...show all the workings step by step
59. An investor has a long position in a non-dividend-paying stock, and additionally, has a long collar on this stock consisting of a 40-strike put and 50-strike call. Determine which of these graphs represents the payoff diagram for the overall position at the time of expiration of the options. (A) (B) Fayo Stock Price stock Price (C) (D) Pay off Stock Price (E) IFM-01-18 Page 30 of 105 Foyo# 60. Farmer Brown grows wheat, and will be selling his crop in 6 months. The current price of wheat is 8.50 per bushel. To reduce the risk of fluctuation in price, Brown wants to use derivatives with a 6-month expiration date to sell wheat between 8.60 and 8.80 per bushel. Brown also wants to minimize the cost of using derivatives. The continuously compounded risk-free interest rate is 2%. Which of the following strategies fulfills Farmer Brown's objectives?32. Judy decides to take a short position in 20 contracts of S&P 500 futures. Each contract is for the delivery of 250 units of the index at a price of 1500 per unit, exactly one month from now. The initial margin is 5% of the notional value, and the maintenance margin is 90% of the initial margin. Judy earns a continuously compounded risk-free interest rate of 4% on her margin balance. The position is marked-to-market on a daily basis. On the day of the first marking-to-market, the value of the index drops to 1498. On the day of the second marking-to-market, the value of the index is X and Judy is not required to add anything to the margin account. Calculate the largest possible value of X. (A) 1490.50 (B) 1492.50 (C) 1500.50 (D) 1505.50 (E) 1507.50 IFM-01-18 Page 16 of 105 33. Several years ago, John bought three separate 6-month options on the same stock. Option I was an American-style put with strike price 20. Option II was a Bermuda-style call with strike price 25, where exercise was allowed at any time following an initial 3-month period of call protection. Option III was a European-style put with strike price 30. When the options were bought, the stock price was 20. When the options expired, the stock price was 26. The table below gives the maximum and minimum stock price during the 6 month period: Time Period: 15 3 months of Option Term 2" 3 months of Option Term Maximum Stock Price 24 28 Minimum Stock Price 18 22 John exercised each option at the optimal time. Rank the three options, from highest to lowest payoff. (A) I> II > III (B) I > III > II (C) II > I > III (D) III > I > II (E) III > II > I29 The dividend yield on a stock and the interest rate used to discount the stock's cash flows are both continuously compounded. The dividend yield is less than the interest rate, but both are positive. The following table shows four methods to buy the stock and the total payment needed for each method. The payment amounts are as of the time of payment and have not been discounted to the present date. METHOD TOTAL PAYMENT Outright purchase A Fully leveraged purchase B Prepaid forward contract C Forward contract D Determine which of the following is the correct ranking, from smallest to largest, for the amount of payment needed to acquire the stock. (A) C 42.31 (E) The range is empty. 12. Consider a European put option on a stock index without dividends, with 6 months to expiration and a strike price of 1,000. Suppose that the effective six-month interest rate is 2%, and that the put costs 74.20 today. Calculate the price that the index must be in 6 months so that being long in the put would produce the same profit as being short in the put. (A) 922.83 (B) 924.32 (C) 1,000.00 (D) 1,075.68 (E) 1,077.17 IFM-01-18 Page 8 of 105 13. A trader shorts one share of a stock index for 50 and buys a 60-strike European call option on that stock that expires in 2 years for 10. Assume the annual effective risk-free interest rate is 3%. The stock index increases to 75 after 2 years. Calculate the profit on your combined position, and determine an alternative name for this combined position. Profit Name (A) -22.64 Floor (B) -17.56 Floor (C) -22.64 Cap (D) -17.56 Cap (E) -22.64 "Written" Covered Call
