Options, Futures, and Other Derivatives

John C. Hull

Chapter 6 Interest Rate Futures - all with Video Answers

Educators

Chapter Questions

00:33

Problem 1

A US Treasury bond pays a $7 \%$ coupon on January 7 and July 7 . How much interest accrues per $\$ 100$ of principal to the bondholder between July $7,2004,$ and August $9,2004 ?$ How would your answer be different if it were a corporate bond?

Trinity Steen

Numerade Educator

00:33

Problem 2

It is January $9,2005 .$ The price of a Treasury bond with a $12 \%$ coupon that matures on October $12,2009,$ is quoted as $102-07 .$ What is the cash price?

Trinity Steen

Numerade Educator

01:20

Problem 3

How is the conversion factor of a bond calculated by the Chicago Board of Trade? How is it used?

Adriano Chikande

Numerade Educator

00:46

Problem 4

A Eurodollar futures price changes from 96.76 to 96.82 . What is the gain or loss to an investor who is long two contracts?

Heather Zimmers

Numerade Educator

01:18

Problem 5

What is the purpose of the convexity adjustment made to Eurodollar futures rates? Why is the convexity adjustment necessary?

Vysakh M

Numerade Educator

01:55

Problem 6

The 350 -day LIBOR rate is $3 \%$ with continuous compounding and the forward rate calculated from a Eurodollar futures contract that matures in 350 days is $3.2 \%$ with continuous compounding. Estimate the 440 -day zero rate.

Narayan Hari

Numerade Educator

07:43

Problem 7

It is January $30 .$ You are managing a bond portfolio worth $\$ 6$ million. The duration of the portfolio in 6 months will be 8.2 years. The September Treasury bond futures price is currently $108-15,$ and the cheapest-to-deliver bond will have a duration of 7.6 years in September. How should you hedge against changes in interest rates over the next 6 months?

John Lee

Numerade Educator

02:32

Problem 8

The price of a 90 -day Treasury bill is quoted as 10.00 . What continuously compounded return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90 -day period?

Vipender Yadav

Numerade Educator

00:47

Problem 9

It is May $5,2005 .$ The quoted price of a government bond with a $12 \%$ coupon that matures on July 27,2011 , is $110-17$. What is the cash price?

Hoan Nguyen

Numerade Educator

02:00

Problem 10

Suppose that the Treasury bond futures price is $101-12$. Which of the following four bonds is cheapest to deliver?
$$\begin{array}{lcc}\hline \text {Bond} & \text {Price} & \text {Conversion factor} \\
\hline 1 & 125-05 & 1.2131 \\2 & 142-15 & 1.3792 \\3 & 115-31 & 1.1149 \\
4 & 144-02 & 1.4026 \\\hline\end{array}$$

Majid Borumand

Numerade Educator

00:45

Problem 11

It is July $30,2005 .$ The cheapest-to-deliver bond in a September 2005 Treasury bond futures contract is a $13 \%$ coupon bond, and delivery is expected to be made on September 30,2005 Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semiannual compounding is $12 \%$ per annum. The conversion factor for the bond is $1.5 .$ The current quoted bond price is $\$ 110 .$ Calculate the quoted futures price for the contract.

Matt Just

Numerade Educator

03:08

Problem 12

An investor is looking for arbitrage opportunities in the Treasury bond futures market. What complications are created by the fact that the party with a short position can choose to deliver any bond with a maturity of over 15 years?

Oluwadamilola Ameobi

Numerade Educator

01:55

Problem 13

Suppose that the 9 -month LIBOR interest rate is $8 \%$ per annum and the 6 -month LIBOR interest rate is $7.5 \%$ per annum (both with actual/365 and continuous compounding). Estimate the 3 -month Eurodollar futures price quote for a contract maturing in 6 months.

Narayan Hari

Numerade Educator

03:26

Problem 14

Suppose that the 300 -day LIBOR zero rate is $4 \%$ and Eurodollar quotes for contracts maturing in $300,398,$ and 489 days are $95.83,95.62,$ and $95.48 .$ Calculate 398 -day and 489-day LIBOR zero rates. Assume no difference between forward and futures rates for the purposes of your calculations.

James Kiss

Numerade Educator

03:04

Problem 15

Suppose that a bond portfolio with a duration of 12 years is hedged using a futures contract in which the underlying asset has a duration of 4 years. What is likely to be the impact on the hedge of the fact that the 12 -year rate is less volatile than the 4-year rate?

Mike Stern

Numerade Educator

00:43

Problem 16

Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue $\$ 5$ million of commercial paper with a maturity of 180 days. If the paper were issued today, the company would realize $\$ 4,820,000$. (In other words, the company would receive $\$ 4,820,000$ for its paper and have to redeem it at $\$ 5,000,000$ in 180 days time.) The September Eurodollar futures price is quoted as $92.00 .$ How should the treasurer hedge the company's exposure?

Stark Ledbetter

Numerade Educator

00:47

Problem 17

On August $1,$ a portfolio manager has a bond portfolio worth $\$ 10$ million. The duration of the portfolio in October will be 7.1 years. The December Treasury bond futures price is currently $91-12$ and the cheapest-to-deliver bond will have a duration of 8.8 years at maturity. How should the portfolio manager immunize the portfolio against changes in interest rates over the next 2 months?

Sheryl Ezze

Numerade Educator

05:41

Problem 18

How can the portfolio manager change the duration of the portfolio to 3.0 years in Problem $6.17 ?$

Pragya Ahuja

Numerade Educator

01:13

Problem 19

Between October $30,2006,$ and November $1,2006,$ you have a choice between owning a US government bond paying a $12 \%$ coupon and a US corporate bond paying a $12 \%$ coupon. Consider carefully the day count conventions discussed in this chapter and decide which of the two bonds you would prefer to own. Ignore the risk of default.

Achintya Suden

Numerade Educator

01:55

Problem 20

Suppose that a Eurodollar futures quote is 88 for a contract maturing in 60 days. What is the LIBOR forward rate for the 60 - to 150 -day period? Ignore the difference between futures and forwards for the purposes of this question.

Narayan Hari

Numerade Educator

01:55

Problem 21

The 3 -month Eurodollar futures price for a contract maturing in 6 years is quoted as $95.20 .$ The standard deviation of the change in the short-term interest rate in 1 year is 1.1\%, Estimate the forward LIBOR interest rate for the period between 6.00 and 6.25 years in the future.

Narayan Hari

Numerade Educator

02:48

Problem 22

Explain why the forward interest rate is less than the corresponding futures interest rate calculated from a Eurodollar futures contract.

Jennifer Stoner

Numerade Educator

04:50

Problem 23

Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 90 -day rate is $10 \%$ per annum, and the 180 -day rate is $10.2 \%$ per annum, both expressed with continuous compounding and actual/actual day count. The Eurodollar futures price for a contract maturing in 91 days is quoted as $89.5 .$ What arbitrage opportunities are open to the bank?

James Kiss

Numerade Educator

03:56

Problem 24

A Canadian company wishes to create a Canadian LIBOR futures contract from a US Eurodollar futures contract and forward contracts on foreign exchange. Using an example, explain how the company should proceed. For the purposes of this problem, assume that a futures contract is the same as a forward contract.

Natalie Britton

Numerade Educator

04:33

Problem 25

The futures price for the June 2005 CBOT bond futures contract is $118-23$
(a) Calculate the conversion factor for a bond maturing on January 1,2021 , paying a coupon of $10 \%$
(b) Calculate the conversion factor for a bond maturing on October $1,2026,$ paying a coupon of $7 \%$
(c) Suppose that the quoted prices of the bonds in (a) and (b) are 169.00 and 136.00 respectively. Which, bond is cheaper to deliver?
(d) Assuming that the cheapest-to-deliver bond is actually delivered, what is the cash price received for the bond?

Breanna Ollech

Numerade Educator

05:04

Problem 26

A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next 3 months. The portfolio is worth $\$ 100$ million and will have a duration of 4.0 years in 3 months. The futures price is $122,$ and each futures contract is on $\$ 100,000$ of bonds. The bond that is expected to be cheapest to deliver will have a duration of 9.0 years at the maturity of the futures contract. What position in futures contracts is required?
(a) What adjustments to the hedge are necessary if after 1 month the bond that is expected to be cheapest to deliver changes to one with a duration of 7 years?
(b) Suppose that all rates increase over the next 3 months, but long-term rates increase less than short-term and medium-term rates. What is the effect of this on the performance of the hedge?

James Kiss

Numerade Educator