Passive versus Active Portfolio Management • Review of Market Efficiency • Anomalies • Market Timing • A theoretical model of active portfolio management (Treynor-Black) • Quantitative Investment Management
Passive Management • Buy and Hold • Indexation • Active management must beat these strategies on a net risk adjusted return basis! • What if markets are efficient?
Treynor-Black Model • Suppose you can identify securities that you expect to outperform (or underperform) on a risk-adjusted basis • How do you exploit this model?
Treynor-Black Model: Assumptions • Analysts can only produce quality analysis on a small number of securities • There is a passive market portfolio (M) • Forecasts of return (E(rM) and risk (s) exist • Determine abnormal return (a) for analyzed securities • Find optimal weights of analyzed securities to create active component (A) • Combine A, M and risk-free asset to achieve efficiency
Treynor-Black: Construction (Step 1) • Assume: ri = rf + bi(rM - rf) + ei • For analyzed security k: rk = rf + bk(rM - rf) + ek + ak => estimate ak, bk, s2(ek) • To construct A: wk = (ak/s2(ek))/(S[ai/s2(ei)]) => determine aA, bA, s2(eA)
Treynor-Black: Construction (Step 2) • w0 = (aA/s2(eA))/[(E(rM)-rf)/s2M] • w* = w0/(1+(1-A)w0) • w0 is the proportion of A in the new, enhanced market portfolio (M‘)