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An Introduction to Derivatives and Risk Management: With Stock-Trak Coupon

Don M. Chance, Robert Brooks

Chapter 10

Futures Arbitrage Strategies - all with Video Answers

Educators

Chapter Questions

05:25

Problem 1

On November 1 , the one-month LIBOR rate is 4.0 percent and the two-month LIBOR rate is 5.0 percent. Assume that Fed funds futures contracts trades at a 25 basis point rate under one-month LIBOR at the start of the delivery month. The December Fed funds futures is quoted at 94.75. Assuming no basis risk between Fed funds and one-month LIBOR at the start of the delivery month, identify whether an arbitrage opportunity is available. Contract size is $$\$ 5,000,000$$. Be sure to illustrate the arbitrage strategy for one contract. To show the dollar arbitrage, assume the one-month LIBOR rate on December 1 was 7 percent.

Manasvee Singh
Manasvee Singh
Numerade Educator
01:20

Problem 2

Repeat problem 1, but now assume the one-month LIBOR rate on December 1 was 5.5 percent.

Carson Merrill
Carson Merrill
Numerade Educator

Problem 3

On July 5 , a stock index futures contract was at 394.85 . The index was at 392.54 , the risk-free rate was 2.83 percent, the dividend yield was 2.08 percent, and the contract expired on September 20. Determine if an arbitrage opportunity was available, and explain what transactions were executed.

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Problem 4

Rework problem 3 assuming that the index was at 388.14 at expiration. Determine the profit from the arbitrage trade, and express it in terms of the profit from the spot and futures sides of the transaction. How does your answer relate to that in problem 3 ?

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Problem 5

It is August 20, and you are trying to determine which of two bonds is the cheaper bond to deliver on the December Treasury bond futures contract. The futures price is $8912 / 32$. Assume delivery will be made on December 14 , and use 7.9 percent as the repo rate. Find the cheaper bond to deliver.
a. Bond $\mathrm{X}$ : 9 percent noncallable bond maturing in about 28 years with a price of $10014 / 32$ and a CF of 1.1106. Coupons are paid on November 15 and May 15. The accrued interest is 2.37 on August 20 and 0.72 on December 14.
b. Bond Z: An 11 1/4 percent noncallable bond maturing in about 25 years with a price of 121 14/82 and a CF of 1.3444. Coupons are paid on February 15 and August 15. The accrued interest is 0.15 on August 20 and 3.7 on December 14.

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Problem 6

On September 26 of a particular year, the March Treasury bond futures contract settlement price was 94-22. Compare the following two bonds and determine which is the cheaper bond to deliver. Assume delivery will be made on March 1. Use 5.3 percent as the repo rate.
a. Bond A: A $123 / 4$ percent bond callable in about 19 years and maturing in about 24 years with a price of $1489 / 32$ and a CF of 1.4433 . Coupons are paid on November 15 and May 15. The accrued interest is 4.64 on September 26 and 3.73 on March 1.
b. Bond B: A $137 / 8$ percent bond callable in about 20 years and maturing in about 25 years with a price of $15927 / 32$ and a CF of 1.5689 . Coupons are paid on November 15 and May 15. The accrued interest is 5.05 on September 26 and 4.06 on March 1 .

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02:13

Problem 7

Identify two ways to express interest rate parity based on how interest rates are quoted. Explain why, in practice, they contain the same information.

Sandile Ndlovu
Sandile Ndlovu
Numerade Educator

Problem 8

On March 16, the March T-bond futures setciement price was 101 21/32. Assume the $121 / 2$ percent bond maturing in about 22 years is the cheapest bond to deliver. The CF is 1.4639. Assume that the price at 3:00 P.M. was 150 15/32. Determine the price at 5:00 P.M. that would be necessary to justify delivery.

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Problem 9

On March 16, the June T-bond futures contract was priced at $10017 / 32$ and the September contract was at $9917 / 32$. Determine the implied repo rate on the spread. Assume the cheapest bond to deliver on both contracts is the $111 / 4$ maturing in 28 years and currently priced at $14021 / 32$. The CF for delivery in June was 1.3598, and the CF for delivery in September was 1.3581. Delivery is on the first of the month, and the coupons are paid on February 15 and August 15. The accrued interest is 3.29 on June 1 and 6.16 on September 1.

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Problem 10

On September 12, the cheapest-to-deliver bond on the December Treasury bond futures contract is the $9 \mathrm{~s}$ of November 2018. The bond pays interest semiannually on May 15 and November 15. Its price is 125 12/32. The December futures price is 112 24/32. The bond has a conversion factor of 1.1002 . Its accrued interest on September 12 is 2.91 and its accrued interest on December 1 is 4.92 , which reflects the payment of the coupon on November 15. Assuming delivery on December 1, determine the implied repo rate. Then write an interpretation of your result.

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Problem 11

(Concept Problem) In this chapter, there are two equations presented for the implied repo rate related to bond futures contracts shown below. Explain these equations and discuss the differences between them.
$$
\begin{aligned}
& \hat{\mathrm{r}}=\left[\frac{(\mathrm{CF})\left(\mathrm{f}_0(\mathrm{~T})\right)+\mathrm{AI}_{\mathrm{T}}+\mathrm{CI}_{0, \mathrm{~T}}}{\mathrm{~B}_0+\mathrm{AI}_0}\right]^{(\mathrm{t} / \mathrm{T})}-1 \text { and } \\
& \hat{\mathrm{r}}=\left[\frac{(\mathrm{CF}(\mathrm{t})) \mathrm{f}_0(\mathrm{t})+\mathrm{AI}_{\mathrm{t}}+\mathrm{CI}_{\mathrm{L}, \mathrm{T}}}{(\mathrm{CF}(\mathrm{t})) \mathrm{f}_0(\mathrm{t})+\mathrm{AI}_1}\right]^{1 /(\mathrm{T}-\mathrm{t})}-1
\end{aligned}
$$

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Problem 12

Assume that on March 16, the cheapest bond to deliver on the June T-bond futures contract is the $14 \mathrm{~s}$, callable in about 19 years and maturing in about 24 years. Coupons are paid on November 15 and May 15. The price of the bond is $16128 / 32$, and the CF is 1.584 . The June futures price is $10017 / 32$. Assume a 5.5 percent reinvestment rate. Determine the implied repo rate on the contract. Interpret your result. Note that you will need to determine the accrued interest. Assume delivery on June 1.

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02:48

Problem 13

Explain how the repurchase agreement plays a role in the pricing of futures contracts. What is the implied repo rate?

Jennifer Stoner
Jennifer Stoner
Numerade Educator
02:48

Problem 14

Explain the implied repo rate on a U.S. Treasury bond futures spread position.

Jennifer Stoner
Jennifer Stoner
Numerade Educator

Problem 15

Identify and discuss four non-traded delivery options related to U.S. Treasury bond futures contracts.

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02:15

Problem 16

Define the conversion factor. Why are U.S. Treasury bond futures contracts designed with conversion factors?

Ethan Fuhrman
Ethan Fuhrman
Numerade Educator
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Problem 17

Identify and explain some factors that make the execution of stock index futures arbitrage difficult in practice.

Rashmi Sinha
Rashmi Sinha
Numerade Educator

Problem 18

What is program trading? Why is it so controversial?

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Problem 19

Explain the relationship between carry arbitrage and the implied repo rate.

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Problem 20

On August 20 a stock index futures, which expires on September 20 , was priced at 429.70. The index was at 428.51. The dividend yield was 2.7 percent. Discuss the concept of the implied repo rate on an index arbitrage trade. Determine the implied repo rate on this trade, and explain how you would evaluate it.

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05:04

Problem 21

A corporate cash manager who often invests her firm's excess cash in the Eurodollar market is considering the possibility of investing $$\$ 20$$ million for 180 days directly in a Eurodollar $\mathrm{CD}$ at 6.15 percent. As an alternative, she considers the fact that the 90 -day rate is 6 percent and the price of a Eurodollar futures expiring in 90 days is 98.75 (the IMM index). She believes that the combination of the 90-day CD plus the futures contract would be a better way of lending $$\$ 20$$ million for 180 days. Suppose she executes this strategy and the rate on 90-day Eurodollar CDs ninety days later is 5.9 percent. Determine the annualized rate of return she earns over 180 days and compare it to the annualized rate of return on the 180-day $\mathrm{CD}$.

James Kiss
James Kiss
Numerade Educator

Problem 22

(Concept Problem) Referring to problem 3, suppose transaction costs amounted to 0.5 percent of the value of the stock index. Explain how these costs would affect the profitability and the incidence of index arbitrage. Then calculate the range of possible futures prices within which no arbitrage would take place.

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