(a) Explain the term ‘parameter structural stability’?

(b) A financial econometrician thinks that the stock market crash of October 1987 fundamentally changed the risk–return relationship given by the CAPM equation. He decides to test this hypothesis using a Chow test. The model is estimated using monthly data from January 1981–December 1995, and then two separate regressions are run for the sub-periods corresponding to data before and after the crash. The model is

(5.85)

so that the excess return on a security at time t is regressed upon the excess return on a proxy for the market portfolio at time t. The results for the three models estimated for a given stock are as follows:

1981M1–1995M12

(5.86)

1981M1–1987M10

(5.87)

1987M11–1995M12

(5.88)

(c) What are the null and alternative hypotheses that are being tested here, in terms of α and β?

(d) Perform the test. What is your conclusion?