Question

An investor buys a bond with the following characteristics:

• Maturity - 10 years
• Coupon - 4.5%, paid once per year
• Nominal Value - £100

The yield to maturity at the time of purchase is 8.50%. The investor sells the bond immediately after the sixth coupon payment, when the yield to maturity rises to 9.50%.

• c.Use the modified Macaulay duration to calculate what the price of the above bond would have been immediately after purchase, if the yield to maturity had dropped to 6.5%.

• d.An accurate answer for part (c) is £85.32. Explain why your answer to part (c) differs from this. What are the implications of this effect for bond investors?

Answer 1

		N	A	B=A/(1.085^N)	C	D=C/(1.085^N)
		Period	Cash flow	PV of Cash Flow	Period*Cash flow	PV of (Period* Cash flow)
		1	$4.50	4.147465438	$4.50	4.147465438
		2	$4.50	3.822548791	$9.00	7.645097581
		3	$4.50	3.523086443	$13.50	10.56925933
		4	$4.50	3.247084279	$18.00	12.98833712
		5	$4.50	2.992704405	$22.50	14.96352202
		6	$4.50	2.758252908	$27.00	16.54951745
		7	$4.50	2.542168578	$31.50	17.79518005
		8	$4.50	2.343012515	$36.00	18.74410012
		9	$4.50	2.159458539	$40.50	19.43512685
		10	$104.50	46.21882587	$1,045.00	462.1882587
			TOTAL	73.75460777		585.0258647
		Maculay Duration	7.93205852	(585.0258647/73.75460777)
		Modified Duration	(Maculay Duration)/(1+(YTM/2))
		Modified Duration	7.60868922	(7.93/(1+(0.085/2))
		Price at the time of Issue	$73.75
		If the YTM drops to 6.5%
		Decrease in YTM =1.5%
		Expected increase in price=1.5*Modified Duration
		Expected increase in price=	$11.90	(1.5*7.93)
		The price would have been	$85.65	($73.75+$11.90)
		The difference is due to effect of Bond convexity