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Suppose that the risk-free interest rate is 10% per annum with continuous compounding. The dividend yield on a stock is 3.5% per annum. The stock currently is selling at $265 and the futures price for a contract deliverable in five months is $270.

a. What is the forward price predicted by the forrmula F0 = S0 e(r-q)T? (sample answer: 130.50)
b. Is there an arbitrage opportunity? (sample answer: yes; or no)
c. If there is an arbitrage opportunity, then will you long futures or short futures? (sample answer: Long; or Short)
d. What is the arbitrage profit per share if there is an arbitrage opportunity in today’s dollar (PV of the profit) ignoring the transaction fee? (sample answer: 1.25)

User TZubiri
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Final answer:

To calculate the forward price, use the formula F0 = S0 * e^(r-q)T where r is the risk-free interest rate, q is the dividend yield, S0 is the stock price, and T is the time period.

Step-by-step explanation:

To calculate the forward price using the formula F0 = S0 * e^(r-q)T, we first need to calculate the risk-free interest rate (r) and the dividend yield (q) per period. In this case, the risk-free interest rate is 10% per annum with continuous compounding, which means r = 0.1. The dividend yield on the stock is 3.5% per annum, so q = 0.035. The current stock price (S0) is $265 and the time period (T) is five months.

Using the formula, F0 = S0 * e^(r-q)T, we can substitute in the values: F0 = 265 * e^(0.1-0.035)^(5/12). Calculating this expression, the forward price predicted by the formula is approximately $268.50.

b. To determine if there is an arbitrage opportunity, we compare the forward price with the futures price. The futures price for a contract deliverable in five months is $270, which is higher than the forward price. Therefore, there is an arbitrage opportunity.

c. To take advantage of this arbitrage opportunity, you would short the futures. This means you would sell the futures contract with the expectation that the price will decrease.

d. To calculate the arbitrage profit per share, subtract the forward price from the futures price: $270 - $268.50 = $1.50. However, since there are no transaction fees mentioned, the arbitrage profit per share would be $1.50.

User Richardpringle
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