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

2. 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

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

4. 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

5. 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

6. 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

7. 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

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

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

10. DecompositionVarianceStandard Dev. 1. Specific Risk36.80 Common Factor 2. Indexes18.41 3. Industries193.24 4. 2xCOV(51.80) Total Common159.87 Total Risk196.67

11. 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

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

13. DecompositionVarianceStandard Dev. 1. Residual Specific Risk32.74 Residual Common Factor 2. Indexes5.57 3. Industries7.13 4. 2xCOV(2.34) 5. Total Residual Common10.38 6. Total Residual43.11 7. Systematic 8. Total Risk 153.56 196.67

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

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