An investor buys a bond with the following characteristics: Maturity - 10 years Coupon - 4.5%, paid once...

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An investor buys abond with the following characteristics:
Maturity - 10 years
Coupon - 4.5%, paid once per year
Nominal Value - £100
The yield to maturityat the time of purchase is 8.50%. The investor sells the bondimmediately after the sixth coupon payment, when the yield tomaturity rises to 9.50%.
c.Use the modified Macaulayduration to calculate what the price of the above bond would havebeen immediately after purchase, if the yield to maturity haddropped 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?

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3.9 Ratings (593 Votes)


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

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An investor buys abond with the following characteristics:Maturity - 10 yearsCoupon - 4.5%, paid once per yearNominal Value - £100The yield to maturityat the time of purchase is 8.50%. The investor sells the bondimmediately after the sixth coupon payment, when the yield tomaturity rises to 9.50%.c.Use the modified Macaulayduration to calculate what the price of the above bond would havebeen immediately after purchase, if the yield to maturity haddropped 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?