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CFA Institute Exam CFA-Level-II Topic 3 Question 91 Discussion

Actual exam question for CFA Institute's CFA-Level-II exam
Question #: 91
Topic #: 3
[All CFA-Level-II Questions]

Michelle Norris, CFA, manages assets for individual investors in the United States as well as in other countries. Norris limits the scope of her practice to equity securities traded on U .S . stock exchanges. Her partner, John Witkowski, handles any requests for international securities. Recently, one of Norris's wealthiest clients suffered a substantial decline in the value of his international portfolio. Worried that his U .S . allocation might suffer the same fate, he has asked Norris to implement a hedge on his portfolio. Norris has agreed to her client's request and is currently in the process of evaluating several futures contracts. Her primary interest is in a futures contract on a broad equity index that will expire 240 days from today. The closing price as of yesterday, January 17, for the equity index was 1,050. The expected dividends from the index yield 2% (continuously compounded annual rate). The effective annual risk-free rate is 4.0811%, and the term structure is flat. Norris decides that this equity index futures contract is the appropriate hedge for her client's portfolio and enters into the contract.

Upon entering into the contract, Norris makes the following comment to her client:

"You should note that since we have taken a short position in the futures contract, the price we will receive for selling the equity index in 240 days will be reduced by the convenience yield associated with having a long position in the underlying asset. If there were no cash flows associated with the underlying asset, the price would be higher. Additionally, you should note that if we had entered into a forward contract with the same terms, the contract price would most likely have been lower but we would have increased the credit risk exposure of the portfolio."

Sixty days after entering into the futures contract, the equity index reached a level of 1,015. The futures contract that Norris purchased is now trading on the Chicago Mercantile Exchange for a price of 1,035. Interest rates have not changed. After performing some calculations, Norris calls her client to let him know of an arbitrage opportunity related to his futures position. Over the phone, Norris makes the following comments to her client:

"We have an excellent opportunity to earn a riskless profit by engaging in arbitrage using the equity index, risk-free assets, and futures contracts. My recommended strategy is as follows: We should sell the equity index short, buy the futures contract, and pay any dividends occurring over the life of the contract. By pursuing this strategy, we can generate profits for your portfolio without incurring any risk."

Determine the price of the futures contract on the equity index as of the inception date, January 18.

Show Suggested Answer Hide Answer
Suggested Answer: A

The futures price can be calculated by growing the spot price at the difference between the continuously compounded risk-free rate and the divedend yield as a continuously compounded rate. The continuously compounded risk-free rate is ln (l.040811) = 4%, so the futures price for a 240-day future is:

(Study Session 16, LOS 59.b)


Contribute your Thoughts:

Virgina
29 days ago
I'm not sure about this arbitrage idea. Doesn't that introduce additional risks that Norris should be considering?
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Bernadine
1 months ago
Haha, Norris is really going for that riskless profit! Gotta love those creative portfolio managers.
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Yuki
6 days ago
Client: I trust your expertise, let's make it happen!
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Belen
9 days ago
Norris: Absolutely, we need to take advantage of this arbitrage opportunity.
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Charlene
12 days ago
Client: Sounds like a good plan, let's go for that riskless profit!
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Shawana
1 months ago
Wait, I'm confused. Why is Norris recommending an arbitrage strategy? Shouldn't she just hold the futures contract until expiration?
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Bettye
1 months ago
This question is testing our knowledge of futures pricing. We need to use the cost-of-carry model to calculate the fair value of the futures contract.
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Sarina
20 days ago
Client: Sounds good, let's go for it.
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Jade
24 days ago
Michelle: We're hedging with a futures contract on the equity index.
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Merilyn
29 days ago
Client: What's the plan with my portfolio, Michelle?
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Rutha
2 months ago
I agree with Paulene, I also think the answer is A) 1,064.
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Lillian
2 months ago
I disagree, I believe the correct answer is B) 1,071.
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Kiera
2 months ago
Hmm, the futures price should be based on the spot price, expected dividends, and the risk-free rate. I think option C is the correct answer.
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Kendra
1 months ago
Yes, the futures price is influenced by various factors including the spot price, expected dividends, and the risk-free rate. Option C does seem to be the most likely choice.
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Moon
2 months ago
I agree with you, option C seems to be the correct answer.
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Paulene
2 months ago
I think the answer is A) 1,064.
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