Suppose you own $26,000. A stock costs $50 today. A put option written on the stock with maturity of 6 months and a strike price of $47.5 costs $2 (this gives you the right but not an obligation to sell 1 stock in 6 months for the fixed price of $47.5).

(1). What is the profit (payoff minus cost) of investing all your money in stocks if after 6 months the stock turns out to be $40, $45, $50, $55 or $60?

(2). What is the profit if you invest all your money in buying put options (instead of stocks) if after 6 months the stock turns out to be $40, $45, $50, $55 or $60?

(3). What is the profit if you buy 500 stocks and 500 put options if after 6 months the stock turns out to be $40, $45, $50, $55 or $60?

(4). What is the profit if you write (sell) 10,000 put options (assume the risk free rate is zero) if after 6 months the stock turns out to be $40, $45, $50, $55 or $60?