Serotoninl7

2021-11-25

You fit a CAPM that regresses the excess return of Coca-cola on the excess market return using 20 years of monthly data. You estimate .
What is the 99% confidence interval for $\beta$?

Lupe Kirkland

Step 1
Sample Statistic = Slope of Regression i.e. $\beta$
$\beta =1.37$, 99% confidence interval, $n=20$
$\alpha =1-\left(\frac{\text{Confidence interval}}{100}\right)$
$=1-\left(\frac{99}{100}\right)$
Degree of freedom $\left(df\right)=n-2$
$=20-2$
$=18$
As per the t distribution table, the critical value at df 18 is 2.552.
Standard Error or Standard Deviation $=\sqrt{19.82}=4.45197$
$\text{Margin of Error}=\text{Critical value}×\text{Standard Error}$
$=2.552×4.45197$
$=11.36142$
Step 2
Confidence Interval $=\text{Sample Statistic}±\text{Margin of Error}$
$=1.37±11.36142$
$\text{Upper Interval}=1.37+11.36412=12.73142$
$\text{Lower Interval}=1.37-11.36412=-9.99412$
Therefore, 99% confidence interval is -9.99412 to 12.73142

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