construct stock portfolios with returns on two stocks or two stock market indices (Energy and Manufacturing)

c Part A Question 1 You are required to construct stock portfolios with returns on two stocks or two stock market indices (Energy and Manufacturing). You can download stock return data from yahoo finance or other sources. The data can be of any frequencies and from any markets. Additionally, you need to find out a risk-free interest rate appropriate for the market you have chosen. Estimate the expected returns on the two stocks or stock indices. Estimate the variances and standard deviations of the two returns. What is the covariance between the two returns? What is the correlation coefficient between the two returns? Plot the efficient frontier of the portfolios constructed with these two stocks or stock indices. Find out the minimum variance portfolio constructed with these two stocks or stock indices, solving for the weights of the two stocks or stock indices in the portfolio. What are the expected return and risk of this minimum variance portfolio? Construct an optimal portfolio with these two stocks or stock indices and solve for the weights of the two stocks in the portfolio. What are the expected return and risk of the optimal portfolio? (20 marks) Results vary according to the stock return data chosen by the student. Question 2 Bond price, yield and duration exercises Go to the London Stock Exchange’s bonds’ website http://www.londonstockexchange.com/exchange/prices-and-markets/retail-bonds/retail-bonds-search.html Select Corporates then click Search Choose 6-10 bonds. Fixed coupon rate bonds only. Record the key parameters of the bond needed for solving (b) – (e) e.g., for bond code AE57, click its name, you’ll see Work out their yields with the given coupons and listed prices. Using your cases to support the statements that: Bonds with the coupon rate < YTM will be priced at a discount; Bonds with the coupon rate > YTM will be priced at a premium; Bonds with the coupon rate = YTM will be priced at the face value. Calculate their durations. Verify that: Other things being equal, bonds with a higher coupon rate have a shorter duration; Other things being equal, bonds with a higher YTM have a shorter duration; Other things being equal, bonds with a longer time to maturity have a longer duration. Note: if you have difficulties in finding a pair of two bonds that are equal in maturity and YTM or coupon rate, it is acceptable that one of the bonds is real while the other is hypothetical. (15 marks) Results vary according to the stock return data chosen by the student. Question 3 The spot exchange rate and the three-month forward exchange rate of sterling vis-à-vis the US dollar are quoted in New York as follows: S0 = $1.6358/£ with a spread 355 – 361 F0,90 = $1.6385/£ with a spread 382 - 388 The interest rate at which the trader can borrow or lend in the US is 2.50% per annum and that in the UK is 2.25% per annum now and they are expected to remain unchanged in the next three months. Calculate and compare the forward premium and interest rate differential to verify that arbitrage opportunities exist in this case. Set up procedures to exploit the arbitrage opportunities. Work out how big the arbitrage profit is, taking into account the transaction costs in the foreign exchange market as indicated by the bid-ask spread in the quotations. (15 marks) Part B Question 1 The population mean of stock market returns is 6% with a population standard deviation of 18%. Over the last 4 years market returns have averaged – 2%. Your client is very upset and claims that results this bad should never occur: Construct a 95% confidence interval for the population mean for a sample of 4 year returns. What is the probability of -2% returns over a 4 year period? (15 marks) Question 2 We want to test the hypothesis that the mean P.E. ratio of companies that receive a takeover offer is the same as the mean P.E. ratio of companies that do not receive a takeover offer in the same industry. Explain under what conditions we would commit a type 1 and a type 2 error. (10 marks) Question 3 X is the monthly return for a large stock index, Y is the monthly return for a small stock index; there are 60 monthly observations. X ¯=0.76 ?_(i=1)^n¦?(X_i- X ¯)?^2 =769.081 Y ¯=1.037 ?_(i=1)^n¦?(Y_i- Y ¯)?^2 =1,243.309 ?_i^n¦?(X_i-X ¯ )(Y_i-Y ¯ )=720.535? Calculate the sample variance and standard deviation for X and Y Calculate the sample covariance and correlation between X and Y (10 marks) Question 4 Your business is considering 3 different business projects with different cash flows. Calculate which has the highest net present value: Project A: Spend £100,000 now. Receive £50,500 in 3 years’ time, plus £40,000 in 4 years’ time and £120,000 in 5 years’ time. The discount rate is 4% Project B: Spend £190,000 now. Receive £35,000 each year for 10 years; the first receipt will be at the end of this year. The discount rate is 5% Project C: Spend £210,000 now. Receive £70,000 for 6 years; the first receipt will be at the end of year 7. The discount rate is 4%. (15 marks)