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.