# BUS-495 Fall 2011 Final Exam: December 14 Answer Key

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1 Name: Score: BUS-495 Fall 011 Final Exam: December 14 Answer Key 1. (6 points; 1 point each) If you are neutral on a particular stock for the short term and looking to generate some income using options, you can construct an iron butterfly with options written on that stock. Answer the following questions regarding an iron butterfly strategy. Currently, the options have these prices: (1)call: strike \$65, premium \$0.45; ()call: strike \$60, premium \$.00; (3)put: strike \$60, premium \$.00; and (4)put: strike \$55, premium \$0.35. Ignore bid-ask spread and transaction costs. (a) The iron butterfly strategy has two long positions: a call with strike \$65 and a put with strike \$55. Plot the combined payoff of these two long positions as a function of S T, the underlying stock s price at expiration. (b) The iron butterfly strategy has two short positions: a call with strike \$60 and a put with strike \$60. Plot the combined payoff of these two short positions as a function of S T, the underlying stock s price at expiration. (c) Plot the combined payoff function with all the four positions together. 1

2 (d) What is the maximum profit of the iron butterfly strategy? =\$3.. (e) What is the maximum loss of the iron butterfly strategy? 3.-5=-\$1.8 (f) What is the break-even range of the iron butterfly strategy? =\$ =\$63. The strategy breaks even when the stock price ends up in between \$56.8 and \$63... ( points) Because the option s market value is at least as large as its intrinsic value, it is not ideal to exercise an American option early. But there is an exception. Discuss the occasion in which the investor is better off exercising an American option before expiration. If the underlying stock is issued by a company in a financial distress, the imminent bankruptcy makes the wait till maturity a huge opportunity cost. The investor in this case is better off to exercise the option premature. 3. (3 points) You are attempting to value a call option with an exercise price of \$400 and one year to expiration. The underlying stock pays no dividends and currently priced at \$400. You believe it has a 50% chance of increasing to \$500 and a 50% chance of decreasing to \$300. The risk-free rate of interest is 1%. Calculate the call option s value using the two-state binomial pricing model. The call s payoff is -C 100 0, given the stock s payoff is First step is to make the stock s payoff difference in the two states is the same as the call. We can achieve that by buying only half a share Then, we must add some borrowing at interest rate 1 + r = The goal is to make the payoff to become zero in the bad state

3 Add the stock holding and the borrowing to see The payoff is the same as the call option. Therefore, C = C = (3 points) Companies AAA and BBB can borrowed at the following rates per annum for a \$5 million loan with 10-year maturity: Fixed rate Floating rate Company AAA 5.0% LIBOR+.1% Company BBB 6.0% LIBOR+.5% Company AAA wants to borrow at a floating rate to pay for floating liabilities and Company BBB wants to have a fixed rate loan. A plain vanilla interest rate swap between Companies AAA and BBB can be beneficial to both. Design a swap that will net a bank, acting as intermediary, 0.% per annum and will appear equally attractive to AAA and BBB.. Note: this is only one possibility. As long as your result produces that AAA pays net LIBOR-.1%, BBB fixed 5.8%, and bank.%, it is correct. 5. (4 points; points each) The regression of monthly returns on Beeple stock against the S&P 500 index produces a beta of 1.. A hedge fund manager believes that Beeple is underpriced, with an alpha of 1% over the coming month. (a) If he holds Beeple stocks that are currently worth \$31.5 million, and wishes to hedge market exposure for the next month using 1-month maturity S&P 500 futures contracts, how many contracts should he enter? Should he buy or sell contracts? The S&P 500 currently is at 1,50 an the contract multiplier is \$50. price changes in portfolio (hedge ratio) = price changes in futures = \$31.5m = 10. Since the manager is long on the stocks, he should short the futures. (b) If the monthly risk-free rate is 1% and the CAPM is adequate in calculating required rate of return, what is the profit the manager can expect? Assume the component stocks in the S&P 500 index do not pay dividends. P ortfolio : 31, 50, 000 [1 + r f + 1. (r m r f ) + α] = 31, 50, 000 [.75 (r m ) + 1.0] = 37, 500, 000(r m.01) + 31, 875, 000. F utures : 10 50(F 0 S 1 ) = 30, 000 [S 0 (1 + r f ) S 1 ] = 30, 000 [S 0 (1 + r f ) S 0 (1 + r m )] = 30, 000 S 0 [(1 + r f ) (1 + r m )] = 30, 000 1, 50 ( r m +.01) = 37, 500, 000(r m.01) Combined : \$31, 875, 000. Profit is then \$65, (3 points; 1 point for part a and points for part b) If you take a long position on a gold futures contract (100 troy ounces) that calls for delivery 5 days from now. The futures price evolves in the next 5 days according to the following table. 3

4 Day Futures Price 0 (today) \$1, ,650? 3 1,70 4 1,730 5 (delivery) 1,710 (a) If you hold your long position till expiration, what is your total profit? (1,710-1,700) 100 = \$1, 000. (b) If the initial margin is 10% and the maintenance margin is 5% and you got a margin call on day, what is the highest possible per-ounce price for the silver futures on that day? Day Futures Price P/L per ounce Daily Proceeds Account 0 (today) \$1,700 \$17, , \$5,000 1,000? 3 1,70 4 1,730 5 (delivery) 1,710 Assume the highest possible price on day is x, 1,000+(x 1,650) x <.05 x < \$1, (1 point) Which of the following statement is the LEAST likely to be correct? (a) Two call options are identical except the strike price. The call with a smaller strike price will have a higher value. (b) An increase in stock price volatility raises a call option s value while reduces a put option s, if we hold everything else constant. (c) An increase in risk-free interest rate will reduce the present value of the exercise price and therefore increase a call option s value. (d) Two call options are identical except time to expiration. The call with longer maturity will have a higher value. (b). 8. (1 point) Which of the following statements is the LEAST likely to be correct? (a) Credit risk in a plain vanilla interest rate swap is limited to the difference between the values of the fixed rate and floating rate obligations. (b) Because there is no storage cost in stocks, arbitrage is easy between the futures and spot markets. Therefore, backwardation is not possible in financial futures. (c) Futures are more liquid than forwards because they are standardized, traded on exchanges and, guaranteed by the clearing houses. (d) Hedgers use the futures markets to protect themselves in their mainline businesses. Therefore, they are not necessarily profit-seekers in futures trading. (b). 9. (1 point) Which of the following statements is the LEAST likely to be correct? (a) A standard stock option contract traded on CBOE requires delivery of 100 shares when being excised. (b) A protective put is to have downside protection when you own stocks. 4

5 (c) European options are at least as valuable as American ones. (d) Since exercising out-of-the-money options will result in losses, they must be worthless. (c) or (d). 10. (1 point) Delivery of stock index futures (a) requires delivery of 1 share of each stock in the index. (b) is made by delivering 100 shares of each stock in the index. (c) is made by delivering a value-weighted basket of stocks. (d) is made by a cash settlement based on the index value. (d). 5

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