You have analyzed the returns of the largest Turkish stocks for your previous homework.
You plan to use the results of the previous homework as input for classical Markowitz mean- variance portfolio optimization. You may use MATLAB or R for your computations.
Again Excel is acceptable.
I expect hard copies of professionally written and presented documents as output. Submis- sions via email are not accepted. Do not hand in print-outs of computer codes, unlabeled graphs etc. Pay attention in each problem for what's being asked as deliverable, label your results accordingly and turn in a professionally prepared document for full-grade.
You have generated mean return vectors, µ and variance-covariance matrices, Σ through two methods; historical return statistics and CAPM. You also gathered β and α vectors out of your CAPM regressions. Make sure your results are correct, or at least sensible, before you go on to use them for portfolio optimization.
1. Set up the model to form an optimal portfolio of the set of risky stocks and solve it for different levels of expected portfolio return. The basic model has no constraints other than the budget constraint. Choose a reasonable range of required portfolio returns and solve the problem for a number of values at regular intervals to be able to graph the efficient frontier. Graphs the set of stocks, the feasible set of portfolios and the efficient frontier on the standard deviation-mean return graph similar to what we saw in class.
2. Find the global minimum variance portfolio. Report the weights of each stock, along with the expected return and standard deviation of the portfolio. Show it on the graph.
3. Now introduce a risk-free asset in the form of a government bond. Most recent yield for short-term Turkish bond is 8.5%. Find the optimal risky portfolio (the tangency portfolio) by maximizing the Sharpe ratio. Draw the capital allocation line on your graph. Report the weights of each stock, along with the expected return and standard deviation of the portfolio.
Warning: If the Turkish interest rate is higher than the return of the global minimum variance portfolio, use the long-term US bond rate of 2.499% instead.
4. Suppose you have risk aversion factor of 5 with a quadratic mean-variance utility func- tion. Where does your optimal portfolio fall along the capital allocation line? Report the optimal weights of the tangency portfolio and the risk-free asset, along with the expected return and standard deviation of your portfolio.
5. Now assume that the short sales are not allowed. Repeat problems 1-4. Compare your results to the portfolios with no short-sale constraints.
6. Now use Σ and µ generated by CAPM in problem 7 of the previous homework. Repeat the constrained optimization of the previous problem with this new set of parameters. How do the results change?
7. Next form a market neutral optimal portfolio by adding zero-Beta constraint to the previous problem. Use β vector you found problem 7 of the previous homework for a con- straint of the form ω'β = 0, where ω is the weight vector.
Attachment:- Homework.rar