NE, MARCUS
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Table 27.4 The Optimal Risky Portfolio with Constraint on the Active Portfolio (wA ≤1)
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• How accurate is your forecast?
• Regress forecast alphas on actual, realized alphas to adjust alpha for the accuracy of the analysts’ previous forecasts.
• 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.
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Table 27.5 The Optimal Risky Portfolio with the Analysts’ New Forecasts
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Adjusting Forecasts for the Precision of Alpha
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Steps in the Black-Litterman Model
1. Estimate the covariance matrix from recent historical data.
2. Determine a baseline forecast.
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Figure 27.4 Organizational Chart for Portfolio Management
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The Black-Litterman Model
CHAPTER 27
The Theory of Active Portfolio Management
McGraw-Hill/Irwin
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Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
Treynor-Black Model
• Use the TB model for the management of security analysis with proper adjustment of alpha forecasts.
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BL 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.
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Figure 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.
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Figure 27.5 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level
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Figure 27.6 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level
• Table D shows:
– Performance increases are very modest. – M-square increases by only 19 basis points.
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Table 27.2 Stock Prices and Analysts’ Target Prices for June 1, 2006
• Black-Litterman model
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Table 27.1 Construction and Properties of the Optimal Risky Portfolio
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Let’s add these new forecasts to the spreadsheet model and re-calculate Table D.
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Figure 27.1 Rates of Return on the S&P 500 (GSPC) and the Six Stocks
information ratio in the universe of securities, 3.the precision of the security analysts.
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Overview
• Treynor-Black model – The optimization uses analysts’ forecasts of superior performance. – The model is adjusted for tracking error and for analyst forecast error.
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Value 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
3. Integrate the manager’s private views.
4. Develop revised (posterior) expectations.
5. Apply portfolio optimization.
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• The business cycle and other macroeconomic variables may be better forecasters of expected returns.
• Historical variance is a good predictor of expected future variance.
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BL vs. TB
Black-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
• 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.
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Table 27.3 The Optimal Risky Portfolio
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Results
• The Sharpe ratio increases to 2.32, a huge risk-adjusted return advantage.
– 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.