Trading Strategies with Options

Transcription

1 Trading Strategies with Options One of the unique aspects of options is the ability to combine positions and design the payoff structure, which best suites your expectations. In a world without options, the basic investment choice is to simply buy or sell a share of stock. Assuming that you buy today at S 0 =$45 and sell in six months at S T, the payoff at maturity would look like Figure 1. Figure 1. Payoff and Profit Payoff (Profit) Profit Payoff stock price in 6 months Figure 1 shows the payoff from buying the stock. This is the value of the stock in 6 months. On the other hand profit is the difference between the stock price in 6 months less the original purchase price of $45. We will use this distinction between payoff and profit throughout this note. Suppose that you own a share of stock with a current price of $45 and plan to hold it for the next 6 months. If you thought that the stock price was going to remain at $45 for the next six months, you might be tempted to adjust your position to be consistent with your expectations. One choice would be to sell the stock now and invest the proceeds in the risk-free asset, 6%. If the stock price stays at $45, this strategy would yield.06.5 $45 e 45 = $1.37. Alternatively, if a six-month call option with a strike price of $45 were available at a price of $4.15, we could write a call option on the stock and collect the premium. The combination of owning the stock and writing a call is referred This note was prepared by Professor Robert M. Conroy. Copyright 2003 by the University of Virginia Darden School Foundation, Charlottesville, VA. All rights reserved. To order copies, send an to dardencases@virginia.edu. No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of the Darden School Foundation.

2 to as writing a covered call. The profit for the sell now and invest in risk-free asset strategy is fixed at $1.37, and the profit for the hold stock and write option strategy is shown in figure 2. Figure 2. Payoff and Profit Covered Call Profit st ock price in 6 mont hs This covered call position provides a higher potential income than selling and investing at the risk free rate. Of course, there is a downside risk if the stock price drops. However, this combination of the stock and writing a call would be more attractive to an investor who really believed that the stock price was not going to change much in the next six-months. In the sections that follow we will examine the profit profile for a number of standard option strategies. Note that I believe that graphing the profit is more meaningful than graphing the payoff. We will use the following information to look at different strategies. Exhibit 1. Wall Street Journal-January 14 Listed Options Quotations XYZ -Call- -Put- Closing Price Strike Price Exp. Vol. Last Vol. Last Apr Jan Apr Jul Jan Feb Jan Feb Apr Feb Page 2

3 Bull Spread A bull spread entails the purchase of one call at price, C 1, and exercise price X 1, and the sale of another call at price, C 2, and exercise price X 2, where X l < X 2. Both are on the same stock, both have the same maturity date, T, and C 1 > C 2. The profit at maturity is Stock T Buy Call with low Sell Call with high Total Profit strike price strike price S T >X 2 -C 1 + (S T X 1 ) +C 2 (S T X 2 ) -C 1 + C 2 X 1 + X 2 X 1 S T X 2 -C 1 + (S T X 1 ) +C 2-0 -C 1 +C 2 + S T X 1 S T X 1 -C C 2-0 -C 1 +C 2 Using the following call options from Exhibit 1., The profit would be Buy Call Sell Call April 60 April 70 Cost=11.30 Cost= 4.60 Stock T Buy Call with low Sell Call with high Total Profit strike price X 1 strike price X 2 S T > (S T 60) (S T 70) S T (S T 60) S T S T The graph of the profit for this strategy is Figure 3. Bull Spread Payoff Stock price at maturity Page 3

4 Butterfly Spreads Butterfly spreads involve taking a position in three options with different strike prices. All of the options are on the same underlying asset and have the same maturity. We buy a call option with a low strike price, X L, buy a call option with a high strike price, X H, and sell two call options with a strike price, X M, between X L and X H, or X L < X M <X H. The payoff on this is Stock price Buy 1 Call with Sell 2 Call Mid Buy 1 Call Total T Low Strike Strike High Strike S T >X H -C L + (S T X L ) +2C M 2(S T X M ) -C H + (S T X H ) 2C M C L C H +2X M X L X H X M S T X H -C L + (S T X L ) +2C M 2(S T X M ) -C H + 0 2C M C L C H +2X M S T X L X L S T X M -C L + (S T X L ) +2C M - 0 -C H + 0 2C M C L C H + (S T X L ) S T < X L -C L C M - 0 -C H + 0 2C M C L C H Again let s use Exhibit 1 to see the profit for a specific butterfly spread. For this one we can choose the following call options: Buy Call Sell 2 Calls Buy Call Jan 60 Jan 65 Jan 70 Cost=9.70 Cost= 4.80 Cost=1.00 These call options give the profit as, Stock price Buy 1 Call with Sell 2 Calls Buy 1 Call with Total T strike of 60 with strike of 65 strike of 70 S T > (S T 60) (S T 65) (S T 70) S T (S T 60) (S T 65) S T 60 S T (S T 60) S T S T < Finally the graph of the profit is shown in figure 4. Page 4

5 Figure 4. Butterfly Spread Payoff stock price at maturity Calendar Spreads Calendar spreads involve the purchase and sale of options with the same strike prices but different expiration dates. In a calendar spread we sell the short dated call and buy the long dated call. From Exhibit 1, we could choose Buy Call Sell Call April 70 February 70 Cost= 4.60 Cost= 2.50 At the maturity of the short dated call, February, the profit will depend not only on the value of the stock at that time but also the value of the April 70 call option at that time. The value of the long dated call is determined using the Black-Scholes model. The inputs for the model at the date of the maturity of the short dated call (one month from now), are Underlying Asset Value (UAV) = S T (Stock price at time, T) Time to Maturity (T) = 2 months (time remaining) Risk-free rate (R f ) = assume 1.5% Exercise price (X) = $70 Volatility (σ) =? Page 5

6 The major unknown is the volatility. One estimate of the volatility for the April 70 call option is the implied volatility given its current price. Based on the price of $4.60 the implied volatility 1 is.338. Hence the value of the long dated call in one month is Underlying Asset Value (UAV) = S T (Stock price at time, T) Time to Maturity (T) = 2 months (time remaining) Risk-free rate (R f ) = assume 1.5% Exercise price (X) = $70 Volatility (σ) =.338 April 70 Call Value =? Exhibit 2 shows the profit for the short dated call and the value of the long dated call at the maturity date of the short dated call. Figure 5 is a graph of the profit. Figure 5. Calendar Spread Profit Total Profit $2.50 $2.00 $1.50 $1.00 $0.50 $- $(0.50) $(1.00) $(1.50) $(2.00) $(2.50) Stock price at maturity of short dated call The implied volatility is based on the following inputs: Underlying Asset Value (UAV) = $69.55 Time to Maturity (T) = 3 months Risk-free rate (R f ) = assume 1.5% Exercise price (X) = $70 Volatility (σ) =.338 Call Value = $4.60 Page 6

7 Other Combinations The actual possible combination of puts and calls is actually infinite. Some very popular combinations are Straddle buying a call and a put with the same strike price and expiration date. Strip buying one call and two puts with the same strike price and expiration date. Strangle buying one put and one call with the same expiration dates but different strike prices. Page 7

8 Exhibit 2 Profit on Calendar Spread Profit at Maturity of Short dated Call Short dated Call Long date Call Profit Black-Scholes Value Total Stk T MAX(S-X,0) D1 D2 Call Call-4.60 Profit $ (0.91) (1.05) $ 0.78 $ (3.82) $ (1.32) $ (0.85) (0.99) $ 0.88 $ (3.72) $ (1.22) $ (0.79) (0.93) $ 0.98 $ (3.62) $ (1.12) $ (0.73) (0.87) $ 1.09 $ (3.51) $ (1.01) $ (0.68) (0.81) $ 1.21 $ (3.39) $ (0.89) $ (0.62) (0.76) $ 1.34 $ (3.26) $ (0.76) $ (0.56) (0.70) $ 1.48 $ (3.12) $ (0.62) $ (0.51) (0.64) $ 1.63 $ (2.97) $ (0.47) $ (0.45) (0.59) $ 1.79 $ (2.81) $ (0.31) $ (0.39) (0.53) $ 1.95 $ (2.65) $ (0.15) $ (0.34) (0.48) $ 2.13 $ (2.47) $ 0.03 $ (0.28) (0.42) $ 2.32 $ (2.28) $ 0.22 $ (0.23) (0.37) $ 2.52 $ (2.08) $ 0.42 $ (0.18) (0.31) $ 2.73 $ (1.87) $ 0.63 $ (0.12) (0.26) $ 2.95 $ (1.65) $ 0.85 $ (0.07) (0.21) $ 3.18 $ (1.42) $ 1.08 $ (0.02) (0.16) $ 3.42 $ (1.18) $ 1.32 $ (0.10) $ 3.67 $ (0.93) $ 1.57 $ (0.05) $ 3.94 $ (0.66) $ 1.84 $ $ 4.21 $ (0.39) $ 1.61 $ $ 4.49 $ (0.11) $ 1.39 $ $ 4.78 $ 0.18 $ 1.18 $ $ 5.09 $ 0.49 $ 0.99 $ $ 5.40 $ 0.80 $ 0.80 $ (0.50) $ 5.72 $ 1.12 $ 0.62 $ (1.00) $ 6.05 $ 1.45 $ 0.45 $ (1.50) $ 6.39 $ 1.79 $ 0.29 $ (2.00) $ 6.74 $ 2.14 $ 0.14 $ (2.50) $ 7.09 $ 2.49 $ (0.01) $ (3.00) $ 7.46 $ 2.86 $ (0.14) $ (3.50) $ 7.83 $ 3.23 $ (0.27) $ (4.00) $ 8.21 $ 3.61 $ (0.39) $ (4.50) $ 8.60 $ 4.00 $ (0.50) $ (5.00) $ 8.99 $ 4.39 $ (0.61) $ (5.50) $ 9.39 $ 4.79 $ (0.71) Page 8