Investments, tenth edition

  Step 1: The Covariance Matrix from Historical Data 

 This straightforward task is the first in the chain that makes up the BL model. Suppose 

step 1 results in the following annualized covariance matrix, estimated from recent his-

torical excess returns:  

 Notice that step 1 is common to both the BL and the Treynor-Black (TB) models. This 

activity appears in the organizational chart in  Figure 27.4 .  

  Step 2: Determination of a Baseline Forecast 

 Because past data are of such limited use in inferring expected returns for the next month, 

BL propose an alternative approach. They start with a    baseline  forecast    derived from the 

assumption that the market is in equilibrium where current prices of stocks and bonds 

reflect all available information and, as a result, the theoretical market portfolio with 

weights equal to market-value proportions is efficient. Suppose that current market values 

of outstanding bonds and stocks imply that the weight of bonds in the baseline portfolio is 

 w  

 B 

   5  .25, and the weight of stocks is  w  

 S 

   5  .75. When we apply these portfolio weights to 

the covariance matrix from step 1, the variance of the baseline portfolio emerges as

 

    Var(R

M

)

5 w

B

2

 Var(R

B

)

1 w

S

2

 Var(R

S

)

1 2w

B

w

S

 Cov(R

B

, R

S

) (27.8)

 

5 .25

2

3 .0064 3 .75

2

3 .0289 1 2 3 .25 3 .75 3 .00408 5 .018186    

 The CAPM equation (Equation 9.2 in Chapter 9) gives the relationship between the 

market portfolio risk (variance) and its risk premium (expected excess return) as

 

   E(R

M

)

5 A 3 Var(R

M

) 

 (27.9)   

 where     A  is the average coefficient of risk aversion. Assuming    A

5 3  yields the equilibrium 

risk premium of the baseline portfolio as:  E ( R  

 M 

 )  5  3  3  .018186  5  .0546  5  5.46%.  The