Assume that a two-month forward contract (100 shares per contract; cash settlement at maturity) is written on a stock that will not pay any dividend in the next two months.
Assume that:
* The forward contract can be traded at $100 per share right now (with long or short position);
* Riskfree rate (borrow or deposit) is quoted as APR=12%, compounded monthly;
* There is no margin requirement or collateral required for forward contract, short sales, or loan;
* At the riskfree rate, you are also allowed to deposit your proceeds received from short sales.
(a) How do you synthesize (create) a portfolio (with shares and cash position) that will have the same settlement cashflow in two months as if you are holding one forward contract with long position (forward buyer). Specify exactly how many shares you need to buy (or short sell) and how much cash you need to borrow or deposit at the riskfree rate.
(b) Assume that the stock now can be traded at $100 (to buy or to sell). How do you form an arbitrage strategy to take advantage of this?
(Need to show the components of your arbitrage portfolio and arbitrage cashflows to justify that your arbitrage strategy works!)
(c) Assume that the stock now can be traded at $50 (to buy or to sell). How do you form an arbitrage strategy to take advantage of this?
(Need to show the components of your arbitrage portfolio and arbitrage cashflows to justify that your arbitrage strategy works!)
(d) (10 Points) What will be the "right" price for the stock right now in order to prevent arbitrage opportunity?
(e) If the stock is currently traded at the "right" price as you find in (d) and if the stock market reaches a consensus that the expected value of the stock is $120 at the end of two month, what can you conclude about the overall risk preference of the market?