Many institutions have fixed future liabilities to meet (such as pension payments) and they

fund these future liabilities using default-free fixed income securities. When discount bonds

of all maturities are available, these institutions can simply buy discount bonds to fund their

liabilities. For example, if there is a fixed liability equal to 1 million dollars five years from

now, an institution can buy a discount bond maturing in five years with a face value of 1

million dollars. Unfortunately, there may not be the ight" discount bonds for a fixed future

liability and coupon bonds must be used. Then an institution faces reinvestment risk on the

coupons.

For example, suppose that the yield curve is flat 10% and we have the following coupon

bonds (paying annual coupons):

Bond	Prices	Principal	Coupon	Years to Maturity
A	118.95	100	15	5
B	130.72	100	15	10

and we have a 1 million liability five years from now.

1. Suppose that the yield curve will remain unchanged for the following five years and you

have decided to use bond A to fund the liability. That is, you want to invest in bond

A and invest the coupons at the prevailing interest rates to produce a future value at

the end of year five of 1 million. How much should you invest in bond A?

2. Now suppose that right after you invested in bond A, the yield curve makes a parallel

move down by 1% to 9%. What is the future value five years from now of your

investment? What is the future value if the yield curve moves up by 1% to 11%?

Please explain why the future value changes differently depending on the direction of

the change in the yield curve.