# A ZERO COUPON BOND with \$100 face value is redeemable at par in exactly four years.

June 6, 2016

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 currently 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?

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%

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.

(4 marks)

(ii) Based on the annual portfolio returns, calculate the expected (average) portfolio return and the standard deviation of portfolio returns.

(4 marks)

(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.

(4 marks

(b) Assuming the Capital Asset Pricing Model (CAPM) holds, calculate 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 Rmis expected to be 8% and the riskfree rate Rfis 1%.

(2 marks)

2. Portfolio 2: the estimated correlation coefficient between the 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 Rmand Rfare as for Portfolio 1.

(4 marks)

In each of parts (b1) – (b2), clearly show the derivation of your results.

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 choose and why?

Do I calculate expected return/profolio variance/WACC? How do I calculate?