Answered: Suppose 6-month Treasury bills are…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose 6-month Treasury bills are trading at a YTM of 1.6%, 12-month T-bills are trading at a YTM of 2.9%. If 18-month Treasury notes with a coupon rate of 3% are trading at par ($100), then what is the 18-month spot rate?

Expert Solution

Step 1: Explaining the above given information

We are given the 6 month spot rate and 12 month spot rate as 1% and 2% respectively. The YTM of the T-bills are the spot rates.

Now we are also given the price of an 18 month T note with 5% coupon as $100 (as it is trading at par).

Price of the T note is the PV of all future coupons and par value discounted at the spot rate.

The formula will be as below:

$P r i c e space equals space fraction numerator C o u p o n over denominator left parenthesis 1 plus S subscript 1 right parenthesis to the power of 1 end fraction space plus space fraction numerator C o u p o n over denominator left parenthesis 1 plus S subscript 2 right parenthesis squared end fraction plus fraction numerator C o u p o n space plus space P a r space V a l u e over denominator left parenthesis 1 plus S subscript 3 right parenthesis cubed end fraction$

By rearranging the above formula, we can solve for S3 which is 18-month spot rate. Please note that the spot rates need to be divided by 2 as the compounding is semiannual.

Coupon is computed with the formula below:
Semiannual Coupon = coupon rate/2 x par value

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