Question

An investor wishes to be sure she has $20 million in 15 months’ time.  At present, 1-year and 2-year zero-coupon bonds are priced to yield 9.7%. The investor sets up a bond portfolio using the duration-matching principle.  Three months after setting up the portfolio, the yields on both bonds increase to 10.2% and then remain at that level for a further 12 months.  Assume that all months are of equal length, that all bonds have a par value of $100, and that investors may trade any number of bonds, including fractions of bonds.

1) Calculate the prices today of the 1-year zero-coupon bond and the 2-year zero-coupon bond.  Show your calculations.  

2) How much (in total) does the investor need to invest today?  

3) How much should be invested today in the 1-year bond?  How much should be invested today in the 2-year bond?  Show your calculations.  

4) How many 1-year bonds should be bought today?  How many 2-year bonds should be bought today?  Show your calculations.

5) Show that the investor will achieve her target sum.  Be precise about the timing and amounts of any transactions required. Show your calculations.  

Answer 1

Q1) Prices of the bond

Q2) Total Investment Needed

Q3) Proportion of Investment

Q4) Number of bonds