Short Selling & Option Investment (30 Marks)

In this question, you will compare two strategies on stock investment: Short Selling vs Options

1. Short selling: You are bearish on XYZ stock and decide to sell short 100 shares at the current price of $50 per share. What is your initial investment value and How high can the price of the stock go before you get a margin call if the initial margin is 50% and the minimum requirement margin is 30%? (6 Marks)
2. Option: Suppose the 12-month call for XYZ stock with $50 exercise price is currently selling for $4.5, the 12-month put for XYZ with the same exercise price is currently selling for $5. You are using these two options to create a synthetic short position. Describe your trading strategy on the synthetic short position (positions in the call and put so it will mimic the short position) (2 marks). What is the initial cash flow for this strategy (at per share base)? (2 marks)
3. Calculate & Compare the rate of returns for the above two strategies (Short-Selling vs Option strategy) when the stock price changes to $40, $45, $50, $55, on the option expiration date. Briefly state one advantage of using options compared with short selling based on your results (13 marks. Notes: ignore the impact of commissions and other transaction costs).
4. Suppose the risk-free rate is 10% currently and the stock will not pay dividend in the next year, given the current market conditions as described in questions a) and b) as above, is there any arbitrage opportunities? If yes, what is the trading strategy to explore this arbitrage opportunity? How much profit per share will you get? (7 Marks)