Active Portfolio Management

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(RA – RB) = var(RA) + var(RB) - 2cov(RA, RB) • 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 = RA – RB • 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 • RA - RF = alpha + (beta)(RB – RF) + 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 Common Factor Risk Specific* Risk Index Risk Industry Risk *Asset Selection Risk

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

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