1. (not required)
(a) . Assuming the single index model holds, what is the optimum portfolio assuming (1) no short sales and (2) the risk-free is the mean historical risk free rate? What is the mean return and standard deviation of this optimum portfolio?

(b) Assume that you are at Jan 1 2016 (and therefore only have information available up to an including Dec 2015). Assuming the single index model holds, what is the optimum portfolio assuming (1) short sales and (2) the risk-free is the mean historical risk free rate? What is the mean return and standard deviation of this optimum portfolio?
14 marks

2. (you can find the answer in the book)
Comment on the stability of stock weightings of an optimum portfolio generated using the single index model. How would you test to see if the optimum portfolio weightings are timevarying? Provide an empirical examination of the stability of weightings of the optimum portfolio you generated in question 1.
12 marks

3.( you can find the answer in the book)
Assess the performance of your two optimum portfolios (from question 1). You should assess performance using at least 4 tests of performance, including at least 2 that rely on multi-beta asset price modelling. For the tests that use multi-beta asset price modelling, data is available from Ken French database of asset price factors at
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
Interpret the performance measures and provide a comment on the performance of the optimum portfolios.
12 marks
4. ( for this question please: write 4 pages, use 2 articles that mentioned in the question which is I already uploaded, plus the other 4 articles that I uploaded)
Compare and contrast the single-index model with multi-index models in computing the variance-covariance matrix of stock returns. In your answer outline how you would compute these models in practice and any limitations/difficulties of these models – draw on articles such as Chen, Roll and Ross (1986) and Burmeister, Roll and Ross (2003).
20 marks