Investments, tenth edition

  Ticker 

Symbol     Security Name  

  BETA     ALPHA  

  RSQ  

  Residual 

Std Dev  

  Std Error 

Beta  

  Standard 

Error Alpha  

  Adjusted 

Beta  

 AMZN  

 Amazon.com  

 2.25  

0.006  

0.238  

0.1208  

0.5254  

0.0156  

1.84 

 F  

Ford  

1.64 

  2 0.012   0.183  

0.1041  

0.4525  

0.0135  

1.43 

 NEM  

Newmont Mining Corp. 

 0.44  

0.002  

0.023  

0.0853  

0.3709  

0.0110  

0.62 

 INTC  

Intel Corporation 

 1.60 

  2 0.010   0.369  

0.0627  

0.2728  

0.0081  

1.40 

 MSFT  

Microsoft Corporation 

 0.87  

0.001  

0.172  

0.0569  

0.2477  

0.0074  

0.91 

 DELL  

Dell Inc. 

 1.36 

  2 0.014   0.241  

0.0723  

0.3143  

0.0094  

1.24 

 BA  

Boeing Co. 

 1.42  

0.004  

0.402  

0.0517  

0.2250  

0.0067  

1.28 

 MCD  

McDonald’s Corp. 

 0.92  

0.016  

0.312  

0.0409  

0.1777  

0.0053  

0.95 

 PFE  

Pfizer Inc. 

 0.65 

  2 0.006   0.131  

0.0504  

0.2191  

0.0065  

0.77 

 DD  

DuPont  

0.97 

  2 0.002   0.311  

0.0434  

0.1887  

0.0056  

0.98 

 DIS  

Walt Disney Co. 

 0.91  

0.005  

0.278  

0.0440  

0.1913  

0.0057  

0.94 

 XOM  

ExxonMobil Corp. 

 0.87  

0.011  

0.216  

0.0497  

0.2159  

0.0064  

0.91 

 IBM  

IBM Corp. 

 0.88  

0.004  

0.248  

0.0459  

0.1997  

0.0059  

0.92 

 WMT  

Walmart  

0.06  

0.002  

0.002  

0.0446  

0.1941  

0.0058  

0.38 

 HNZ  

HJ Heinz Co. 

 0.43  

0.009  

0.110  

0.0368  

0.1599  

0.0048  

0.62 

 LTD  

Limited Brands Inc. 

 1.30  

0.001  

0.216  

0.0741  

0.3223  

0.0096  

1.20 

 ED  

Consolidated Edison Inc. 

 0.15  

0.004  

0.101  

0.0347  

0.1509  

0.0045  

0.43 

 GE  

General Electric Co. 

 0.65 

  2 0.002   0.173  

0.0425  

0.1850  

0.0055  

0.77 

  

 MEAN  

0.97  

0.001  

0.207  

0.0589  

0.2563  

0.0076  

0.98 

  

 STD DEVIATION 

 0.56  

0.008  

0.109  

0.0239  

0.1039  

0.0031  

0.37 

 Table 8.3 

 Market sensitivity statistics: Regressions of total stock returns on total S&P 500 returns over 60 months, 2004–2008 

 Source: Compiled from CRSP (University of Chicago) database. 

 What was Intel’s index-model  a  per month during the period covered by the  Table 8.3  regression if during 

this period the average monthly rate of return on T-bills was .2%? 

 CONCEPT CHECK 

8.4 

bod61671_ch08_256-290.indd   280

bod61671_ch08_256-290.indd   280

6/21/13   4:10 PM

6/21/13   4:10 PM

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  C H A P T E R  

8

 Index 

Models 

281

 The   Resid Std Dev  column is the standard deviation of the monthly regression  residuals, 

also sometimes called the standard error of the regression. The standard errors of the alpha 

and beta estimates allow us to evaluate the precision of the estimates. Notice that the stan-

dard errors of alpha tend to be far greater multiples of the estimated value of alpha than is 

the case for beta estimates. 

 Intel’s   Resid Std Dev 

 is 6.27% per month and its  

R  

2

 

 is .369. This tells us that 

   s

Intel

2

(e)

5 6.27

2

5 39.31  and, because  R  

2

   5  1  2   s  

2

 ( e )/ s  

2

 , we can solve for Intel’s total 

standard deviation by rearranging as follows:

 

   s

Intel

5 B

s

Intel

2

(e)

1

2 R

2

R

1/2

5 a

39.31

.631

b

1/2

5 7.89% per month   

 This is Intel’s monthly standard deviation for the sample period. Therefore, the annualized 

standard deviation for that period was 7.89    

"12 5 27.33%  .

 The last column is called Adjusted Beta. The motivation for adjusting beta estimates 

is that, on average, the beta coefficients of stocks seem to move toward 1 over time. One 

explanation for this phenomenon is intuitive. A business enterprise usually is established 

to produce a specific product or service, and a new firm may be more unconventional than 

an older one in many ways, from technology to management style. As it grows, however, a 

firm often diversifies, first expanding to similar products and later to more diverse opera-

tions. As the firm becomes more conventional, it starts to resemble the rest of the economy 

even more. Thus its beta coefficient will tend to change in the direction of 1. 

 Another explanation for this phenomenon is statistical. We know that the average beta 

over all securities is 1. Thus, before estimating the beta of a security, our best forecast 

would be that it is 1. When we estimate this beta coefficient over a particular sample 

period, we sustain some unknown sampling error of the estimated beta. The greater the dif-

ference between our beta estimate and 1, the greater is the chance that we incurred a large 

estimation error and that beta in a subsequent sample period will be closer to 1. 

 The sample estimate of the beta coefficient is the best guess for that sample period. 

Given that beta has a tendency to evolve toward 1, however, a forecast of the future beta 

coefficient should adjust the sample estimate in that direction. 

  Table 8.3  adjusts beta estimates in a simple way.  

16

   It takes the sample estimate of beta 

and averages it with 1, using weights of two-thirds and one-third:

 

 

   Adjusted beta

5