You are looking to purchase a 3.6% coupon bond (with semiannual coupons), par value ofonly $800, with a maturity of exactly 3 years. The next coupon payment will occur in 6months. You have the following information on the yield curve (APR8 compoundedannually):1.Maturity(in years)T-stripAPR2.0%0.597:241.01.596:122.02.7%2.52.85%3.02.95%What is the price of this bond?а.b. What is your estimate of the YTM of this bond (to within 0.1%)? Explain yourreasoning?You purchase the bond at the price you calculated in part (a). Immediately after thepurchase, the Federal Reserve issues a statement that spooks the bond market, andprices fall. You see that the YTM of the bond has jumped to 6.5% APR (compoundedannually). You decide that you should now sell this bond. What return would youhave earned on this bond during the brief period in which you owned it?с.

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Asked Oct 29, 2019
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You are looking to purchase a 3.6% coupon bond (with semiannual coupons), par value of
only $800, with a maturity of exactly 3 years. The next coupon payment will occur in 6
months. You have the following information on the yield curve (APR8 compounded
annually):
1.
Maturity
(in years)
T-strip
APR
2.0%
0.5
97:24
1.0
1.5
96:12
2.0
2.7%
2.5
2.85%
3.0
2.95%
What is the price of this bond?
а.
b. What is your estimate of the YTM of this bond (to within 0.1%)? Explain your
reasoning?
You purchase the bond at the price you calculated in part (a). Immediately after the
purchase, the Federal Reserve issues a statement that spooks the bond market, and
prices fall. You see that the YTM of the bond has jumped to 6.5% APR (compounded
annually). You decide that you should now sell this bond. What return would you
have earned on this bond during the brief period in which you owned it?
с.
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You are looking to purchase a 3.6% coupon bond (with semiannual coupons), par value of only $800, with a maturity of exactly 3 years. The next coupon payment will occur in 6 months. You have the following information on the yield curve (APR8 compounded annually): 1. Maturity (in years) T-strip APR 2.0% 0.5 97:24 1.0 1.5 96:12 2.0 2.7% 2.5 2.85% 3.0 2.95% What is the price of this bond? а. b. What is your estimate of the YTM of this bond (to within 0.1%)? Explain your reasoning? You purchase the bond at the price you calculated in part (a). Immediately after the purchase, the Federal Reserve issues a statement that spooks the bond market, and prices fall. You see that the YTM of the bond has jumped to 6.5% APR (compounded annually). You decide that you should now sell this bond. What return would you have earned on this bond during the brief period in which you owned it? с.

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Expert Answer

Step 1

As a first step we need to calculate the missing APR in the table.

Assuming half yearly coupn payments,

Price of T strip = 97.24 = 100 / (1 + r/2)2

Hence, r = 2.82%

Price of T strip maturing in 1.5 years = 96.12 = 100 / (1 + r/2)3

Hence, r = 2.66%

Step 2

Part (a)

Please see the white board. Price of the bond is present value of all the future payments derived using half year APR corresponding to a period, as discount rate of that period.

The price of the bond = $ 815.07 (please see the last row highlighted in yellow)

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Disc. Cash Haf yearly Total Cash Repayment APR 2 Discount factor Period time APR flows flows coupon DF (1+r/2)A C 3.6%/2 CF CR r/2 CF x DF n 2 xt R n) x 800 0.50 1 2.00% 1.00% 0.990099 14.40 14.40 14.26 1.00 2 2.82% 1.41% 0.972400 14.40 14.40 14.00 1.50 3 2.66% 1.33% 0.961200 14.40 14.40 13.84 2.00 4 2.70% 1.35% 0.947774 14.40 14.40 13.65 2.50 2.85% 1.43% 0.931697 14.40 14.40 13.42 3.00 6 2.95% 1.48% 0.915895 14.40 800.00 814.40 745.90 Total 815.07

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Step 3

Part (b)

C = semi annual coupon = 14.40

FV = 800; PV = 815.07; t = 2 x 3 = 6 half years

Hence, approximate and estimated semi annual YTM = [14.40 + (...

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FV-PV C+ t YTM FV+PV 2

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