Active or Passive? Issues and Strategies • Market Efficiency • Anomalies • Market Timing • A theoretical model of active portfolio management (Treynor-Black) • Quantitative Investment Management
Equity Portfolio Management: Active or Passive? • Passive: • LT buy and hold • Indexation • Replication of an index (broad or specialized • Sampling and Tracking Error • = 0 • Rebalancing
Indexation • Identify a Benchmark Index • replicate benchmark index performance • a true passive strategy will not attempt to outperform index • Tracking Error = measure of accuracy
Tracking Error: Measure 1 • TE1 =where Rpt and Rbt are portfolio and benchmark returns respectively
Tracking Error: Measure 1 • TE2 = σeThis represents the standard deviation of the error terms of a regression equation explaining returns from the portfolio with returns from the benchmark. • We will revisit σe later
Rebalancing an Equity Portfolio • Why? • to manage tracking error (if indexing or not) • to maintain a desired set of weights or risk level • client needs change • Market risk level changes • bankruptcies, mergers, IPOs • Why not? • it’s costly!
Rebalancing: Example 1 • Portfolio is no longer equally weighted • To rebalance: • Sell Y, buy X and Z • Positions must be reset to $10445/3 = $3482 • Sell 4440 - 3482 = $958 of Y (48 shares) • Buy 3482 - 2672 = $810 of X (51 shares) • Buy 3482 - 3325 = $157 of Z (4 shares)
Rebalancing: Example 1 • LT effects of this strategy? • Alternatives? • Example 2: Rebalancing to reestablish a specific level of systematic risk (Target Beta = 1.2)
Rebalancing: Example 2 • Reestablishing a beta of 1.2: • No unique solution for more than 2 securities • Need to sell high stocks and buy low stocks • For example, sell Y, buy Z, hold X constant • p = (.256)(1.3)+(WY)(1.7)+(1-.256-WY)(.8) • Find Y such that p = 1.2 • WY = .302 => WZ = 1-.256-.302 = .442 • $3488 in X, $3151 in Y, $4611 in Z
Active Equity Strategies • Beat the market on a risk adjusted basis! • Need a benchmark • More expensive: turnover, research • Must outperform on a fee-adjusted basis
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‘)
Active Equity Strategies • Styles: • Sector Rotation: move in/out of sectors as economy improves/declines • Earnings Momentum: overweight stocks displaying above average earnings growth • Enhanced Index Fund - majority of funds track index, some funds are actively managed • Quantitative Investment Management