Investments, tenth edition

  Step 3: Integrating the Manager’s Private Views 

 The BL model allows the manager to introduce any number of views about the baseline 

forecasts into the optimization process. Appended to the views, the manager specifies his 

degree of confidence in them. Views in the BL model are expressed as values of various 

linear combinations of excess returns, and confidence in them as a covariance matrix of 

errors in these values.  

  

  Bonds (  B  )  

  Stocks (  S  )  

 Expected return (%) 

 .0140  

.0681 

 Covariance matrix 

of baseline forecasts 

  

  

  Bonds 

 

.000064  

.0000408 

  Stocks 

 

.0000408  

.000289 

 Suppose the manager takes a contrarian’s view concerning the baseline forecasts, that 

is, he believes that in the next month bonds will outperform stocks by .5%. The follow-

ing equation expresses this view:

   1 3 R

B

 1 (21) 3 R

S

 5 .5%  

 Example  27.1 

Views in the Black-Litterman Model 

bod61671_ch27_951-976.indd   964

bod61671_ch27_951-976.indd   964

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7/31/13   7:24 PM

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  C H A P T E R  

2 7

  The Theory of Active Portfolio Management 

965

 A view must come with a degree of confidence, that is, a standard deviation to measure 

the precision of  Q.  The manager’s view is really  Q     1   á, where á represents zero-mean 

error in the view with a standard deviation that reflects the manager’s less than perfect 

confidence. Noticing that the standard deviation of the difference between the expected 

rates on stocks and bonds is 1.65% (calculated below in Equation 27.13), suppose that the 

manager assigns a value of  s (á)  5  1.73%.  

9

   To summarize, if we denote the array of returns 

by  R   5  ( R  

 B 

 ,  R  

 S 

 ), then the manager’s view,  P,  applied to these returns is  

10

  

    PR

T

5 Q 1 e

 P

5 (1, 21)

 R

5 (R

B

, R

S

)

 Q

5 .5% 5 .005

 

 s

2

(

e) 5 .0173

2

5 .0003  

(27.11)