Portfolio Management
Risk and return in combination
Portfolio return is the weighted average of asset returns, but portfolio risk is not: variance depends on weights, individual variances and covariance (or correlation). Diversification works because correlation is imperfect; risk can be eliminated entirely only when correlation is −1, and portfolio standard deviation equals the weighted average of asset standard deviations only when correlation is +1. Distinguish systematic (market, non-diversifiable) from unsystematic risk.
Asset pricing and performance
CAPM: E(Ri) = Rf + βi[E(Rm) − Rf]. Beta measures sensitivity to market movements, and portfolio beta is the weighted average of constituent betas. The security market line prices systematic risk only; the capital market line prices total risk and applies to efficient portfolios. Alpha is the gap between expected or realised return and the CAPM-required return. Performance ratios: the Sharpe ratio uses total risk (excess return ÷ standard deviation), the Treynor ratio uses beta, and the information ratio uses tracking error against a benchmark.
Traps: computing portfolio risk as a simple weighted average of standard deviations; inserting the market return instead of the market risk premium; mixing up Sharpe and Treynor; calling a high-beta stock attractive when its alpha is negative.
Worked example
Rf = 6%, E(Rm) = 12%, beta = 1.4. Required return = 6 + 1.4(6) = 14.4%. An analyst forecasts 16%, so alpha = +1.6% and the share plots above the SML - undervalued on this model. If fairly priced, it would plot exactly on the line at 14.4%.