FM for Actuaries

Bond Management 281
Time to
Coupon rate
maturity 1% 3% 6% 10%
1
2
5
10
20
50
100
∞
8.8 Consider a bond with m coupons per year of rate r per annum. Show that
when the time to maturity tends to infinity, its duration tends to
1+ i m
i
(in years) where i is compounded m times per year. Note that the duration
limit is independent of the coupon rate r, and is decreasing in i.
8.9 The interest-rate risk of a non-callable bond is higher for
(1) higher coupons,
(2) longer maturities,
(3) higher interest rates.
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
8.10 You want to construct a bond portfolio to immunize the interest-rate risk of
a liability of $2,000 after 10 years. You have the choice of three bonds with
the following information:
Bond 1 Bond 2 Bond 3
Coupon rate 0% 3% 5%
Face value $100 $1,000 $1,000
Macaulay duration 12 years 8 years 9 years