At time t stock A is trading at 100$ and its fair value is 110$. Arbitrager has 400$ of his own money and 1600$ of borrowed funds. The creditor has no ability to evaluate his trading strategy and judges him on his past performance.

a) Suppose that at t+1 the price of the stock will surely be 105$ and at t+2 the price of the stock will be equal to fair value of 110$. How much should arbitrager invest at time t? (If you are unable to provide the quantitative answer, please provide the intuition). Explain.

b) Suppose that at t+1 the price of the stock will be either 105$ with 70% likelihood or 95$ with 30% likelihood. At t+2 the price of the stock surely converges to fair value. Is arbitrager going to buy more, less or the same of the stock at time t then in case a)? Explain.

c) Using the example above please comment on whether arbitragers are effective at correcting mispricings in volatile markets?