Investments, tenth edition

  Distribution of Alpha Values 

 Equation 27.7 implies that the quality 

of security analysts’ forecasts, as mea-

sured by the  R -square in regressions of 

realized abnormal returns on their fore-

casts, is a critical issue for construction 

of optimal portfolios and resultant per-

formance. Unfortunately, these num-

bers are usually impossible to come by. 

 Kane,  Kim,  and  White  

5

    obtained  a 

unique database of analysts’ forecasts 

from an investment company specializ-

ing in large stocks with the S&P 500 as 

a benchmark portfolio. Their database 

includes a set of 37 monthly pairs of 

forecasts of alpha and beta values for 

between 646 and 771 stocks over the 

period December 1992 to December 

1995—in all, 23,902 forecasts. The 

investment company policy was to 

truncate alpha forecasts at  1 14%  and 

 2 12% per month.  

6

    The  histogram  of 

these forecasts is shown in  Figure 27.3 . Returns of large stocks over these years were about 

average, as shown in the following table, including one average year (1993), one bad year 

(1994), and one good year (1995):    

 The histogram shows that the distribution of alpha forecasts was positively skewed, 

with a larger number of pessimistic forecasts. The adjusted  R -square in a regression of 

these forecasts with actual alphas was .001134, implying a tiny correlation coefficient of 

.0337. As it turned out, the optimistic forecasts were of superior quality to the pessimistic 

ones. When the regression allowed separate coefficients for positive and negative fore-

casts, the  R -square increased to .001536, and the correlation coefficient to .0392. 

 These results contain “good” and “bad” news. The “good” news is that after adjusting 

even the wildest forecast, say, an alpha of 12% for the next month, the value to be used by 

a forecaster when  R -square is .001 would be .012%, just 1.2 basis points per month. On 

an annual basis, this would amount to .14%, which is of the order of the alpha forecasts 

of the example in  Spreadsheet 27.1 . With forecasts of this small magnitude, the problem 

of extreme portfolio weights would never arise. The bad news arises from the same data: 

the performance of the active portfolio will be no better than in our example—implying an 

 M -square of only 19 basis points. 

 An investment company that delivers such limited performance will not be able to cover 

its cost. However, this performance is based on an active portfolio that includes only six 

 Figure 27.3 

Histogram of alpha forecast  

−15

−10

−5

0

5

10

15

0

4,000

3,000

2,000

1,000

6,000

5,000

7,000