Question 9

Susan Baker is a new hire at Crinson Bank’s Chicago office. She has joined the risk arbitrage desk where she will be training to take advantage of price discrepancies in the U.S. T-note futures and spot markets.

Her managing director, Gerald Bigelow, has asked her to calculate parameters for potential arbitrage opportunities for the bank given current market conditions. At the time he asked the question, the cheapest-to-deliver T-notes were at par, with a coupon rate of 8.5 percent. When trading futures, the risk arbitrage desk borrows at 12 percent and lends at 4 percent.

Looking at the calendar, Baker calculates that there are 184 days to the first coupon payment and 181 days from the first coupon payment to the second. Any interest accrued will be paid when the T-note is delivered against the futures contract, but Bigelow asks Baker not to concern herself in the calculations with the impact of reinvesting the coupons or with transaction costs.

To get a feel for the market, Baker first prices a 6-month futures contract that has 184 days to expiration in a “simplified scenario.” She decides to use the same interest rate for borrowing and lending, taking the average of the bank’s borrowing and lending rates. Calculating the futures price under these simplified assumptions, Baker tells Bigelow that the futures contract should trade at 99.7059. Bigelow explains that the futures price is below par even though the spot price is at par because of the benefit to a short seller of receiving the T-note coupon payments.

Having calculated the futures price in the “simplified scenario,” Baker modifies it to reflect the bank’s current borrowing and lending rates, and calculates the corresponding no-arbitrage bands. She tells Bigelow that the lower band will be at 97.7468. Bigelow checks her calculations, confirming that the higher band will be at 101.6294.

Once they know the no-arbitrage bands for current market conditions, Baker and Bigelow check the screen. They see that the market price of the futures contract for which they’ve been calculating no-arbitrage bands is 103. Together, they execute Baker’s first arbitrage play.

Part 1)
Regarding Baker’s and Bigelow’s statements about the futures price in the simplified scenario:

Part 2)
Which of the following most accurately describes the arbitrage strategy that Baker and Bigelow executed?

Part 3)
Regarding Baker’s and Bigelow’s statements about the no-arbitrage bands, which is CORRECT?

Part 4)
If the T-notes that Baker priced in the “simplified scenario” were not the cheapest to deliver, and the cheapest-to-deliver note had a conversion factor of 1.07, what would be the no-arbitrage futures price?

Part 5)
How much does Baker expect to earn in profits on her first arbitrage play (in dollars per contract, ignoring transaction costs and any reinvestment of coupon payments)?

Part 6)
If the bank enters an arbitrage play involving the cheapest-to-deliver Treasury bond, which of the following statements is INCORRECT?

答案如下

Question 9

Part 1)
Your answer: B was incorrect. The correct answer was D) Baker’s statement is correct and Bigelow’s statement is incorrect.

Since the futures contract has 184 days to expiration and the next coupon payment on the T-note is also 184 days away, the coupon will be received on the last day of the contract. Thus, the futures value using the cash and carry model will be the spot price plus interest on borrowing the money to buy the note minus interest received (in this case, the coupon payment). The interest rate Baker calculates for the “carry” will be the average of the 12 percent borrowing rate and 4 percent lending rate, or 8 percent. Since the coupon payment received will equal one-half of the 8.5% coupon rate on the note, we calculate:

100 x (1 + 0.08)^{184 / 365} - 4.25 = 99.7059 

Baker’s statement is correct. Bigelow’s statement is incorrect on many levels, including the fact that a short seller does not receive coupon payments.

Part 2)
Your answer: B was incorrect. The correct answer was C) Borrow funds, buy spot asset, sell futures, collect accrued interest on spot asset, deliver asset against short futures, and repay loan with interest.

The arbitrage that Baker and Bigelow executed is a classic cash and carry arbitrage because the futures contract was trading above its fair value. The idea behind a cash and carry arbitrage is to make a profit on a futures contract that is trading over its fair value by buying the underlying asset with borrowed money and then selling the overpriced futures contract. The underlying asset can then be delivered against the short futures contract when the future expires.

When a Treasury futures contract is trading over its fair value, the cost of buying the underlying asset (including interest charges on the borrowed funds less interest received on the Treasury security) will be more than made up for by the price received on the sale of the futures contract.

Part 3)
Your answer: B was incorrect. The correct answer was C) Baker’s statement is correct and Bigelow’s statement is correct.

Using the cash and carry model and the risk arbitrage desk’s borrowing rate of 12 percent, the calculation of the higher band is: 

100 x (1 + 0.12)^{184 / 365} - 4.25 = 101.6294 

Using the reverse cash and carry model and the bank’s lending rate of 4 percent, the calculation of the lower band is:

100 x (1 + 0.040)^{184 / 365} - 4.25 - 0.0000 = 97.7468. 

Baker’s statement is correct and Bigelow’s statement is correct.

Part 4)
Your answer: B was incorrect. The correct answer was C) 93.1831.

If the cheapest-to-deliver note has a conversion factor of 1.07, the no-arbitrage futures price is:

(99.7059 / 1.07) = 93.1831.

Part 5)
Your answer: B was correct!

Since the futures are overpriced relative to the spot price, we calculate profit per contract as a cash and carry arbitrage relative to the upper bound: 

103 - [100 x (1 + 0.12)^{184 / 365} - 4.25] = 1.371 

Since Baker will make 1.371 points on each contract, and a Treasury future has a face value of $100,000, Baker expects to make $1,371 on each contract she trades.

Part 6)
Your answer: B was incorrect. The correct answer was C) The long position has the advantage in the arbitrage play.

An arbitrage play involving the cheapest-to-deliver bond may not be risk free since the cheapest-to-deliver bond may change during the life of the contract. This provides an advantage to the short (not the long) since the short position makes the decision about which bond to deliver.

thanks！

good

非常感谢！

晕，好麻烦，偶在国外啊

thx