CAS Exam 9 Spring 2016, Question 9
Study guide: Exam 9
An actuary is testing the expected return-beta relationship implied by the Capital Asset Pricing Model (CAPM) using a two-step regression procedure. To run the regression, the actuary collected monthly rates of return on various stocks, the S&P 500 index, and 1-month (risk-free) T-bills over a five-year sample period.
The first-pass estimates were used as inputs for the following second-pass regression:
\overline{r_i - r_f} = \gamma_0 + \gamma_1 b_i + \gamma_2 \sigma^2(e_i)
The second-pass regression produced the following coefficients:
| Coefficient | Statistically Significant? |
|---|---|
\gamma_0 = 0.003 |
No |
\gamma_1 = 0.175 |
Yes |
\gamma_2 = 0.300 |
Yes |
The market risk premium is 9%.
Part a (1.5 points)
Briefly describe what each coefficient represents and, using the information above, assess whether or not each coefficient is consistent with CAPM.
Part b (0.5 points)
Briefly describe two criticisms with this regression approach for testing CAPM.
No current syllabus covers this question; it is kept for the record.
Answer this question and see the worked solution