Suppose stock price S$=50,$ put option price P$=$ $$2\mathrm{.}00$ for $6$ mo maturity and exercise price E$=$$$50.$ You buy $200$ shares now. You believe there is a $50\%$ chance the stock price will increase to $$60$ and $50\%$ chance it will decline to $$40$ in the next $6$ months. How can you hedge against a decline in stock price by using options? Calculate the potential benefit or loss from hedging. What is the benefit$/$loss if the probabilities are $70\%$ for increase and $30\%$ for decrease.