Question 1) A zero coupon bond with $100 face value is redeemable at par in exactly four years. You see from financial times that you can at present buy it for $68.3. Your alternative is to invest in a saving account, which pays no periodic interest and give a return of 10.5%. Would you buy the bond?
Question 2) Over the past three years (Year 1 to Year 3) the stocks of two companies, one plc and two plc, generated annual returns to shareholders as follows:
ONE Plc TWO Plc
Year 1 –5% 2%
Year 2 15% 1%
Year 3 12% 4%
(i) For each of the three years (Year 1, Year 2, Year 3), calculate the annual return generated by a portfolio that is made up of the two stocks one and two with 80 percent of the portfolio invested in stock one and the rest in stock two.
(ii) Based on the annual portfolio returns, calculate the expected (average) portfolio return and the standard deviation of portfolio returns.
(iii) Can the standard deviation of the portfolio returns be approximated as the weighted average of the individual stock returns? Explain why or why not.
(b) Suppose the Capital Asset Pricing Model (CAPM) holds, compute the expected returns and the risk premia of the following two portfolios.
1. Portfolio 1 has a beta of 1.5; the return on the market portfolio Rm is expected to be 8% and the risk free rate Rf is 1%.
2. Portfolio 2: the estimated correlation coefficient between returns on Portfolio 2 and the market portfolio returns is 0.1, the standard deviation of the market portfolio returns is 3%, and the standard deviation of the returns of Portfolio 2 is 8%; the values of Rm and Rf are as for Portfolio 1.
In each of parts (b1) – (b2), clearly demonstrate the derivation of your results.
Question 3) You have £10,000 and are offered two investment products by a fund manager. The first product is a portfolio that consists of £6,000 worth of risk free treasury bills and £4,000 worth of QW plc shares. The second product is a portfolio that consists of £1,000 worth of QW plc shares and £9,000 worth of CX plc shares. The following information is available:
Return on treasury bills 4% per annum (0.04 p.a.)
Expected rate of return on QW plc shares 15% per annum (0.15 p.a.)
Standard deviation of QW plc shares 0.35
Expected rate of return on CX plc shares 7.7% per annum (0.077 p.a.)
Standard deviation of CX plc shares 0.15
Correlation coefficient between QW and CX shares 0.40
Which one of these investment portfolios would you select and why?
Compute expected return/profolio variance/WACC?