Investments, tenth edition

  The Estimate of Beta 

 The regression output in  Table 8.1  shows the beta estimate for HP to be 2.0348, more than 

twice that of the S&P 500. Such high market sensitivity is not unusual for technology 

stocks. The standard error (SE) of the estimate is .2547.  

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 The value of beta and its SE produce a large  t -statistic (7.9888), and a  p -value of prac-

tically zero. We can confidently reject the hypothesis that HP’s true beta is zero. A more 

interesting  t -statistic might test a null hypothesis that HP’s beta is greater than the market-

wide average beta of 1. This  t -statistic would measure how many standard errors separate 

the estimated beta from a hypothesized value of 1. Here too, the difference is easily large 

enough to achieve statistical significance:

   

Estimated value

2 Hypothesized value

Standard error

5

2.03

2 1

.2547

5 4.00  

 However, we should bear in mind that even here, precision is not what we might like it to 

be. For example, if we wanted to construct a confidence interval that includes the true but 

unobserved value of beta with 95% probability, we would take the estimated value as the 

center of the interval and then add and subtract about two standard errors. This produces a 

range between 1.43 and 2.53, which is quite wide.