Reference no: EM133369123

Questions:

1) You will be paying $30,000 per year tuition at the end of the next two years. Bonds currently yield 6%
a) What are present value and duration of your obligation?
b) What maturity zero-coupon bond would immunize your obligation?
c) Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Interest rates immediately increase to 7%. What will be your net position (difference between the bond value and tuition obligation)? What happens with a change to 5%?
2) Pension funds pay lifetime annuities to recipients. Assuming the firm stays in business indefinitely, the cash flow would resemble a perpetuity. You are managing a pension fund that pays $4 million per year to its beneficiaries. The yield-to-maturity of all bonds is 15%.
a) If the duration of a five-year maturity, 12% coupon rate bond (annual payments) is four years and the duration of a twenty-year maturity, 6% coupon rate bond (annual payments) is eight years how much of each bond (in market value) would you need to fully fund and immunize your obligation?
b) What is the par value of your holdings in the twenty-year bond?
3) A 12.75-year maturity zero-coupon bond selling at a yield-to-maturity of 8% has convexity of 150.3 and modified duration of 11.81 years. A 30-year 6% coupon bond making annual coupon payments also selling at a yield-to-maturity of 8% has nearly identical modified duration of  11.79 years but considerably higher duration of 231.2.
a) Let the yield-to-maturity increase to 10%. What will be the actual percentage capital loss on each bond? What percentage capital loss would be predicted with the duration-to-convexity rule?
b) Repeat part (a) but use a yield-to-maturity decrease to 6%.
c) Compare the performances in parts (a) and (b), then explain the attraction of convexity.