S&R index

  PROBLEMS 3.1 Suppose that you buy the S&R index for $1000, buy a 1000-strike put, and borrow $980.39. Perform a payoff and profit calculation mimicking Table 3.1. Graph the resulting payoff and profit diagrams for the combined position. 3.2 Suppose that you short the S&R index for $1000 and sell a 1000-strike put. Construct a table mimicking Table 3.1 that summarizes the payoff and profit of this position. Verify that your table matches Figure 3.5. For the following problems assume the effective 6-month interest rate is 2%, the S&R 6- month forward price is $1020, and use these premiums for S&R options with 6 months to expiration: Strike Call Put $950 $120.405 $51.777 1000 93.809 74.201 1020 84.470 84.470 1050 71.802 101.214 1107 51.873 137.167 3.3 Suppose you buy theS&Rindex for $1000 and buy a 950-strike put. Construct payoff and profit diagrams for this position.Verify that you obtain the same payoff and profit diagram by investing $931.37 in zero-coupon bonds and buying a 950-strike call. 3.4 Suppose you short the S&R index for $1000 and buy a 950-strike call. Construct payoff and profit diagrams for this position. Verify that you obtain the same payoff and profit diagram by borrowing $931.37 and buying a 950-strike put. 3.5 Suppose you short the S&R index for $1000 and buy a 1050-strike call. Construct payoff and profit diagrams for this position. Verify that you obtain the same payoff and profit diagram by borrowing $1029.41 and buying a 1050-strike put. 3.6 Verify that you earn the same profit and payoff by (a) buying the S&R index for $1000 and (b) buying a 950-strike S&R call, selling a 950-strike S&R put, and lending $931.37. 3.7 Verify that you earn the same profit and payoff by (a) shorting the S&R index for $1000 and (b) selling a 1050-strike S&R call, buying a 1050-strike put, and borrowing $1029.41. 3.8 Suppose the premium on a 6-month S&R call is $109.20 and the premium on a put with the same strike price is $60.18. What is the strike price? 3.9 Construct payoff and profit diagrams for the purchase of a 950-strike S&R call and sale of a 1000-strike S&R call.Verify that you obtain exactly the same profit diagram for the purchase of a 950-strike S&R put and sale of a 1000-strike S&R put. What is the difference in the payoff diagrams for the call and put spreads? Why is there a difference? 3.10 Construct payoff and profit diagrams for the purchase of a 1050-strike S&R call and sale of a 950-strike S&R call. Verify that you obtain exactly the same profit diagram for the purchase of a 1050-strike S&R put and sale of a 950-strike S&R put. What is the difference in the initial cost of these positions? 3.11 Suppose you invest in theS&Rindex for $1000, buy a 950-strike put, and sell a 1050- strike call. Draw a profit diagram for this position. What is the net option premium? If you wanted to construct a zero-cost collar keeping the put strike equal to $950, in what direction would you have to change the call strike? 3.12 Suppose you invest in theS&Rindex for $1000, buy a 950-strike put, and sell a 1107- strike call. Draw a profit diagram for this position. How close is this to a zero-cost collar? 3.13 Draw profit diagrams for the following positions: a. 1050-strike S&R straddle. b. Written 950-strike S&R straddle. c. Simultaneous purchase of a 1050-strike straddle and sale of a 950-strike S&R straddle. 3.14 Suppose you buy a 950-strike S&R call, sell a 1000-strike S&R call, sell a 950-strike S&R put, and buy a 1000-strike S&R put. a. Verify that there is no S&R price risk in this transaction. b. What is the initial cost of the position? c. What is the value of the position after 6 months? d. Verify that the implicit interest rate in these cash flows is 2% over 6 months. 3.15 Compute profit diagrams for the following ratio spreads: a. Buy 950-strike call, sell two 1050-strike calls. b. Buy two 950-strike calls, sell three 1050-strike calls. c. Consider buying n 950-strike calls and selling m 1050-strike calls so that the premium of the position is zero. Considering your analysis in (a) and (b), what can you say about n/m? What exact ratio gives you a zero premium? 3.16 In the previous problem we saw that a ratio spread can have zero initial premium. Can a bull spread or bear spread have zero initial premium? A butterfly spread? Why or why not? 3.17 Construct an asymmetric butterfly using the 950-, 1020-, and 1050-strike options. How many of each option do you hold? Draw a profit diagram for the position. 3.18 Verify that the butterfly spread in Figure 3.14 (see below) can be duplicated by the following transactions (use the option prices in Table 3.4, see below): a. Buy 35 call, sell two 40 calls, buy 45 call. b. Buy 35 put, sell two 40 puts, buy 45 put. c. Buy stock, buy 35 put, sell two 40 calls, buy 45 call. 3.19 Here is a quote from an investment website about an investment strategy using options: One strategy investors are applying to the XYZ options is using “synthetic stock.” A synthetic stock is created when an investor simultaneously purchases a call option and sells a put option on the same stock. The end result is that the synthetic stock has the same value, in terms of capital gain potential, as the underlying stock itself. Provided the premiums on the options are the same, they cancel each other out so the transaction fees are a wash. Suppose, to be concrete, that the premium on the call you buy is the same as the premium on the put you sell, and both have the same strikes and times to expiration. a. What can you say about the strike price? b. What term best describes the position you have created? c. Suppose the options have a bid-ask spread. If you are creating a synthetic purchased stock and the net premium is zero inclusive of the bid-ask spread, where will the strike price be relative to the forward price? d. If you create a synthetic short stock with zero premium inclusive of the bid-ask spread, where will the strike price be relative to the forward price? e. Do you consider the “transaction fees” to really be “a wash”? Why or why not? 3.20 Construct a spreadsheet for which you can input up to five strike prices and quantities of put and call options bought or sold at those strikes, and which will automatically construct the total expiration payoff diagram for that position. Modify the spreadsheet to permit you to choose whether to graph a payoff or profit function.