Question

At one point, some Treasury bonds were callable. Consider the prices on the following three Treasury...

At one point, some Treasury bonds were callable. Consider the prices on the following three Treasury issues as of May 15, 2016:

7.35 May 20 n 122.50000 122.56250 .56250 5.45
9.10 May 20 119.62500 119.68750 .06250 5.41
12.85 May 20 151.78125 151.96875 .62500 5.49


The bond in the middle is callable in February 2017. What is the implied value of the call feature? Assume a par value of $1,000. (Hint: Is there a way to combine the two noncallable issues to create an issue that has the same coupon as the callable bond?) (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

Call value $ ________

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Answer #1

Bond 2 is callable, Bond 1 and 3 are non-callable. To create an issue that has the same coupon as the callable bond, it should be equal to the weighted average of the non-callable bond.

Assuming x percent of the money invested in Non-callable Bond 1 and 1-x percent of the money invested in Bond 3,

R2 = R1(X) + R3(1-X)

9.10 = 7.35X + 12.85(1-X)

9.10 = 7.35X + 12.85 - 12.85X

3.75 = 5.5X

X=0.681818

If we invest 0.681818 in Bond 1 then in Bond 3 (1-0.681818) = 0.318182 then,

P2=W1P1 + W3P3

P2=0.681818(122.5625) + 0.318182(151.96875)

P2=131.9190341

The actual price of Bond 2 is 119.68750 and the implied value of Bond 2 is 131.9190341, thus the call is:

=Implied bond value - actual bond value

=131.9190341 - 119.68750

=12.2315341

If the par value is $1000, the value of call feature is $122.315341

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