CFA Practice Question

There are 206 practice questions for this study session.

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%. Suppose the forward contract is entered into at $113.28, and the price of the underlying asset is $109 at expiration. What is the rate of return for John?
Correct Answer: 4.5%

  • ST = 109
  • VT(0, T) = V9/12(0, 9/12) = 109 - 113.28 = -$4.28
As John is "short," the value of the contract to him is positive: $4.28. However, he incurred a loss on the asset of 110 - 109 = $1. The net gain is $3.28. The rate of return for the 8-month period is (3.28/110) - 1 = 2.98%. When annualized, the rate of return equals (1.0298)12/8 - 1 = 4.5%.

Not surprisingly, this rate is the annual risk-free rate. The transaction was executed at the no-arbitrage forward price of $113.28, and therefore it would be impossible for John to earn a return higher or lower than the risk-free rate.

User Contributed Comments 6

User Comment
PhiWong Another way to look at it is: Since John already long the foward, he is lock in for the selling price and therefore his rate of return would be precisely the risk-free rate.
PASS0808 John's return =value of the contract +return of holding the asset =-(109-113.28)+(109-110)=113.28-110=3.28
HenryQ It is better to keep the 109 out of the pictures does not matter what future spot price can be 104, 105, does not impact the return as it is already locked in by the contract...
vi2009 As long as the forward contract is entered at the arbs-free price, the rate of return is the RF rate.
mchu good question
Shalva Yes, useful tip to remember - if locked to no-arbitrage price, you'll earn only RF return
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