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# PROBLEM 4(a-c) A bond speculator currently has positions in two separate corporate bond portfolios: Long holding in Portfolio 1 and a short holding...

PROBLEM 4(a-c)
A bond speculator currently has positions in two separate corporate bond portfolios:
a. Long holding in Portfolio 1 and a short holding in Portfolio 2.
b. All of the bonds have the same credit quality.

Other Relevant information on these positions include:
Market Coupon Compounding Yield to
Portfolio Bond Value (Mil.) Rate Frequency Maturity Maturity
1 A \$6.00 0.0% Annual 3 yrs 7.31%
B \$4.00 0.0% Annual 14 yrs 7.31%
2 C \$11.50 4.6% Annual 9 yrs 7.31%

Treasury bond futures (based on \$100,000 face value of 20 year T-bonds having an 8 percent semi coupon) with a
maturity exactly six months from now are currently priced at 109-24 with a corresponding yield to maturity of 7.081
percent. The "yield betas" between the futures contract and Bonds A, B, and C are 1.13, 1.03, and 1.01, respectively.
Finally, the modified duration for the T-bond underlying the futures contract is 10.355 years.
a. Calculate the modified duration (expressed in years) for each of all yields increase by
60 basis points on an annual basis?

b. Without performing the calculations, explain which of the portfolios will actuall have its
value impacted to the greatest extent (in absolute terms) by the shift yields. (Hint: This
explanation requires knowledge of the concept of bond convesity).

c. Assuming the bond speculator wants to hedge her net bond position, what is the optimal
number of futures contracts that must be bought or sold? Start by calculating the optimal
hedge ratio between the futures contract and the two bond portfolios separately and then
combine them.

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