Explanation:
Because the asset pays income at a rate of 5% every six months, the one-year income yield is compounded semi-annually:
Substitute the values:
The market forward is overpriced relative to theory.
Use a cash-and-carry arbitrage:
A) Cash and carry will realize $1.92 in future profit
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Question 716.2. An investment asset has a current price of $60.00 while the risk-free rate is 3.0% per annum with continuous compounding. The asset pays income twice a year and the income is equal to 5.0% of the asset price at the time of income payment; in other words, the asset's yield is 10.0% per annum with semi-annual compounding. If a one-year forward contract on the asset has a price of $58.00, and if we make the typical theoretical cost of carry assumptions (e.g., no trading transaction costs), then which of the following best summarizes the arbitrage opportunity? [note: inspired by Hull's Example 5.3]
A
a) Cash and carry will realize $1.92 in future profit
B
b) Cash and carry will realize $2.44 in future profit
C
c) Reverse cash and carry will realize $3.83 in future profit
D
d) There is no arbitrage opportunity: the forward is not mis-priced