Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 6: Basic Option Strategies A bird in the hand is an apt way to describe the strategy of today’s options investor. Taking the immediate income of writing a covered call, the battle-tested investor is strategically managing market risk. Lawrence Severn Futures and Options World, October 1995

Copyright © 2001 by Harcourt, Inc. All rights reserved.2 Important Concepts in Chapter 6 n Profit equations and graphs for buying and selling stock, buying and selling calls, buying and selling puts, covered calls, protective puts and conversions/reversals n The effect of choosing different exercise prices n The effect of closing out an option position early versus holding to expiration

Copyright © 2001 by Harcourt, Inc. All rights reserved.3 Terminology and Notation n Note the following standard symbols u C = current call price, P = current put price u S 0 = current stock price, S T = stock price at expiration u T = time to expiration u X = exercise price    = profit from strategy n The following will represent the number of calls, puts and stock held u N C = number of calls u N P = number of puts u N S = number of shares of stock

Copyright © 2001 by Harcourt, Inc. All rights reserved.4 Terminology and Notation (continued) n These symbols imply the following: u N C or N P or N S > 0 implies buying (going long) u N C or N P or N S < 0 implies selling (going short) n The Profit Equations u Profit equation for calls held to expiration   = N C [Max(0,S T - X) - C] For buyer of one call (N C = 1) this implies  = Max(0,S T - X) - CFor buyer of one call (N C = 1) this implies  = Max(0,S T - X) - C For seller of one call (N C = -1) this implies  = -Max(0,S T - X) + C For seller of one call (N C = -1) this implies  = -Max(0,S T - X) + C

Copyright © 2001 by Harcourt, Inc. All rights reserved.5 Terminology and Notation (continued) n The Profit Equations (continued) u Profit equation for puts held to expiration   = N P [Max(0,X - S T ) - P] For buyer of one put (N P = 1) this implies  = Max(0,X - S T ) - PFor buyer of one put (N P = 1) this implies  = Max(0,X - S T ) - P For seller of one put (N P = -1) this implies  = -Max(0,X - S T ) + PFor seller of one put (N P = -1) this implies  = -Max(0,X - S T ) + P

Copyright © 2001 by Harcourt, Inc. All rights reserved.6 Terminology and Notation (continued) n The Profit Equations (continued) u Profit equation for stock   = N S [S T - S 0 ] For buyer of one share (N S = 1) this implies  = S T - S 0For buyer of one share (N S = 1) this implies  = S T - S 0 For short seller of one share (N S = -1) this implies  = -S T + S 0For short seller of one share (N S = -1) this implies  = -S T + S 0

Copyright © 2001 by Harcourt, Inc. All rights reserved.7 Terminology and Notation (continued) n Different Holding Periods u Three holding periods: T 1 < T 2 < T u For a given stock price at the end of the holding period, compute the theoretical value of the option using the Black-Scholes or other appropriate model. F Remaining time to expiration will be either T - T 1, T - T 2 or T - T = 0 (we have already covered the latter) F For a position closed out at T 1, the profit will be F where the closeout option price is taken from the Black-Scholes model for a given stock price at T 1.

Copyright © 2001 by Harcourt, Inc. All rights reserved.8 Terminology and Notation (continued) n Different Holding Periods (continued) u Similar calculation done for T 2 u For T, the profit is determined by the intrinsic value, as already covered n Assumptions u No dividends u No taxes or transaction costs u We continue with the America Online options. See Table 6.1, p. 224.

Copyright © 2001 by Harcourt, Inc. All rights reserved.9 Stock Transactions n Buy Stock  Profit equation:  Profit equation:  = N S [S T - S 0 ] given that N S > 0 u u See Figure 6.1, p. 225 for AOL, S 0 = $ u u Maximum profit = infinite, minimum = -S 0 n Sell Short Stock  Profit equation:  Profit equation:  = N S [S T - S 0 ] given that N S < 0 u u See Figure 6.2, p. 226 for AOL, S 0 = $ u u Maximum profit = S 0, minimum = -infinity

Copyright © 2001 by Harcourt, Inc. All rights reserved.10 Call Option Transactions n Buy a Call  Profit equation:  = N C [Max(0,S T - X) - C] given that N C > 0. Letting N C = 1,   = S T - X - C if S T > X   = - C if S T  X u See Figure 6.3, p. 227 for AOL June 125, C = $13.50 u Maximum profit = infinite, minimum = -C u Breakeven stock price found by setting profit equation to zero and solving: S T * = X + C

Copyright © 2001 by Harcourt, Inc. All rights reserved.11 Call Option Transactions (continued) n Buy a Call (continued) u See Figure 6.4, p. 229 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Table 6.2, p. 230 and Figure 6.5, p u Note how time value decay affects profit for given holding period.

Copyright © 2001 by Harcourt, Inc. All rights reserved.12 Call Option Transactions (continued) n Write a Call  Profit equation:  = N C [Max(0,S T - X) - C] given that N C < 0. Letting N C = -1,   = -S T + X + C if S T > X   = C if S T  X u See Figure 6.6, p. 233 for AOL June 125, C = $13.50 u Maximum profit = +C, minimum = -infinity u Breakeven stock price same as buying call: S T * = X + C

Copyright © 2001 by Harcourt, Inc. All rights reserved.13 Call Option Transactions (continued) n Write a Call (continued) u See Figure 6.7, p. 234 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 6.8, p u Note how time value decay affects profit for given holding period.

Copyright © 2001 by Harcourt, Inc. All rights reserved.14 Put Option Transactions n Buy a Put  Profit equation:  = N P [Max(0,X - S T ) - P] given that N P > 0. Letting N P = 1,   = X - S T - P if S T < X   = - P if S T  X u See Figure 6.9, p. 236 for AOL June 125, P = $11.50 u Maximum profit = X - P, minimum = -P u Breakeven stock price found by setting profit equation to zero and solving: S T * = X - P

Copyright © 2001 by Harcourt, Inc. All rights reserved.15 Put Option Transactions (continued) n Buy a Put (continued) u See Figure 6.10, p. 237 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 6.11, p u Note how time value decay affects profit for given holding period.

Copyright © 2001 by Harcourt, Inc. All rights reserved.16 Put Option Transactions (continued) n Write a Put  Profit equation:  = N P [Max(0,X - S T )- P] given that N P < 0. Letting N P = -1   = -X + S T + P if S T < X   = P if S T  X u See Figure 6.12, p. 239 for AOL June 125, P = $11.50 u Maximum profit = +P, minimum = -X + P u Breakeven stock price found by setting profit equation to zero and solving: S T * = X - P

Copyright © 2001 by Harcourt, Inc. All rights reserved.17 Put Option Transactions (continued) n Write a Put (continued) u See Figure 6.13, p. 240 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 6.14, p u Note how time value decay affects profit for given holding period. n Figure 6.15, p. 242 summarizes these payoff graphs.

Copyright © 2001 by Harcourt, Inc. All rights reserved.18 Calls and Stock: the Covered Call u One short call for every share owned  Profit equation:  = N S (S T - S 0 ) + N C [Max(0,S T - X) - C] given N S > 0, N C 0, N C < 0, N S = -N C. With N S = 1, N C = -1,   = S T - S 0 + C if S T X   = S T - S 0 + C if S T  X   = X - S 0 + C if S T > X u See Figure 6.16, p. 244 for AOL June 125, S 0 = $ , C = $13.50 u Maximum profit = X - S 0 + C, minimum = -S 0 + C u Breakeven stock price found by setting profit equation to zero and solving: S T * = S 0 - C

Copyright © 2001 by Harcourt, Inc. All rights reserved.19 Calls and Stock: the Covered Call (continued) u See Figure 6.17, p. 246 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 6.18, p u Note the effect of time value decay. u Other considerations for covered calls: F alleged attractiveness of the strategy F misconception about picking up income F rolling up to avoid exercise u Opposite is short stock, buy call

Copyright © 2001 by Harcourt, Inc. All rights reserved.20 Puts and Stock: the Protective Put u One long put for every share owned  Profit equation:  = N S (S T - S 0 ) + N P [Max(0,X - S T ) - P] given N S > 0, N P > 0, N S = N P. With N S = 1, N P = 1,   = S T - S 0 - P if S T X   = S T - S 0 - P if S T  X   = X - S 0 - P if S T < X u See Figure 6.19, p. 250 for AOL June 125, S 0 = $ , P = $11.50 u Maximum profit = infinite, minimum = X - S 0 - P u Breakeven stock price found by setting profit equation to zero and solving: S T * = P + S 0 u Like insurance policy

Copyright © 2001 by Harcourt, Inc. All rights reserved.21 Puts and Stock: the Protective Put (continued) u See Figure 6.20, p. 252 for different exercise prices. Note differences in maximum loss and breakeven. u For different holding periods, compute profit for range of stock prices at T 1, T 2 and T using Black-Scholes model. See Figure 6.21, p u Note how time value decay affects profit for given holding period.

Copyright © 2001 by Harcourt, Inc. All rights reserved.22 Synthetic Puts and Calls u Rearranging put-call parity to isolate put price u This implies put = long call, short stock, long risk-free bond with face value X. u This is a synthetic put. u In practice most synthetic puts are constructed without risk-free bond, i.e., long call, short stock.

Copyright © 2001 by Harcourt, Inc. All rights reserved.23 Synthetic Puts and Calls (continued)  Profit equation:  = N C [Max(0,S T - X) - C] + N S (S T - S 0 ) given that N C > 0, N S 0, N S < 0, N S = N P. Letting N C = 1, N S = -1,   = -C - S T + S 0 if S T X   = -C - S T + S 0 if S T  X   = S 0 - X - C if S T > X u See Figure 6.22, p. 255 for synthetic put vs. actual put. u Table 6.3, p. 256 shows payoffs from reverse conversion (long call, short stock, short put), used when actual put is overpriced. Like risk-free borrowing. u Similar strategy for conversion, used when actual call overpriced.

Copyright © 2001 by Harcourt, Inc. All rights reserved.24 Summary Software Demonstration 6.1, p. 257 shows the Excel spreadsheet stratlyz2.xls for analyzing option strategies.