Question

a) An HSBC bond has a face value of 1000, a coupon rate of 8%, 3 years until maturity and a yield to maturity of 7%. Calculate bond duration. D= ? *[cash flowt/(1+YTM)t]}/price of bond where t is time to maturity and YTM stands for yield to maturity. N.B: You need to show how you have calculated duration. A single value will not suffice.

b) HSBC has issued a 9-year bond with YTM of 10% and duration of 7.194 years. If the market yield changes by 0.5% what is the percentage change in the bond’s price? Use modified duration to do your calculations.

c) HSBC has issued a 6% coupon paying bond with modified duration of 10 years, convexity of 120 and YTM of 8%. If YTM changes to 9.5% what is the percentage change in price? d) You are the manager of a bond portfolio which is worth £10 million. You have liabilities with duration of 10 years and you have two choices to match that duration. You can choose to buy a zero coupon bond with maturity of 5 years or buy a perpetuity. The bond and the perpetuity have a yield of 4%. Find how much of the bond and the perpetuity will you hold in your portfolio to match that duration?

Answer 1

a)

N	CF	PVF	PVF x CF	PVF x CF x N
1	80	0.934579	74.77	74.77
2	80	0.873439	69.88	139.75
3	1080	0.816298	881.60	2644.81
		Sum	1026.24	2859.32
			Duration	2.79

Duration = Sum of PVF x CF x N / Sum of PVF x CF = 2,859.32 / 1,026.24 = 2.79

b) Modified Duration = Duration / (1 + YTM) = 7.194 / (1 + 10%) = 6.54

% Change in Bond Price = Mod. Duration x Change in yield = 6.54 x 0.5% = 3.27%

c) % Change in Price = - Duration x Chg + 0.5 x Convexity x Chg^2

= -10 x 1.5% + 0.5 x 120 x 1.5%^2

= -13.65%

d) Duration of zero coupon = 5 and Duration of perpetuity = 1 + y / y = (1 + 4%) / 4% = 26

Assume y% is invested in zero coupon

=> 10 = y x 5 + (1 - y) x 26

=> y = (26 - 10) / (26 - 5) = 76.19% invested in bond

and 1 - y = 23.81% invested in perpetuity.