Active Portfolio Management Joel R. Barber Department of Finance, BA 205A Florida International University

Style Set of exposures to common factors Determined by regressing portfolio return on common factors Regression coefficients called manager’s style Standard deviation of residual called residual risk

Benchmark Return on index matched to investor’s style or Return on passive portfolio matched to investor’s style

Tracking Error Standard deviation of difference between active and benchmark portfolio returns var(R A – R B ) = var(R A ) + var(R B ) - 2cov(R A, R B ) Sometimes used to measures active risk An indexed portfolio has minimum tracking error with respect to index

Performance Alpha Historical – –difference between historical returns on active and passive portfolio with same style –Alpha = R A – R B –Positive average alpha indication of superior performance –Always possible to achieve zero alpha through passive strategy

Alpha Continued Predicted alpha Jensen’s alpha –Determined by regressing excess return on excess market return –R A - R F = alpha + (beta)(R B – R F ) + residual –Equals performance alpha with respect to market benchmark for a portfolio

Passive Management Simple strategy –Diversified –Does not rely on superior information Examples –Indexing –Matching portfolio to investor’s style Characteristics –Constant portfolio weights –Small residual variance

BARRA Risk Decomposition Total risk –Common Factor: common to all assets –Specific risk factor: uncorrelated with specific risk of other assets Default decomposition

Total Risk Specific* Risk Common Factor Risk Index Risk Industry Risk *Asset Selection Risk

DecompositionVarianceStandard Dev. 1. Specific Risk36.80 Common Factor 2. Indexes Industries xCOV(51.80) Total Common Total Risk196.67

Systematic-Residual Risk Systematic Risk (Market Timing) - risk associated with market portfolio Residual Risk – risk of component uncorrelated with the market portfolio Select (settings window) –Market: S&P500 –Benchmark: none

Total Risk Systematic* Risk Residual Risk Residual Common Specific Risk *Market Timing Risk

DecompositionVarianceStandard Dev. 1. Residual Specific Risk32.74 Residual Common Factor 2. Indexes Industries xCOV(2.34) 5. Total Residual Common Total Residual Systematic 8. Total Risk

Active Risk Decomposition Benchmark risk – risk associated with benchmark Active risk – risk associated with deviations from benchmark Select – market: none – benchmark: S&P500

Total Risk Benchmark Risk Active Risk* Active Common Specific Risk *Tracking error. Variances do not add