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

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Finance

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?

Answer & Explanation Solved by verified expert
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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Transcribed Image Text

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?

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