment; using beta when total risk is the right denominator; and mistaking drift in strategic asset allocation for deliberate active positioning.