CFA Practice Question

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CFA Practice Question

John has an asset that is worth $110. He plans to sell it in 8 months. The risk-free interest rate is 4.5%. As found in basic question 1, the forward contract should be selling at $113.28. If the counterparty is willing to engage in such a contract at a forward price of $120, what should John do to take advantage of the situation? What is the annualized risk-free rate of return?
Correct Answer: Deliver the asset; 9.03%

As $113.28 is lower than $120, clearly this overpriced contract should be sold. John should hold the asset and sell the forward contract. At the contract expiration date he will deliver the asset and receive $120 for it. The rate of return will be (120/113.28) - 1 = 5.93%. The annualized risk-free rate of return is (1.0593)12/8 - 1 = 9.03%. John's position is not only perfectly hedged but also earns an arbitrage profit.

User Contributed Comments 14

User Comment
derektl2 Johns ROR is 120/110 annualized since the asset initially cost 110. His abnormal return (alpha) is what is calculated in the answer.
americade good point!
PhiWong Instead of holding the asset, could John sell the asset on spot, deposit the money for 8 months and long the forward at $113.28? Would that give him an annualized return of 13.53%(4.5% + 9.03%)?
danlan2 PhiWong, the counterparty is willing to engage in a contract at a forward price of $120, but we do not know if the counterparty is willing to purchase the asset on spot.

Derektl2 and americade, since we are dealing with forward, I think the rate of return is based on the forward price and not the underlying asset.
danlan2 Derektl2 and americade, you may be right, the rate of return can be based on underlying product.
simonjdp Wrong!, The asset has financing cost (ie oppurtunity cost). To enter the position one should borrow $110 at 4.5% and buy the asset.The cost of the asset over the period is thus $113.28 for which the return is calculated.
mdags I agree w/ simonjdp, b/c if forward was correctly priced @ 113.28, annualized RoR = 0%.
mdags Scratch that: If fwd. was correctly priced @ 113.28, annualized RoR = RFR = 4.5%. 9.03% represents arb. profit. Now I see...
jainrajeshv RoR for the John should be (6.7/110)* (12/8) = 9.14%.
vi2009 ROR = (120 / 113.28)^12/8 - 1 = 9.03%
You can x-ref the CFA Vol I example.
Because you sell and get 120 at arbs versus 113.28 which is no arbs.

Forward contract priced at $120 versus $113.28 (arbs-free). So John can sell at $120 instead of $113.28 to make some arbs profit therefore he hold the assets (or borrow $ at RF and buy even more assets) + enter into a short forward position to sell at $120.
bodduna John's opportunity cost of buying an asset&holding it for 8 months.
$110*(1.045)^0.6667-110 = 3.2759.
So His cost is $110 + $3.2759 = $113.2759.
If he did not buy the at $110.He would have entered a long forward contract @113.2759 and short forward contract @120. and earn interest on $110 @4.5% per year. Johns long position is hedge since he earns $3.2759 interest for 8 months.
or John can create arbitrage free profit. Short forward contract @120 and long forward contract @113.2759.
Annualised risk free rate = (120/113.2759)^1.5-1 = 9.03%
joywind I think the reason behind the dispute above is that: the question here is actually asking the rate of the return John can get from 'taking advantage of the arbitrage position' instead of the total rate of return from the whole pic.
Sagarsan88 2nd iconv
Nom 5.93*12/8
C/y 12/8
Eff cmp
Ans 9.03
happyha Why the heck is the answer using R^8/12, which indicates annually compounding interest, which is not what the question says, monthly compounding
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