
Explanation:
Since the forward price of the contract over Cosmetic World is higher than its current price, the investor can profit by borrowing the funds at the current rate to purchase shares at current prices and short forward contracts to sell the shares at higher forward prices.
If the investor borrows $76.2 dollar at the risk-free rate to purchase shares now, the loan amount, in 3 months, will grow to:
$76.20 \times (1.05)^{3/12} \times 5,000 \text{ shares} = \$385,675.72$
Since the investor will use the proceeds to short a forward contract (sell the shares at the forward price of $86.8), the cash flow from the short sell is:
$86.80 \times 5,000 \text{ shares} = \$434,000$
The arbitrage net cash flow is $434,000 - 385,675.72 = \$48,324.28$
This represents a classic cash-and-carry arbitrage strategy. The no-arbitrage forward price should be $76.2 \times (1.05)^{3/12} = \$77.14, but the actual forward price of $86.8 is much higher, creating a significant risk-free profit opportunity of approximately $48,324.
Q.670 Priyanka Singh is a derivative investment manager at Hind Investments based in Mumbai. Priyanka is analyzing the shares of Cosmetic World Company that are currently trading at $76.2 per share. Cosmetic World has the largest market shares in the cosmetics market of Asia, and the company has been profitable for over a decade. The 3-month forward contract on the stock is being offered for the price of $86.8. Priyanka Singh wants to trade 5,000 shares of Cosmetic World with the intention of closing the position in 3 months. If the risk-free interest rate is 5%, then determine the arbitrage profit.
A
$77,158
B
$68,485
C
$50,798
D
$48,324
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