You work for a insurance company that has a payment of $20,000 guaranteed to policy holders in 10 years.

The insurance company needs to invest today in a financial instrument that will guarantee this payment, regardless of changes in interest rates.

The insurance company wants to protect (immunize) themselves against interest rate risk. They are considering two approaches:

Approach 1: Buy 10-year maturity zero coupon discount bonds

Both types of bonds have a $1,000 face value

Approach 2: Buy 10-year Duration coupon bond (annual coupons)

Show how each approach will immunize the insurance company against changes in interest rates:

Approach 1: Buy a 10-year maturity zero coupon discount bond. Assume the YTM on this bond is 5%.

How many bonds will the insurance company need to buy? What will be there initial investment?

Coupon Rate

0%

Bond Price

Maturity (years)

10

# Bonds

($20,000 / bond par value)

YTM

5%

Amount Invested

Face Value

1,000

Duration

Future payment

20,000

Term (t)

CFt

DFt

PV of CF (CFt x DFt)

PV x t

Because there are not intervening cash flows, future changes in interest rates have no reinvestment income effect.

Total