Investments, tenth edition

  

  1993  

  1994  

  1995  

  1926–1999 Average  

  SD (%)  

 Rate of return, % 

 9.87  

1.29  

37.71  

12.50  

20.39 

5

 Alex Kane, Tae-Hwan Kim, and Halbert White, “Active Portfolio Management: The Power of the Treynor-Black 

Model,” in  Progress in Financial Market Research,  ed. C. Kyrtsou (New York: Nova, 2004). 

6

 These constraints on forecasts make sense because on an annual basis they imply a stock would rise by more 

than 380% or fall below 22% of its beginning-of-year value. 

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  C H A P T E R  

2 7

  The Theory of Active Portfolio Management 

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stocks. As we show in Section 27.5, even small information ratios of individual stocks can 

add up (see line 11 in  Table 27.1 ). Thus, when many forecasts of even low precision are 

used to form a large active portfolio, large profits can be made. 

 So far we have assumed that forecast errors of various stocks are independent, an 

assumption that may not be valid. When forecasts are correlated across stocks, precision 

is measured by a covariance matrix of forecasting errors, which can be estimated from 

past forecasts. While the necessary adjustment to the forecasts in this case is algebraically 

messy, it is just a technical detail. As we might guess, correlations among forecast errors 

will call for us to further shrink the adjusted forecasts toward zero.