Reference no: EM133140441

ECOM053 Quantitative Methods in Finance - Queen Mary University of London

Section A

Question 1

a) What is perfect multicollinearity, and what is the implication of ignoring it?

b) What is near multicollinearity, and what is the implication of ignoring it?

c) How should near multicollinearity be dealt with?

Question 2

a) Write the mathematical formula for each of the following models: Moving Average model, Autoregressive model, and ARMA model.

b) What is the definition of a weakly stationary process?

c) Consider the following graph:

Does this series look like it is stationary? Explain your answer.

Question 3

a) What are three advantages of constructing a panel of data?

b) Give an example of a balanced panel and an example of an unbalanced panel.

c) What are the three estimators that can be used to estimate a Fixed Effects model?

d) Which of these three estimators for the Fixed Effects model is/are most efficient?

Section B

Question 4

Consider the following model:

y_t = β₀ + β₁x_1t + β₂x_2t + β₃x_3t + β₃x_3t + u_t

a) You decide to test the null hypothesis H₀: β₁ + β₂ + β₃ = 1. Write down the alternative hypothesis.

b) Following up on part 4(a) above, you conduct the test by running an Ordinary Least Squares regression on a sample of 200 observations. The sum of squared residuals (SSR) for the two models used to calculate the necessary test statistic are 305 and 300, respectively. Calculate the test statistic and state whether the null hypothesis is rejected or not at the 5% significance level. You can find the necessary statistical tables in the appendix at the end of the exam paper.

c) Explain under what circumstances a hypothesis test could be performed using either an F-test or a t-test.

d) Could the F-statistic be negative? Justify your answer.

Question 5

A researcher wants to test whether 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 1979 to December 1996 and then two separate regressions are run for the sub-periods corresponding to data before and after the crash. The model is:

r_t = α + βRM_t + u_t,

so the excess return on a security at time t is regressed on the excess return on a proxy for the market portfolio at time t.

a) Explain what we mean by ‘parameter structural stability'.

b) Now you estimate the CAPM model for the British Airways stock, for three time periods separately. You obtain the following three sets of results from these three respective estimations:

Dates: 1979M1 - 1987M10;

Estimated model:

0.0163 + 1.308RM t

T = 106, SSR = 0.1

Dates: 1987M11 - 1996M12
Estimated model: 0.0360 ?1.613RM_t
T = 110, SSR = 0.2

Dates: 1979M1 - 1996M12
Estimated model: 0.0215 ? 1.491RM t
T = 216, SSR = 0.4

Calculate the test statistic for the Chow test.

c) Following up on part 5(b) above, do you reject or not the null hypothesis of parameter stability? You can find the necessary statistical tables in the appendix at the end of the exam paper.

Question 6

You estimate via Ordinary Least Squares the model . Using 400 monthly observations, the results are given below:

Table 1: OLS estimates using 400 observations, Dependent variable: y

a) What is the interpretation of ? Calculate for Table 1, assuming you know the sum of squared residuals and explained sum of squares are 20,500 and 4,000, respectively.

b) Do you reject the null hypothesis that at the 5% significance level? Justify your answer by using information in Table 1.

c) Assume you add a new variable, z, to the set of regressors. Results are given below in Table 2. What conclusion can be drawn?