Question 1 (25 marks)

Alpha LLC, a US hedge fund, considers investing in both bonds and stocks in Singapore market. Two straight bonds and two SGX stocks are shortlisted by AlphaLLC. Bond P has a par value of $1,000, paying 6 percent coupon rate semi-annually,10 years to maturity, and a credit rating of AA. Bond Q has a par value of $1,000, paying 4 percent coupon rate semi-annually, 8 years to maturity, and a credit rating of AA. Stock X has an expected return of 8 percent, a standard deviation of 10 percent,and a correlation of 0.8 with the market portfolio. Stock Y has an expected return of 9percent, a standard deviation of 12 percent, a correlation with the market portfolio of0.2, and a correlation with Stock X of 0.6. The stock market portfolio has a standard deviation of 10 percent. The correlation between the bond and stock portfolios is -0.27. The yield of 3-month Treasury bill is 1.8 percent. The required yields (YTM) forAA and AAA are 6 and 4 percent over a 3-month Treasury bill yield, respectively. AlphaLLC would hold the bonds until maturity. Assume CAPM holds.

Required:

a) Compute the fair prices for Bond P and Q. Which bond is relatively sensitive to a change in market interest rate? Justify your answers. (9 marks)

b) What are the expected return and standard deviation of a stock portfolio consisting of 70 percent of Stock X and 30 percent of Stock Y? Which stock is relatively sensitive to a change in market risk? (8 marks)

c) Alpha LLC wants to construct a balance portfolio by including both Bond P and Q as the fixed-income securities portfolio into the existing stock portfolio toachieve an expected return of 8 percent since Alpha LLC has a medium investment risk profile. What are the investment weights of Bond P and Q in this balance portfolio? Assume YTM is the required rate of return for the bond.(8 marks)