Reference no: EM132698657

Question B1
In the paper on the "Overreaction Hypothesis and the UK Stock Market" by Clare and Thomas (1995), the authors employed monthly UK stock returns from January 1955 to December 1990 on all firms traded on the London Stock exchange to run a regression

‾R_D,t = α+ et

where ‾R_D,t = ‾R^L_p,t - ‾R^W_p,t ‾R denotes the monthly average excess return over the stock market and t denotes the 18 independent tracking periods. R pa and R pa are the loser's and winner's portfolio returns respectively.

(a) State the overreaction hypothesis and how can one use regression (B 1-1) to test for the overreaction hypothesis?

(b) Suppose the loser stocks are generally more risky, explain the drawback of using regression (B 1-1) when testing the overreaction hypothesis. How would you correct for it?

Using the data employed by Clare and Thomas (1995), suppose you are interested in analyzing whether there are quarterly return differences between the loser and winner portfolios. You estimated the following regression by OLS:
R_D,t = α + β₁Q_1,t + β₂Q_2,t + β₃Q_3,t + e_t.

where R_D,t = R^L_p,t - R^w_p,t, R denotes monthly excess return over the stock market, Q_i is a dummy variable for i=1, 2 and 3 such that Q_i= 1 if return is in the i-th quarter and 0 otherwise.

The result is

α^{^} = 0.02, β^{^}₁ = 0.01, β^₂ = -0.005, β^₃ = 0.03, RSS = 680.0

(c) What is the difference in the mean return between the first and second quarter?

(d) Now define a fourth quarter dummy as Q_4,t= 1 if return is in the fourth quarter and 0 otherwise. Suppose you drop the first quarter dummy from regression (B 1-2) and include the fourth quarter dummy instead such that

R_D,t= α+ β^{^}₄Q_4,t+ β₂Q_2,t + β₃Q_3,t+e_t.

What will the estimated value of α, β₄, β₂, β₃, now be? [4]

(e) Can one run the following regression

R_D,t = ∑⁴_i=1β_iQ_i,t + u_t

to analyse whether there are quarterly return differences between the loser and winner portfolio? Explain.

Question B2

In the paper by Terence C. Mills and Alessandra G. Mills (1991) on "The International Transmission of Bond Market Movements", they investigate the relationships between the government bond yield of four countries, namely the US, the UK, West Germany (WG) and Japan. Mills and Mills (1991) performed unit root tests on each of the four countries bond yield and found the yield to be an I(1) process. They also performed a cointegration test on all four countries bond yield but failed to find any cointegrating relationships amongst them. They then estimated a Vector Autoregression (VAR) of lag order 8. To generate variance decompositions from their model, they considered two Cholesky orderings: the first ordering (I) is (US, UK, WG, Japan) and the second ordering (II) is (Japan, UK, WG, US).

(a) What is the pre-requisite of the variables for a cointegration relationship to exist between them?

(b) Suppose you believe that the US and UK bond prices possess a long-run relationship. Explain how you can undertake a formal test on this conjecture.

(c) Write out the system of four regressions involving the four countries bond yield. For purpose of exposition and simplicity of notation, use only one 1 lag and let ri denote the yield for country i = US, UK, WG and JP.

(d) What is the rationale of using the second ordering when presenting the impulse responses results?