INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 27The Theory of Active Portfolio ManagementINVESTMENTS | BODIE, KANE, MARCUSOverview Treynor-Black model The optimization uses analysts forecasts of superior performance. The model is adjusted for tracking error and for analyst forecast error. Black-Litterman model2INVESTMENTS | BODIE, KANE, MARCUSTable 27.1 Construction and Properties of the Optimal Risky Portfolio3INVESTMENTS | BODIE, KANE, MARCUSSpreadsheet 27.1 Active Portfolio Management4INVESTMENTS | BODIE, KANE, MARCUSSpreadsheet 27.1 An active portfolio of six stocks is added to the passive market index portfolio. Table D shows: Performance increases are very modest. M-square increases by only 19 basis points.5INVESTMENTS | BODIE, KANE, MARCUSTable 27.2 Stock Prices and Analysts Target Prices for June 1, 2006Lets add these new forecasts to the spreadsheet model and re-calculate Table D.6INVESTMENTS | BODIE, KANE, MARCUSFigure 27.1 Rates of Return on the S&P 500 (GSPC) and the Six Stocks7INVESTMENTS | BODIE, KANE, MARCUSTable 27.3 The Optimal Risky Portfolio8INVESTMENTS | BODIE, KANE, MARCUSResults The Sharpe ratio increases to 2.32, a huge risk-adjusted return advantage. M-square increases to 25.53%.9INVESTMENTS | BODIE, KANE, MARCUSResults Problems: The optimal portfolio calls for extreme long/short positions that may not be feasible for a real-world portfolio manager. The portfolio is too risky and most of the risk is nonsystematic risk. A solution: Restrict extreme positions. This results in a lack of diversification. 10INVESTMENTS | BODIE, KANE, MARCUSTable 27.4 The Optimal Risky Portfolio with Constraint on the Active Portfolio (wA 1)11INVESTMENTS | BODIE, KANE, MARCUSFigure 27.2 Reduced Efficiency when Benchmark is Lowered Benchmark risk is the standard deviation of the tracking error, TE = RP-RM. Control it by restricting WA.12INVESTMENTS | BODIE, KANE, MARCUSTable 27.5 The Optimal Risky Portfolio with the Analysts New Forecasts13INVESTMENTS | BODIE, KANE, MARCUSAdjusting Forecasts for the Precision of Alpha How accurate is your forecast? Regress forecast alphas on actual, realized alphas to adjust alpha for the accuracy of the analysts previous forecasts.14INVESTMENTS | BODIE, KANE, MARCUSFigure 27.4 Organizational Chart for Portfolio Management 15INVESTMENTS | BODIE, KANE, MARCUSThe Black-Litterman Model The Black-Litterman model allows portfolio managers to incorporate complex forecasts (called “views”) into the portfolio construction process. Historical returns, even over long periods, have very limited power to infer expected returns for the next month. The business cycle and other macroeconomic variables may be better forecasters of expected returns. Historical variance is a good predictor of expected future variance.16INVESTMENTS | BODIE, KANE, MARCUSSteps in the Black-Litterman Model1. Estimate the covariance matrix from recent historical data. 2. Determine a baseline forecast. 3. Integrate the managers private views.4. Develop revised (posterior) expectations. 5. Apply portfolio optimization.17INVESTMENTS | BODIE, KANE, MARCUSFigure 27.5 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level18INVESTMENTS | BODIE, KANE, MARCUSFigure 27.6 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level19INVESTMENTS | BODIE, KANE, MARCUSBL Conclusions The Black-Litterman (BL) model and the Black-Treynor (TB) model are complements. The models are identical with respect to the optimization process and will chose identical portfolios given identical inputs. The BL model is a generalization of the TB model that allows you to have views about relative performance that cannot be used in the TB model.20INVESTMENTS | BODIE, KANE, MARCUSBL vs. TBBlack-Litterman Model Optimal portfolio weights and performance are highly sensitive to the degree of confidence in the views. The validity of the BL model rests largely upon the way in which the confidence about views is developed.Treynor-Black Model TB model is not applied in the field because it results in “wild” portfolio weights. The extreme weights are a consequence of failing to adjust alpha values to reflect forecast precision.21INVESTMENTS | BODIE, KANE, MARCUSBL vs. TBBlack-Litterman Model Use the BL model for asset allocation. Views about relative performance are useful even when the degree of confidence is inaccurately estimated.Treynor-Black Model Use the TB model for the management of security analysis with proper adjustment of alpha forecasts.22INVESTMENTS | BODIE, KANE, MARCUSValue of Active Management Kane, Marcus, and Trippi show that active management fees depend on: 1. the coefficient of risk aversion, 2. the distribution of the squared information ratio in the universe of securities, 3. t