We suppose that there are two fund managers (A and B) who hold exactly the same position in stocks of the French Petroleum company, Total. Each of them has 10,000 stocks whose current price is 40 EUR/ stock. They plan to sell these stocks in 3 months. However, they forecast a decline in the stock market over this period.

Fund manager A wants to be protected against a possible decline by keeping the opportunity to benefit from a possible increase. He buys 10,000 puts on his stocks (underlying asset = stocks Total, T = 3 months, K = 40, Premium = 4).

Fund manager B decides to sell 10,000 call options (underlying asset = stocks Total, T = 3 months, K = 40, Premium = 3), expecting that option premium can help him to improve his performance.

We consider 2 scenarios in 3 months (at maturity of the options):

Case 1: Total stock price decreases to 35 EUR/ stock;

Case 2: Total stock price increases to 45 EUR/ stock.

Answer the following questions:

1) For the fund manager A, what is his effective selling price (equal to the selling price of the stock plus the gain (or minus the loss) resulting from the put option acquired by the fund manager, multiplied by the number of stocks/ options) when he sells his Total stocks in Case 1? What is this price in Case 2? What is the minimum level of his effective selling price?

2) The same question for the fund manager B: what is his effective selling price (equal to the selling price of the stock plus the gain (or minus the loss) resulting from the call option sold by the fund manager, multiplied by the number of stocks/ options) when he sells his Total stocks in Case 1? What is this price in Case 2? What is the maximum level of his effective selling price?

3) Compare the effective selling prices of managers A and B with another manager M who simply keeps 10,000 Total stocks without buying/ selling any option.