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Investments 3.4 March 2010 with answers

# 02 the bond has a coupon rate of 64 pays interest

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Unformatted text preview: n of 0.11, what percentages of your money must you invest in the T‐bill and P, respectively? ‐ What is the dollar value of these positions? E(rp) = 0.6(14%) + 0.4(10%) = 12.4%; 11% = 5x + 12.4(1 ‐ x); x = 0.189 (T‐bills) (1‐x) =0.811 (risky asset). Thus \$1,000 x 18.9% = \$189 in T‐bills and \$1,000 x 81.1% = \$811 in the risky portfolio. Part c. (3 points) You want to evaluate three mutual funds using the information ratio measure for performance evaluation. The risk‐free return during the sample period is 6%, and the average return on the market portfolio is 19%. The average returns, residual standard deviations, and betas for the three funds are given below. ‐ Sort the three funds according to Jensen’s alpha. What does Jensen’s alpha measure? ‐ Sort the three funds according the information ratio criterion. What does the information ratio measure? Give formulas. 1 0 Information ratio = αP/σ(eP); A: αP = 20 ‐ 6 ‐ .8(19 ‐ 6) = 3.6; 3.6/4 = 0.9; B: αP = 21 ‐ 6 ‐ 1(19 ‐ 6) = 2.0; 2/1.25 = 1.6; C: αP = 23 ‐ 6 ‐ 1.2(19 ‐ 6) = 1.4; 1.4/1.20 = 1.16. QUESTION 3. (15 points) Fixed Income Part a. (3 points) You are given the following coupon bonds with annual coupon payments and face value of 100. Bond Maturity Coupon Price Yield to Face value maturity A 2 3% \$100.41 2.79% \$100 B 2 9% \$104.32 6.63% \$100 Compute the zero rates z1 and z2 (up to two decimal places) for maturities of 1 and 2 years. The zero rates z1 and z2 solve the following system: 3/(1+z1) + 103/(1+z2)2 = 100.41 9/(1+z1) + 109/(1+z2)2 = 104.32 Part b. (3 points) You purchased an annual interest coupon bond one year ago with 6 years remaining to maturity at the time of purchase. The coupon rate is 10% and par value is \$1,000. At the time you purchased the bond, the yield to maturity was 8%. You sell the bond after receiving the first interest payment and the bond's yield to maturity has now changed to 7%. Calculate the annual total rate of return on holding the bond for that year. FV = 1000, PMT = 100, n = 6, i = 8, PV = 1092.46; FV = 1000, PMT = 100, n = 5, i = 7, PV = 1123.01; HPR = (1123.01 ‐ 1092.46 + 100) / 1092.46 = 11.95%. Part c. (3 points) Suppose that all investors expect that interest rates for the 4 years will be as follows: ‐ Provide the formula for the price of a 2...
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