Question

• Three put options on a stock have the same expiration date and strike prices of $192.5, $210, and $227.5, and the market prices of the put options are $10.5, $17.5, and $28, respectively. (a) Explain how a long butterfly spread can be created. (b) Construct a profit (loss) table for the long butterfly spread strategy at expiration of the options. (c) Draw the profit (loss) graph for the long butterfly spread strategy at expiration of the options. (d) For what range of stock prices would the butterfly spread lead to a loss? What is the maximum loss? (e) For what range of stock prices would the butterfly spread lead to a profit? What is the maximum profit?

Answer 1

Given Three PUT options on a stock, same expiration date Put option Strike Price Premium P1 $ 192.50 $ 10.50 P2 $ 210.00 $ 17.50 P3 $ 227.50 $ 28 A. All butterfly spread involves 4 call or 4 put options at three different strik price. Long Butterfly spread using put option is created through : 1. Buying one put option with lower strike price, 2. Buying one put option with higher strike price and 3. Selling two Put options at mid strike price ( at the money put options) Here, Put option will be created through Buy one Put option with strike price of $ 192.50, Buy one Put option with strike price of $ 227.50 and sell two Put option with strike price at $ 210.

B Return on PUT (P1) of strike $ 192.50 is Max (0, P1-stock price), for e.g. at stock price of $ 175, put value return = Max (0, 192.50-175) = $17.50 Return on PUT (P3) of strike $ 227.50 is Max (0, P3-stock price), for e.g. at stock price of $ 175, put value return = Max (0,227.50-175) = $ 52.50 Retun on PUT (P2) of strike $ 210, when stock price goes below $ 210. Then Put buyers will excersie. For stock price of 175, need to pay, 2* (210-175) = $70 Total Investment = 10.50 + 28-12* 17.50 ) = 38.50 - 35 = $ 3.50 As premium paid on P1 and P3 is 10.50 and 28. Whereas premium received on P2 is 2*17.50 = $ 35. Total Profit/Loss = Retun on P1,P2 AND P3 - Investment = 17.5+52.5-70-3.5 = $ 3.50

Retun on Put strk $192.5 17.5 12.5 7.5 2.5 Return on 2 Put of $ 210 -70 -60 Stock Price at expiration 175 180 185 190 195 200 205 210 215 220 0 Retun on Put strk $227.50 52.5 47.5 42.5 37.5 32.5 27.5 22.5 17.5 12.5 7.5 Investmet 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 -50 -40 -30 -20 - 10 0 0 Profit (Loss) -3.50 -3.50 -3.50 -3.50 -1.00 4.00 9.00 14.00 9.00 4.00 0 0 0 0 0 0 225 0 2.5 0 3.5 -1.00 230 0 0 0 3.5 -3.50 235 0 0 0 3.5 -3.50 240 0 0 0 3.5 -3.50 245 0 0 0 3.5 -3.50 250 0 0 0 3.5 -3.50 255 0 0 0 3.5 -3.50 260 0 0 0 3.5 -3.50 265 0 0 0 3.5 -3.50 270 0 0 0 3.5 -3.50 275 0 0 0 3.5 -3.50

C Profit/Loss 14 196 224 0 Stock Price at Expiration -3.5

D. Maximum loss = total investment calculated in previous parts Maximum loss is $3.50, which is investmet. Maxium loss is faced when stock price is below $ 196 or above $ 224. E. Maximum profit = Higher stike price - Mid point stike price - premium paid Maximum profit = $ 227.50-210- 3.5 = $ 14 Profit is realised between stock price of $ 196 and $ 224.