|Exam/Problem Set question 1:
The expected returns of Facebook, Google, and Fiat are 8%, 18%, and 12%, respectively. The variances of these three stocks are 0.03, 0.04, and 0.05, respectively. Fiat is uncorrelated with tech stocks. Facebook and Google have a correlation of 0.8. The risk-free rate is 5%.
(a) ?Calculate the minimum variance portfolio weights of these three stocks and the mean and standard deviation of the minimum variance portfolio (MVP).
(b) ?Calculate the tangency portfolio weights of these three stocks and the mean and standard deviation of the tangency portfolio (T).
(c) Find the efficient portfolio of risky assets only that has the same expected return as Google.
(d) Would you advise a mean-variance investor to hold a portfolio invested 30% in Google, 30% in Facebook and 40% in Fiat? Why or why not?
Exam/Problem Set Question 2:
The current price of Amazon is $100 per share, and will either appreciate by 10% or depreciate by 20% over each of the next two periods. Amazon will distribute a dividend at the end of period 1 equal to 5% of its stock price at that time. The risk-free rate is 5% over each of the next two periods.
(a) What is the value of an American call option on Amazon that expires in two periods and has a strike price of $105?
(b) How much is the option to exercise early worth in this case?
Problem set Question 3:
You have been asked to design efficient portfolios from 7 portfolios, which track various industries or sectors of the U.S. economy. However, the company has not provided the means, variances, or covariances of these portfolios, but merely supplied you with the time-series of monthly returns on the 7 industries (see Excel file). Your task is to:
a) Compute the means, standard deviations, variances, and covariance matrix of the 7 industries.
b) Design two mean-variance optimal/efficient portfolios from the inputs calculated in step 1, by computing the minimum variance portfolio and tangency portfolio of the 7 industries.
c) Make a recommendation on how they should advise their clients when investing among these 7 sectors of the economy.