Math

Finance 473 Debt and Money Market Problem set 2 with solutions, 2011 Andrei Simonov

1. Consider the following three bonds with semi-annual coupon frequency and $1000 face value. Bond Price F G H 884.20 948.90 967.70 Coupon rate (%) 7 8 9 Term to maturity 5 7 4

For each of the three bonds: a. Draw a timeline and indicate the payoffs. b. Compute the (annualized) yield to maturity. c. Calculate the current yield. d. Consider a portfolio composed by 2/3 of F bonds and 1/3 of G bonds. Calculate the price and the yield to maturity of the portfolio. e. Consider a portfolio composed by 2/3 of F bonds and 1/3 of H bonds. Is it easier to determine the yield to maturity in this case? (10p) ANSWER: b. The bond prices are given by (using a PV for the coupons) P = (C/y) (1-(1+y)-n) +M (1+y)-n

This equation is implicit in y and hence to solve it some kind of numerical routine is needed (for example Newton-Raphson). Using the solver in Excel gives the ‘semi-annual’ yields 5.0% for bonds F and H and 4.5% for bond G. To annualize these we simply multiply with 2. c. Current yield = annualcoupon/ price. Hence we get the current yields 7.9%, 8.4% and 9.3% for bonds F, G and H, respectively. d. The price is, of course, given by (2/3)·884.2+ (1/3) ·948.9 = 905.77. The most straightforward way to find the yield to maturity is to simply create a new bond structure out of the portfolio cash flows. This means creating a bond which has semi-annual cash flows of $38.33 (2*35/3+ 45/3) for the first 10 periods and $15 for the last 4 periods. The annualized yield is then determined as in part b. to be 9.60%. e. Since the yield is 10% for both of them the portfolio yield must also be 10% (convince yourself why).

2. Suppose that a bond is purchased between coupon periods. The days between the settlement date and the next coupon period is 115. There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semi-annual coupon payments...