P1.T3.206. Hull's interest rate futures

[Suzanne Evans]

Questions:

206.1. The price of a Treasury bond with a 4.0% coupon that matures on July 1st, 2019 is quoted as 100-04. If today is July 26, 2012 what is the T-bond's cash price?

a. $100.125
b. $100.208
c. $100.397
d. $101.541

206.2. Suppose the Treasury bond futures price is 101-00 and the following three bonds are eligible for delivery:

I. Quoted bond price of $115.00 with a conversion factor (CF) of 1.10
II. Quoted bond price of $130.00 with a conversion factor (CF) of 1.28
III. Quoted bond price of $150.00 with a conversion factor (CF) of 1.44

Which of the bonds is cheapest to deliver (CTD)?

a. Bond I
b. Bond II
c. Bond III
d. All/none are equally cheap

206.3. A portfolio manager has a long position in bond portfolio with a value of $30.0 million. The manager wants to hedge against interest rate movements over the next three months with a T-bond futures contract maturing in four months. In three months, the estimated duration of the underlying long bond portfolio will be 7.0 years. The estimated duration of the anticipated cheapest to deliver (CTD) bond will be 9.1 years. The T-bond futures price is currently 102-16. Which is nearest to the duration-based hedge trade?

a. Long 48 futures contracts
b. Short 48 futures contracts
c. Long 225 futures contracts
d. Short 225 futures contracts

Answers:

• Here in forum

 

[caramel]

For 206.2 I thought the cheapest to deliver bond on maturity is defined to be the one for which the adjusted spot price is the lowest
i.e 115/1.1=104,545455
130/1.28=101.5625

 

[David Harper CFA FRM]

Hi caramel,

The short gets to pick one of the bonds to deliver. To purchase the bond for delivery, the short will pay (as a cost) the quoted bond price (+AI), e.g., $130 above; in exchange for delivering this bond, the short will receive (as income) the settlement price * CF (+AI); e.g., 101*1.28 , so the short looks to maximize his/her NET income by maximizing [settlement price * CF - quoted price]; or equivalently, by minimizing his/her NET cost, MIN[quoted price - settlement price * CF].
... it's really just a minimization of cost/benefit (or maximization of benefit/cost, if you will)

If you got the idea from this 2011 GARP sample question, http://forum.bionicturtle.com/threa...-conversion-factors-markets-and-products.4141
... I submitted that question last year as an error in approach (we are following assigned Hull, so I'm still not sure from where they generated this alternative CTD approach? as i recall, it often but not always coincides)

Hope that helps, thanks!