Question

On March 15, 2018, the price of a T-bill maturing on Sep 15, 2018 is $97.28, the price of a T-bill with maturity on March 15, 2019 is $97.67, and the price of a semiannual coupon (coupon rate 3.75%) treasury note that will mature on Sep 15, 2019 is $99.97. What is the price of a stripe with maturity on Sep 15 of 2019?

Answer 1

Coupon rate= 3.75%;

Thus, annual coupon for Face Value of T-bill with $ 100 face value = 3.75% x 100 = $ 3.75

Since, it is semiannual coupon, hence coupon payment =$ 3.75/2 = $ 1.875

Next, we calculate interest rate for 6-month, 1-year and 18-months using given data.

• For 6-month interest rate r _6-month

The present value of T-bill = Cash flow after 6-month / ( 1+ r _6-month ) ^0.5

or  ( 1+ r _6-month ) ^0.5 = Cash flow after 6-month / Present value of T-bill

= 100/ 97.28 = 1.02791

( 1+ r _6-month ) = 1.0567

or  r _6-month = 0.0567= 5.67%

Similarly , we calculate r _1-yr = 2.39%

Next, we consider the semi-annual coupon paying treasury note.

This has three cash inflows- coupons of $1.875 at 6-month and 12-month each and $ 101.875 ( $ 100 + $ 1.875) on Sep 15, 2019.

Using the interest rates derived above, we can calculate the present value of these coupons:

PV of coupon at 6-month=  $1.875 x $97.28/ $ 100 = $ 1.824

PV of coupon at 1-yr=  $1.875 x $97.67/ $ 100 = $ 1.831

Thus, PV of $ 101.875 ( $ 100 + $ 1.875) on Sep 15, 2019 = $ 99.97 - $ 1.824 - $ 1.831 = $ 96.315

So, present value of a stripe (stripe offer no interest rates and mature at par) with face value $100 maturing on Sep 15, 2019 =

= $ 94.54