Reference no: EM133140433

ECOM053 Quantitative Methods in Finance - Queen Mary University of London

Question 1: An investor models the excess return for Amazon via the market model. Suppose that the sample size is 102 observations, the value of β^{^} for Amazon is β^{^} = 1.107, the standard error associated with the coefficient β^{^} is SE(β^{^}) = 0.0348. She tests the null hypotheses that the value of the stock's beta is one, against a one-sided alternative that the stock's beta is greater than the market's beta. The level of significance is 5%.

1. Write down the regression model which uses the market model's factors as explanatory variables and define the variables.

2. Write down the null and the alternative hypothesis.

3. Conduct the test. What do you conclude? Are the analyst's claims empirically verified? You can find the t-test's critical values in Table A1 in the Appendix at the end of the exam paper.

4. The analyst also tells you that shares in Chris Mining PLC have no systematic risk, in the sense that the returns on its shares are completely unrelated to movements in the market. The value of beta and its standard error are calculated to be 0.5 and 0.25, respectively, and the model is estimated using 52 observations. Write down the null and alternative hypothesis. Form and interpret a 95% and a 99% confidence interval for beta. You can find the t-test's critical values in Table A1 in the Appendix at the end of the exam paper.

5. Do the tested hypotheses concern the values of the coefficients (i.e. β), or their estimated values (i.e. β^{^}, and why?

Question 2
Consider the following model:

Y_t =  α^{^} + β^{^}X_t + e^_t, Equation (1)

where α^ and β^{^} denote the estimates of the line intercept α and slope β, respectively.

Given the following data:

Y: 11 14 20 19 20

X: 1 2 3 4 5

Calculate the OLS estimates for the simple linear model in equation (1).

Estimate the standard error of the regression in equation (1).

Compute the regression's and test whether this is significantly different from zero at 5% and 1% statistical significance levels.

The 5% critical value of the F-distribution is 10.128.
The 1% critical value of the F-distribution is 34.116.

Question 3

Why is it desirable to conduct Monte Carlo simulations using as many replications of the experiment as possible?

Explain in detail how pseudo-random numbers are generated in Excel.

In which range of numbers do we expect the random numbers drawn from a standard normal distribution to fall? Explain why.

Marcus is 45-year old. He has a new job and intends to save £10,000 today and in each of the next 14 years (15 deposits altogether).

He is considering to invest in an investment policy in which he would invest 30% of his assets in a risk-free bond with 3% continuously compounded annual interest and the remaining 70% in a risky asset that has lognormally distributed returns with mean μ = 12% and standard deviation σ = 35%.

Marcus applied Monte Carlo simulation to decide whether he should invest his money in this investment strategy. The Excel spreadsheet below reports the end-of-year wealth based on one simulation that he conducted.

Write down and explain the Excel formula used to calculate the yellowed values in cells E11 and F11.

Attachment:- Quantitative Methods in Finance.rar