Investments, tenth edition

  

  Bonds (  B  )  

  

  Stocks (  S  )  

 Standard deviation 

 .08  

 

 .17 

 Correlation (bonds/stocks) 

  

 .3  

 

 Covariance  

 

  

  

  Bonds 

 

.0064  

 

 .00408 

  Stocks 

 

.00408  

 

 .0289 

bod61671_ch27_951-976.indd   963

bod61671_ch27_951-976.indd   963

7/31/13   7:24 PM

7/31/13   7:24 PM

Final PDF to printer

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964 

P A R T   V I I

  Applied Portfolio Management

equilibrium risk premiums on bonds and stocks can be inferred from their betas on the 

baseline portfolio:

   E(R

B

)

5

Cov(R

B

, R

M

)

Var(R

M

)

 

E(R

M

)

Cov(R

B

, R

M

)

5 Cov(R

B

, w

B

R

B

1 w

S

R

S

)

5 .25 3 .0064 1 .75 3 .00408 5 .00466

E(R

B

)

5

.00466

.018186

3 5.46% 5 1.40% (bond beta 5 0.26)

E(R

S

)

5

.75

3 .0289 1 .25 3 .00408

.018186

3 5.46% 5 6.81% (stock beta 5 1.25)  

(27.10)

   

 Thus, step 2 ends up with baseline forecasts of a risk premium for bonds of 1.40% and for 

stocks of 6.81%. 

 The final element in step 2 is to determine the covariance matrix of the baseline fore-

casts. This is a statement about the  precision  of these forecasts, which is different from 

the covariance matrix of realized excess returns on the bond and stock portfolios. We are 

looking for the precision of the  estimate  of expected return, as opposed to the volatility of 

actual returns. A conventional rule of thumb in this application is to use a standard devia-

tion that is 10% of the standard deviation of returns (or equivalently, a variance that is 1% 

of the return variance). To illustrate, imagine that the covariance matrix of actual return 

was estimated from the returns of the last 100 months. The variance of the average return 

(which is the forecast of the expected return) would then be 1% of the variance of the 

actual return. Hence in this case it would be correct to use .01 times the covariance matrix 

of returns for the expected return. Thus step 2 ends with a forecast and covariance matrix:  

 Now that we have backed out market expectations, it is time to integrate the manager’s 

private views into our analysis.