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Options, Futures, and Other Derivatives

John C. Hull

Chapter 6

Interest rate futures - all with Video Answers

Educators

Chapter Questions

Problem 1

A U.S. 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, 2017, and August 8, 2017? How would your answer be different if it were a corporate bond?

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Problem 2

It is January 9,2018. The price of a Treasury bond with a $6 \%$ coupon that matures on October 12,2030 , is quoted as $102-07$. What is the cash price?

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01:20

Problem 3

How is the conversion factor of a bond calculated by the CME Group? How is it used?

Adriano Chikande
Adriano Chikande
Numerade Educator

Problem 4

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

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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
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
Narayan Hari
Numerade Educator

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?

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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
Vipender Yadav
Numerade Educator

Problem 9

It is May 5, 2017. The quoted price of a government bond with a $12 \%$ coupon that matures on July 27,2034 , is $110-17$. What is the cash price?

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Problem 10

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

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Problem 11

It is July 30,2018 . The cheapest-to-deliver bond in a September 2018 Treasury bond futures contract is a 13\% coupon bond, and delivery is expected to be made on September 30, 2018. 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.

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Problem 12

A trader 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 between 15 and 25 years?

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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
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
James Kiss
Numerade Educator
02:40

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?

Anand Jangid
Anand Jangid
Numerade Educator

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?

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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?

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Problem 18

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

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01:13

Problem 19

Between October 30,2018, and November 1,2018, you have a choice between owning a U.S. government bond paying a $12 \%$ coupon and a U.S. 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
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
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
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
Jennifer Stoner
Numerade Educator

Problem 23

It is April 7, 2017. The quoted price of a U.S. government bond with a $6 \%$ per annum coupon (paid semiannually) is $120-00$. The bond matures on July 27,2033 . What is the cash price? How does your answer change if it is a corporate bond?

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Problem 24

A Treasury bond futures price is $103-12$. The prices of three deliverable bonds are $115-06$, 135-12, and 155-28. Their conversion factors are $1.0679,1.2264$, and 1.4169 , respectively. Which bond is cheapest to deliver?

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05:25

Problem 25

The December Eurodollar futures contract is quoted as 98.40 and a company plans to borrow $$\$ 8$$ million for three months starting in December at LIBOR plus $0.5 \%$.
(a) What rate can the company lock in by using the Eurodollar futures contract?
(b) What position should the company take in the contracts?
(c) If the actual three-month rate turns out to be $1.3 \%$, what is the final settlement price on the futures contracts.
Explain why timing mismatches reduce the effectiveness of the hedge.

Manasvee Singh
Manasvee Singh
Numerade Educator
01:19

Problem 26

A Eurodollar futures quote for the period between 5.1 and 5.35 years in the future is 97.1 . The standard deviation of the change in the short-term interest rate in one year is $1.4 \%$. Estimate the forward interest rate in an FRA.

Linh Vu
Linh Vu
Numerade Educator

Problem 27

It is March 10, 2017. The cheapest-to-deliver bond in a December 2017 Treasury bond futures contract is an $8 \%$ coupon bond, and delivery is expected to be made on December 31, 2017. Coupon payments on the bond are made on March 1 and September 1 each year. The rate of interest with continuous compounding is $5 \%$ per annum for all maturities. The conversion factor for the bond is 1.2191 . The current quoted bond price is $$\$ 137$$. Calculate the quoted futures price for the contract.

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04:50

Problem 28

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
James Kiss
Numerade Educator

Problem 29

A Canadian company wishes to create a Canadian LIBOR futures contract from a U.S. 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.

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Problem 30

On June 25,2017 , the futures price for the June 2017 bond futures contract is 118-23.
(a) Calculate the conversion factor for a bond maturing on January 1, 2033, paying a coupon of $10 \%$.
(b) Calculate the conversion factor for a bond maturing on October 1, 2038, 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 on June 25, 2017, what is the cash price received for the bond?

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05:04

Problem 31

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
James Kiss
Numerade Educator