Question

a. [3 marks] A 10-year 8% Treasury bond has duration equal to 6 years
when the market yield is 17.10% p.a. compounded half-yearly. The
bond’s price at this yield is $57.110 (per $100 face value). Use the
bond’s duration to estimate its price (per $100 face value, rounded
to 3 decimal places) at a market yield of 17.09% p.a. compounded
half-yearly.
b. [2 marks] Suppose you have a fixed liability that you must pay at
the end of 6 years. When the yield today is 17.10% p.a. compounded
half-yearly, what amount of fixed liability at the end of 6 years could
be immunised by buying $100 000 face value of the 10-year 8% Trea-
sury bond referred to in a.? 2 (Calculate the amount of fixed liability
rounded to the nearest whole dollar.)
c. [2 marks] Do you agree or not agree with this statement made by a
finance student? Explain why.
lf two bonds with the same term to maturity and the same
yield have dierent coupon rates, the one with the higher
coupon rate will have the higher (longer) duration.

Answer 1

a). Change in Price P/Price = -Duration*(Change in YTM/(1+YTM))

Change in Price = (57.11*-6)*(17.09%-17.10%)/(1+17.10%) = 0.0293%

New price = old price*(1+change in price) = 57.11*(1+0.0293%) = 57.127

b). For immunization, duration of the liability = duration of the asset.

Liability duration = 6 years; Asset duration (from part a) = 6 years.

Future Value of 100,000 par value bond in 6 years, 8% coupon with YTM 17.10% (semi-annual payment):

Present value of the bond = 57.11*100,000/100 (since the price is 57.11 per 100 par value)

= 57,110

PMT = 8%*100,000/2 = 4,000 (semi-annual payment)

PV = 57,110; PMT = 4,000; N = 12; I/Y = 17.10%/2 = 8.55%, solve for FV.

FV = 74,421.57

The fixed liability amount which can be immunized is 74,421.57

c). No. Everything else remaining same, a bond with a larger coupon will have a shorter duration.