Asset Management Lecture 7

Outline for today Adjustments with the precision of alpha Organization chart of the portfolio management The Black-Litterman Model

Adjusting Forecasts for the Precision of Alpha Absent of analysis, the prior of alpha = 0 A “tight” prior implies a high degree of confidence. The manager has to form a posterior distribution of alpha for portfolio construction.

Adjusting Forecasts for the Precision of Alpha How accurate is your forecast: forecasting record of analyst The realized abnormal return of time T The precision of record, t<T is the paird time series of past records Adjust

Figure 27.4 Organizational Chart for Portfolio Management

The Black-Litterman Model The model This approach uses past data equilibrium input the private “views” of the portfolio manager

The Black-Litterman Model Step 1: Estimate the covariance matrix from historical data Step 2: Determine a baseline forecast Step 3: Integrating the manager’s private views Step 4: Developing revised (posterior) expectations Step 5: Apply portfolio optimization

The Black-Litterman Model Step 1: Estimate the covariance matrix from historical data The textbook example Bonds (B)Stocks (S) SD Corr0.3 Cov Bonds Stocks

The Black-Litterman Model Step 2: Determine a baseline forecast Market is in equilibrium The market portfolio is efficient. The textbook example: W(B)=0.25 W(S)=0.75

The Black-Litterman Model Step 2: Determine a baseline forecast According to CAPM Assuming that the average risk aversion=3 E(R B ) and E(R S ) can be inferred Similarly, E(R S ) can be found as 6.81%.

The Black-Litterman Model Step 2: Determine a baseline forecast Covariance matrix: it is about the precision of the forecast, instead of the actual volatility A conventional rule-of-thumb: 10% of the realized SD (or, 1% of the realized var) Bonds (B)Stocks (S) Expected return Cov Bonds Stocks

The Black-Litterman Model Step 3: Integrating the manager’s private views The view: in the next month, bonds will outperform stocks by 0.5% The expression:

The Black-Litterman Model Step 4: Developing revised (posterior) expectations Baseline view: Bonds (B)Stocks (S) Expected return Cov Bonds Stocks

The Black-Litterman Model Step 4: Developing revised (posterior) expectations Baseline view: Bonds (B)Stocks (S) Expected return Cov Bonds Stocks

The Black-Litterman Model Step 4: Developing revised (posterior) expectations The difference D

The Black-Litterman Model Step 4: Developing revised (posterior) expectations BL Updating formulas Notice the difference has reduced to 2.60%

The Black-Litterman Model Step 5: Apply portfolio optimization Markowitz optimizor Maximize Sharpe Ratio

The Black-Litterman Model Step 1: Estimate the covariance matrix from historical data Step 2: Determine a baseline forecast Step 3: Integrating the manager’s private views Step 4: Developing revised (posterior) expectations Step 5: Apply portfolio optimization