FM for Actuaries

Bond Management 287
8.29 Suppose you have bought a 5-year non-callable default-free coupon bond
with annual coupon rate of 4% at a yield to maturity of 5% effective per annum.
Immediately after you bought the bond, the prevailing market interest
rate jumps to 7% so that the coupons can be reinvested at 7%.
(a) Calculate your n-year holding-period yield for n =1, 2 and 5.
(b) We know that bond price decreases with yield to maturity. What about
the return on the bond investment as a whole?
8.30 Let D A and D L be the Macaulay duration of the assets and liabilities, respectively.
Show that
( )
d VA
D A = D L if and only if
=0.
di V L
What is the significance of this equivalence?
8.31 Show that the Macaulay duration can be calculated as
D = − d ln P = d ln P
dδ d ln v ,
where δ is the force of interest. This result says that the Macaulay duration
is the elasticity of the price with respect to the discount factor.
8.32 Which of the following statements about immunization is/are correct?
(a) Immunization is a method to structure the liability in order to reduce
interest-rate risk.
(b) Immunization requires re-balancing only because interest rate fluctuates.
(c) Immunization may not work if the yield curve is not flat.
8.33 Discuss why dedication strategy is an effective but largely impractical method
of eliminating interest-rate risk.
8.34 A bond-fund manager wants to mimic the performance of the Merrill Lynch
Domestic Master Index, a bond index in the US market comprising of more
than 5,000 investment-grade bonds. Discuss two difficulties in replicating
the bond portfolio of the index.
8.35 You owe Mr Lauder $2,000 in tuition expenses due at the end of the year
and you want to set up a fund to meet the obligation. The investment vehicle
available to you is a 2-year zero-coupon bond earning 8.5% effective. You