Financial Economics 4378 FALL 2013 FINAL EXAM There are 10 questions Total Points 100 Name: Question 1 (10 points) A trader currently holds 300 shares of IBM stock. The trader also has $15,000 in cash. Consider the following two strategies that the trader can follow. Strategy 1: The trader holds the 300 shares for one year, and invests $15,000 cash in a risk free bond for an annual return of 5%. Strategy 2: The trader buys 300 put options on IBM with strike price X=180 that expire in one year. The price of each option is p=10. The trader then holds 300 IBM shares and invests the remaining cash (what is left after buying the put options) in the risk free bond for an annual return of 5%. For what values of IBM share price S T in one year at the expiration date, does Strategy 2 prove to be the better one?
Question 2: (10 points) A trader sells 200 shares of IBM stock short at share price $100 each and hence generates $20,000 in cash. Consider the following two strategies that the trader can follow. Strategy 1: The trader holds the short position of 200 shares for one year, and invests $20,000 cash in a risk free bond for an annual return of 5%. Strategy 2: The trader buys 200 call options on IBM with strike price X=140 that expire in one year. The price of each call option is c=10. The trader holds the short position of 200 shares for one year and invests the remaining cash in the risk free bond for an annual return of 5% (note that now the trader can only invest $18,000 since $2000 is spent on call options). For what values of IBM share price S T in one year at the expiration date, does Strategy 2 prove to be the better one?
Question 3: (Interest Rate Swap Design) (10 points) Two parties A and B have been offered the following rates on a loan. Company Fixed Rate Floating Rate A 16% Libor +7% B 10% Libor + 6% A requires a fixed rate loan. B requires a floating rate loan. a) (3 points) Which company has comparative advantage in Fixed Rate Loan market? Which company has comparative advantage in Floating Rate Loan market? What is size of the potential gain from a swap agreement in the above situation? b) (7 points) Suppose the two parties cannot engage directly with each other and a bank will act as an intermediary. Design a pair of swaps that divides the surplus as follows. A gets 60% of the surplus B gets 20% of the surplus Bank gets 20% of the surplus
Question 4 (10 points) If the following two portfolios contain the same delta points, what should be the number of call options contracts N in portfolio B? Portfolio A: 1000 shares of IBM and long positions in 20 put option contracts on IBM (each contract contains 100 put options) with put delta -0.20. Portfolio B: 500 shares of IBM and N long call option contracts on IBM (each contract contains 100 call options) with call delta +0.50. Question 5 (10 points) If the following portfolio has 4900 delta points, what should be the number of put options contracts N in the portfolio? 1500 shares of BAC stock. 10 LONG call option contracts on BAC (each call contract contains 100 call options) with call delta 0.60. N SHORT put option contracts on BAC (each put contract contains 100 put options) with put delta -0.40.
Question 6 (10 points) Consider two put options on the same stock with the same expiration date. Put option #1 has a strike price of X₁=180 and its price is given by p₁=25. Put option #2 has a strike price of X₂=170 and its price is given by p₂=10. The gross risk free rate of return from today until the expiration date is r=1.1. a) (1 point) Given that we must have (as shown in class), p₁-p₂ X₁-X₂ state whether arbitrage is possible. c) (2 points) Precisely specify the arbitrage position. c) (7 points) Find the arbitrage profit for all possible values of S T the stock price at the expiration date. Specify the minimum and maximum arbitrage profits possible.
Question 7: (10 points) Consider a trading position which involves A short position in a call option with a strike price X = 70 and a price c = 10. A long position in a put option with a strike price X = 70 and price p= 10. Both options have the same underlying stock and the same expiration date. Find and draw the payoff diagram for this position as a function of S T
Question 8 (10 points) State whether the following statement is true or false and explain why in one or two sentences. Be precise and concise for full credit. Statement: If an investor expects that interest rates will go down and if that investor is holding a bond portfolio with a negative duration gap, the investor needs to reduce the duration of the liability side of the portfolio to reduce his/her interest rate risk exposure and protect net worth. Question 9 (10 points) State whether the following statement is true or false and explain why in one or two sentences. Be precise and concise for full credit. Statement: If an investor buys call options on a stock and also sells put options on the same stock, then this investor can offset his/her risk with respect to the underlying stock price by buying shares of the underlying stock.
Question 10: (10 points) Consider a put option and a call option on the same stock. Both the call and the put have a strike price X=110. The call price is c=12 and the put price is p=15. The current stock price is S o =98. The risk free rate of interest from today until expiration is r=10% a) (4 points) Identify if arbitrage is possible and specify the arbitrage position. b) (6 points) For the arbitrage strategy you specified, find the arbitrage profit for all values of stock price at expiration date S T