Fixed Income - future contracts

CFA Level III Portfolio Management
#1

Puhuyesva believes interest rates will fall over the next three months and wants to position the asset portfolio accordingly. She intends to use futures contracts on the 10-year Treasury bond. The three-month contract has a par value of USD100,000 and a basis point value of USD102.30 per contract. Exhibit 1 provides current information about the asset and liability portfolios.

                           **Assets**                   **Liabilities**

Value USD217.3 million USD206.8 million
Modified duration 11.2 years 14.5 years
Basis point value (BPV) USD243,376 USD299,860

The most appropriate action given Puhuyesva’s views on interest rates and the information in Exhibit 1 would be to buy:

  1. 492 contracts.
  2. 614 contracts.
  3. 552 contracts.

B is correct. The number of futures contracts needed to fully remove the duration gap between the asset and liability portfolios is given by Nf=BPVL−BPVABPVf,

where BPV is basis point value (of the liability portfolio, asset portfolio, and futures contract, respectively). In this case, Nf=299,860−243,376102.30=+552.1, where the plus sign indicates a long position in or buying 552 futures contracts. Because the value of assets is more than 2% greater than the value of liabilities (217.3/206.8 − 1 = 5.1%) and Puhuyesva believes interest rates will fall, the duration of assets should be greater than the duration of liabilities so that the surplus will rise if interest rates do fall. Therefore, more than 552 contracts should be bought.

Seriously, guys? I would have went for 552 contracts, the end. What is this? :frowning: why the 2% threshold, what kind of rule is this?

Thanks!
C.

#2

Where did you get this question?

#3

CFA institute online question

#4

Seems bizarre.

I’ve never seen an actual exam question in which the answer was, “Well, it needs to be bigger than this, so choose the only number that’s bigger than this.”

I, for one, wouldn’t worry about it, but I might suggest e-mailing CFA Institute to ask them if this is the sort of thing you can expect on the real exam. Their reply might be very interesting.

#5

552 contracts is the answer if the objective is to “close the duration gap”, no gain/loss from declining rates.

Since the objective here is to “position the asset portfolio accordingly” with the view that interest rates will fall, the strategy is to set the BPV of (assets + futures) to exceed the BPV of liabilities, so 614 contracts (i.e. more than 552) should be the answer.

The 2% threshold does not make sense.

#6

552 contracts is the answer if the objective is to “close the duration gap”, no gain/loss from declining rates.

Since the objective here is to “position the asset portfolio accordingly” with the view that interest rates will fall, the strategy is to set the BPV of (assets + futures) to exceed the BPV of liabilities, so 614 contracts (i.e. more than 552) should be the answer.

I agree that the answer should be more than 552. I disagree that it should be specifically 614. And I disagree that on the real exam CFA Institute would ever have a question where the logic to arrive at the answer is, “Well, it has to be bigger than X, and C is the only answer that’s bigger than X, so it must be C.”

#7

Nice. I actually received an email notification on this reply. Gotta say the new forum layout looks sleek.

But ya, it really brings to question how the CFA Institute outsources the writing of the online questions and whether they do quality control checks on it to make sure it is aligned to what is expected from the exam.

#8

Thanks, guys! I feel better now :smile:
Btw the new forum is cool, I also like the fact that notifications are sent per email.

#9

In the chart, it is easy to know that, with 1 basis point decrease, the portfolio value will decrease 299860-243376=56484, so at this time, we should buy a futures contract, we have been told that, with 1 basis point decrease, we will gain 102.3, in order to complete hedge, with the equation: -56484+102.3x=0 then x=552, so we should long 552 contracts.That is right.
But,if she wants to make money through the decline of the interest rates, she should buy more than 552, equation can be like: (an example). -56484+102.3x=10000 x=650
614 is also another example, not an only answer to reach the target , l think.

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