3 F: F: Consider the following four bonds: 5 years to maturity, 0% coupon 20 yea

Question

3 F: F: Consider the following four bonds: 5 years to maturity, 0% coupon 20 years to maturity, 0% coupon 5 years to maturity, 5% coupon 20 years to maturity, 5% coupon m a A. Assuming the term structure is flat at 5%, compute the price of each bond i. to iv. [2 points] B. What is the current yield for each bond from Part A? [2 points) Compute the new price and the percentage price change for each bond if the term structure instantaneously shifts from 5% to 5.5%. [2 points] Compute the new price and the percentage price change for each bond if the term structure instantaneously shifts from 5% to 4.5%. [2 points] E. How does the bond coupon rate relate to the magnitude of the percentage price change in C. and D.? [2 points] How does the term-to-maturity relate to the magnitude of the percentage price change in C. and D.? [2 points] G. Are the magnitudes of the percentage price changes in C. and D. different for each bond? If So, what contributed to that difference? [2 points] F.

Explanation / Answer

As per Chegg policy can answer only 4 questions

Price = Coupon*(1-(1+rate)-n) / rate + Face value*(1+rate)-n

A)

i Price = 1000*(1+5%)-5 = 783.5262

ii Price =  1000*(1+5%)-20 = 376.8895

iii  Price =  50*(1-(1+5%)-5) / 5% + 1000*(1+5%)-5 = 1000

iv Price =  50*(1-(1+5%)-20) / 5% + 1000*(1+5%)-20 = 1000

B

For first two bonds current yield = 0% (no coupon)

For lst two bonds current yield = 5% ( coupon rate = term rate)

C

rate = 5.5%

i  Price =  1000*(1+5.5%)-5 = 765.1344

ii Price =  1000*(1+5.5%)-20 = 342.7290

iii  Price =  50*(1-(1+5.5%)-5) / 5.5% + 1000*(1+5.5%)-5 = 978.6486

iv Price =  50*(1-(1+5.5%)-20) / 5.5% + 1000*(1+5.5%)-20 = 940.2481

D

rate = 4.5%

i  Price =  1000*(1+4.5%)-5 = 802.4510

ii Price =  1000*(1+4.5%)-20 = 414.6429

iii  Price =  50*(1-(1+4.5%)-5) / 4.5% + 1000*(1+5.5%)-5 = 1021.9499

iv Price =  50*(1-(1+4.5%)-20) / 4.5% + 1000*(1+4.5%)-20 = 1065.0397

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