Suppose that it is now January 1993. Consider the following regression for the standard CAPM for

Suppose that it is now January 1993. Consider the following regression for the standard CAPM β for the returns on a stock

(5.67)

where rgt and rMt are excess returns on Glaxo shares and on a market portfolio, respectively. Suppose that you are interested in estimating beta using monthly data from 1981 to 1992, to aid a stock selection decision. Another researcher expresses concern that the October 1987 stock market crash fundamentally altered the risk–return relationship.

Test this conjecture using a Chow test. The model for each sub-period is 1981M1−1987M10 1987M11–1992M12 (5.69)
1981M1–1992M12 (5.70)
The null hypothesis is where the subscripts 1 and 2 denote the parameters for the first and second sub-samples, respectively. The test statistic will be given by (5.71)
The test statistic should be compared with a 5%, F(2, 140) = 3.06. H0 is rejected at the 5% level and hence it is concluded that the restriction that the coefficients are the same in the two periods cannot be employed. The appropriate modelling response would probably be to employ only the second part of the data in estimating the CAPM beta relevant for investment decisions made in early 1993.