Question

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 $ ________

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