An investor believes the market has systematically over-valued the dollar, and proceeds to short dollars (betting the dollar will fall in value by enough, i.e.,that E will rise by enough). His investment scheme is as follows:
1. Borrow Et dollars at date t. Promise to repay them at date t + 1, with interest at rate iUS.
2. Bet the price of dollars will fall enough, i.e., bet that Et+1 > Et by enough:
- Buy 1 pound for Et dollars at date t
- Earn interest, ending up with 1 + iB pounds
- Buy dollars at date t + 1, obtaining Et+1(1 + iB) dollars for your 1 + iBpounds
- Repay the loan. With interest, the repayment is Et(1 + iUS) dollars
a.) What is the condition for positive profits?
b.) Is it sufficient that Et+1 > Et? Why or why not?
c.) Suppose markets expect the dollar to depreciate against the pound. In order to make a profit, what must happen to E relative to market expectations?