Portfolio Construction and Performance Evaluation
Core concepts
Construction combines asset selection and weighting under constraints. Know the efficient frontier, the capital market line, and the Sharpe ratio as the reward-to-total-risk measure. Distinguish risk-adjusted measures: Sharpe (excess return / total SD), Treynor (excess return / beta), Jensen's alpha (actual return − CAPM-required return), and M² (Sharpe-based, expressed as a return). Understand attribution: allocation effect (asset-class weighting) vs. selection effect (security picking within classes).
Traps
- Use Sharpe when the portfolio is the investor's entire holding; use Treynor/Jensen when it is one component of a diversified portfolio (systematic risk is the relevant risk).
- Jensen's alpha sign is easy to invert: alpha = Rp − [Rf + beta(Rm − Rf)].
- Attribution signs: a positive allocation effect requires overweighting an asset class that outperformed, or underweighting one that underperformed.
- M² is a percentage return, not a ratio-distractors may present it as dimensionless.
- Comparing managers with different risk levels using raw returns is misleading; use risk-adjusted measures.
Worked example
Portfolio return 12%, beta 1.2, Rf 3%, market return 10%. CAPM required return = 3 + 1.2(10 − 3) = 3 + 8.4 = 11.4%. Jensen's alpha = 12 − 11.4 = +0.6%. Sharpe = (12 − 3)/portfolio SD; if SD = 15%, Sharpe = 0.60. Treynor = (12 − 3)/1.2 = 7.5%. Each measure answers a different question-total risk vs. systematic risk-so match the measure to the context.
Rule of thumb
If the portfolio represents all the investor's wealth, total risk matters (Sharpe, M²). If it is one sleeve of a diversified whole, only systematic risk matters (Treynor, Jensen's alpha).