Question

At one point, certain U.S. Treasury bonds were callable.

Consider the prices in the following three Treasury issues as of May 15, 2017:

05/15/2020 7.00 109.03125 109.09375 − .31250 3.770

05/15/2020 8.05 109.56250 109.62500 − .09375 4.580

05/15/2020 9.35 114.62500 114.81250 − .46875 4.060

The bond in the middle is callable in February 2018. 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?)

Answer 1

As the hint implies, we will first look at the coupon rates. Imagine that we have money to invest, and we want a 8.05% return, but we cannot invest in Bond 2. The other option is to invest part of our money into Bond 1 and part into Bond 3, so that the average rate of return is 8.05%

Formula: Rate 2 = Rate 1 * (X) + Rate 3 * (1-X)

8.05 = 7.00 X + 9.35(1 -X)

8.05 = 7.00 X + 9.35 - 9.35 X

9.35 X - 7.00 X = 9.35 - 8.05

2.35 X = 1.3

X = 1.3 / 2.35

X = 0.553191

Expected Price of Bond 2:

Price 2 = (Price 1 * 0.553191) + (Price 3 * 0.446809)

Price 2 = (109.09375 * .553191) + (114.81250 * 0.446809)

Price 2 = (60.349681) + (51.299202)

Price 2 = 111.648883

NOW EXPECTED PRICE - GIVEN PRICE 2:

111.648883 - 109.6250

= 2.02388

ASSUMING BOND VALUES IS $1000

CALL FEATURE IS $ 20.2388