Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 6: Basic Option Strategies A bird...

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 A bird in the hand is an apt way to describe the strategy of today’s options investor. Taking the immediate income of today’s options investor. Taking the immediate income of writing a covered call, the battle-tested investor is writing a covered call, the battle-tested investor is strategically managing market risk.strategically managing market risk.

Lawrence SevernLawrence Severn

Futures and Options World, Futures and Options World, October 1995October 1995


2

Important Concepts in Chapter 6

Profit equations and graphs for buying and selling stock, Profit equations and graphs for buying and selling stock, buying and selling calls, buying and selling puts, covered buying and selling calls, buying and selling puts, covered calls, protective puts and conversions/reversalscalls, protective puts and conversions/reversals

The effect of choosing different exercise pricesThe effect of choosing different exercise prices The effect of closing out an option position early versus The effect of closing out an option position early versus

holding to expirationholding to expiration


3

Terminology and Notation Note the following standard symbolsNote the following standard symbols

C = current call price, P = current put priceC = current call price, P = current put price SS00 = current stock price, S = current stock price, STT = stock price at expiration = stock price at expiration

T = time to expirationT = time to expiration X = exercise priceX = exercise price = profit from strategy

The following will represent the number of calls, puts and stock heldThe following will represent the number of calls, puts and stock held NNCC = number of calls = number of calls

NNPP = number of puts = number of puts

NNSS = number of shares of stock = number of shares of stock


4

Terminology and Notation (continued)

These symbols imply the following:These symbols imply the following: NNC C or Nor NP P or N or NSS > 0 implies buying (going long) > 0 implies buying (going long)

NNCC or N or NPP or N or NSS < 0 implies selling (going short) < 0 implies selling (going short)

The Profit EquationsThe Profit Equations Profit equation for calls held to expirationProfit equation for calls held to expiration

= N= NCC[Max(0,S[Max(0,STT - X) - C] - X) - C]

• For buyer of one call (NFor buyer of one call (NCC = 1) this implies = 1) this implies = =

Max(0,SMax(0,STT - X) - C - X) - C

• For seller of one call (NFor seller of one call (NCC = -1) this implies = -1) this implies

= -Max(0,S = -Max(0,STT - X) + C - X) + C


5


The Profit Equations (continued)The Profit Equations (continued) Profit equation for puts held to expirationProfit equation for puts held to expiration

= N= NPP[Max(0,X - S[Max(0,X - STT) - P]) - P]

• For buyer of one put (NFor buyer of one put (NPP = 1) this implies = 1) this implies

= Max(0,X - S = Max(0,X - STT) - P) - P

• For seller of one put (NFor seller of one put (NPP = -1) this implies = -1) this implies

= -Max(0,X - S = -Max(0,X - STT) + P) + P


6


The Profit Equations (continued)The Profit Equations (continued) Profit equation for stockProfit equation for stock

= N= NSS[S[STT - S - S00]]

• For buyer of one share (NFor buyer of one share (NSS = 1) this implies = 1) this implies

= S = STT - S - S00

• For short seller of one share (NFor short seller of one share (NSS = -1) this = -1) this

implies implies = -S = -STT + S + S00


7


Different Holding PeriodsDifferent Holding Periods Three holding periods: TThree holding periods: T11 < T < T22 < T < T

For a given stock price at the end of the holding period, For a given stock price at the end of the holding period, compute the theoretical value of the option using the Black-compute the theoretical value of the option using the Black-Scholes or other appropriate model.Scholes or other appropriate model. Remaining time to expiration will be either T - TRemaining time to expiration will be either T - T11, T - T, T - T22 or or

T - T = 0 (we have already covered the latter)T - T = 0 (we have already covered the latter) For a position closed out at TFor a position closed out at T11, the profit will be, the profit will be

where the closeout option price is taken from the Black-where the closeout option price is taken from the Black-Scholes model for a given stock price at TScholes model for a given stock price at T11. .

C].X),TT,[C(SN 1Tc 1


8


Different Holding Periods (continued)Different Holding Periods (continued) Similar calculation done for TSimilar calculation done for T22

For T, the profit is determined by the intrinsic value, as For T, the profit is determined by the intrinsic value, as already coveredalready covered

AssumptionsAssumptions No dividendsNo dividends No taxes or transaction costsNo taxes or transaction costs We continue with the America Online options. See We continue with the America Online options. See

Table 6.1, p. 224Table 6.1, p. 224..


9

Stock Transactions

Buy StockBuy Stock Profit equation: Profit equation: = NS[ST - S0] given that NS > 0

See Figure 6.1, p. 225 for AOL, S0 = $125.9375

Maximum profit = infinite, minimum = -S0

Sell Short StockSell Short Stock Profit equation: Profit equation: = NS[ST - S0] given that NS < 0

See Figure 6.2, p. 226 for AOL, S0 = $125.9375

Maximum profit = S0, minimum = -infinity


10

Call Option Transactions

Buy a CallBuy a Call Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] given that - X) - C] given that

NNCC > 0. Letting N > 0. Letting NCC = 1, = 1,

= S= STT - X - C if S - X - C if STT > X > X

= - C if S= - C if STT X X

See See Figure 6.3, p. 227Figure 6.3, p. 227 for AOL June 125, C = $13.50 for AOL June 125, C = $13.50 Maximum profit = infinite, minimum = -CMaximum profit = infinite, minimum = -C Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X + C = X + C


11

Call Option Transactions (continued)

Buy a Call (continued)Buy a Call (continued) See See Figure 6.4, p. 229Figure 6.4, p. 229 for different exercise prices. for different exercise prices.

Note differences in maximum loss and breakeven.Note differences in maximum loss and breakeven. For different holding periods, compute profit for range For different holding periods, compute profit for range

of stock prices at Tof stock prices at T11, T, T22 and T using Black-Scholes and T using Black-Scholes

model. See model. See Table 6.2, p. 230Table 6.2, p. 230 and and Figure 6.5, p. 231Figure 6.5, p. 231.. Note how time value decay affects profit for given Note how time value decay affects profit for given

holding period.holding period.


12


Write a CallWrite a Call Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] given that - X) - C] given that

NNCC < 0. Letting N < 0. Letting NCC = -1, = -1,

= -S= -STT + X + C if S + X + C if STT > X > X

= C if S= C if STT X X

See See Figure 6.6, p. 233Figure 6.6, p. 233 for AOL June 125, C = $13.50 for AOL June 125, C = $13.50 Maximum profit = +C, minimum = -infinityMaximum profit = +C, minimum = -infinity Breakeven stock price same as buying call: Breakeven stock price same as buying call:

SSTT** = X + C = X + C


13


Write a Call (continued)Write a Call (continued) See See Figure 6.7, p. 234Figure 6.7, p. 234 for different exercise prices. for different exercise prices.



model. See model. See Figure 6.8, p. 235Figure 6.8, p. 235 . . Note how time value decay affects profit for given Note how time value decay affects profit for given



14

Put Option Transactions

Buy a PutBuy a Put Profit equation: Profit equation: = N = NPP[Max(0,X - S[Max(0,X - STT) - P] given that ) - P] given that

NNPP > 0. Letting N > 0. Letting NPP = 1, = 1,

= X - S= X - STT - P if S - P if STT < X < X

= - P if S= - P if STT X X

See See Figure 6.9, p. 236Figure 6.9, p. 236 for AOL June 125, P = $11.50 for AOL June 125, P = $11.50 Maximum profit = X - P, minimum = -PMaximum profit = X - P, minimum = -P Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X - P = X - P


15

Put Option Transactions (continued)

Buy a Put (continued)Buy a Put (continued) See See Figure 6.10, p. 237Figure 6.10, p. 237 for different exercise prices. for different exercise prices.



model. See model. See Figure 6.11, p. 238Figure 6.11, p. 238.. Note how time value decay affects profit for given Note how time value decay affects profit for given



16


Write a PutWrite a Put Profit equation: Profit equation: = N = NPP[Max(0,X - S[Max(0,X - STT)- P] given that )- P] given that

NNPP < 0. Letting N < 0. Letting NPP = -1 = -1

= -X + S= -X + STT + P if S + P if STT < X < X

= P if S= P if STT X X

See See Figure 6.12, p. 239Figure 6.12, p. 239 for AOL June 125, P = $11.50 for AOL June 125, P = $11.50 Maximum profit = +P, minimum = -X + PMaximum profit = +P, minimum = -X + P Breakeven stock price found by setting profit equation Breakeven stock price found by setting profit equation

to zero and solving: Sto zero and solving: STT** = X - P = X - P


17


Write a Put (continued)Write a Put (continued) See See Figure 6.13, p. 240Figure 6.13, p. 240 for different exercise prices. for different exercise prices.




holding period.holding period. Figure 6.15, p. 242Figure 6.15, p. 242 summarizes these payoff graphs. summarizes these payoff graphs.


18

Calls and Stock: the Covered Call

One short call for every share ownedOne short call for every share owned Profit equation: Profit equation: = N = NSS(S(STT - S - S00) + N) + NCC[Max(0,S[Max(0,STT - X) - C] given - X) - C] given

NNSS > 0, N > 0, NCC < 0, N < 0, NSS = -N = -NCC. With N. With NSS = 1, N = 1, NCC = -1, = -1,

= S= STT - S - S00 + C if S + C if STT X X

= X - S= X - S00 + C if S + C if STT > X > X

See See Figure 6.16, p. 244Figure 6.16, p. 244 for AOL June 125, S for AOL June 125, S00 = $125.9375, C = $125.9375, C

= $13.50= $13.50 Maximum profit = X - SMaximum profit = X - S00 + C, minimum = -S + C, minimum = -S00 + C + C

Breakeven stock price found by setting profit equation to zero Breakeven stock price found by setting profit equation to zero and solving: Sand solving: STT

** = S = S00 - C - C


19

Calls and Stock: the Covered Call (continued)

See See Figure 6.17, p. 246Figure 6.17, p. 246 for different exercise prices. Note for different exercise prices. Note differences in maximum loss and breakeven.differences in maximum loss and breakeven.

For different holding periods, compute profit for range of For different holding periods, compute profit for range of stock prices at Tstock prices at T11, T, T22 and T using Black-Scholes model. See and T using Black-Scholes model. See

Figure 6.18, p. 247Figure 6.18, p. 247.. Note the effect of time value decay.Note the effect of time value decay. Other considerations for covered calls: Other considerations for covered calls:

alleged attractiveness of the strategyalleged attractiveness of the strategy misconception about picking up incomemisconception about picking up income rolling up to avoid exerciserolling up to avoid exercise

Opposite is short stock, buy callOpposite is short stock, buy call


20

Puts and Stock: the Protective Put One long put for every share ownedOne long put for every share owned Profit equation: Profit equation: = N = NSS(S(STT - S - S00) + N) + NPP[Max(0,X - S[Max(0,X - STT) - P] given N) - P] given NSS > >

0, N0, NPP > 0, N > 0, NSS = N = NPP. With N. With NSS = 1, N = 1, NPP = 1, = 1,

= S= STT - S - S00 - P if S - P if STT XX = X - S= X - S00 - P if S - P if STT < X < X

See See Figure 6.19, p. 250Figure 6.19, p. 250 for AOL June 125, S for AOL June 125, S00 = $125.9375, P = = $125.9375, P =

$11.50$11.50 Maximum profit = infinite, minimum = X - SMaximum profit = infinite, minimum = X - S00 - P - P

Breakeven stock price found by setting profit equation to zero and Breakeven stock price found by setting profit equation to zero and solving: Ssolving: STT

** = P + S = P + S00

Like insurance policyLike insurance policy


21

Puts and Stock: the Protective Put (continued)

See See Figure 6.20, p. 252 Figure 6.20, p. 252 for different exercise prices. for different exercise prices. Note differences in maximum loss and breakeven.Note differences in maximum loss and breakeven.

For different holding periods, compute profit for range For different holding periods, compute profit for range of stock prices at Tof stock prices at T11, T, T22 and T using Black-Scholes and T using Black-Scholes




22

Synthetic Puts and Calls Rearranging put-call parity to isolate put priceRearranging put-call parity to isolate put price

This implies put = long call, short stock, long risk-free This implies put = long call, short stock, long risk-free bond with face value X.bond with face value X.

This is a synthetic put.This is a synthetic put. In practice most synthetic puts are constructed without In practice most synthetic puts are constructed without

risk-free bond, i.e., long call, short stock. risk-free bond, i.e., long call, short stock.

Tr0

cXeSCP


23

Synthetic Puts and Calls (continued)

Profit equation: Profit equation: = N = NCC[Max(0,S[Max(0,STT - X) - C] + N - X) - C] + NSS(S(STT - S - S00) )

given that Ngiven that NCC > 0, N > 0, NSS < 0, N < 0, NSS = N = NPP. Letting N. Letting NCC = 1, N = 1, NSS = -1, = -1,

= -C - S= -C - STT + S + S00 if S if STT XX

= S= S00 - X - C if S - X - C if STT > X > X

See See Figure 6.22, p. 255Figure 6.22, p. 255 for synthetic put vs. actual put. for synthetic put vs. actual put. TableTable 6.3, p. 2566.3, p. 256 shows payoffs from reverse conversion shows payoffs from reverse conversion

(long call, short stock, short put), used when actual put is (long call, short stock, short put), used when actual put is overpriced. Like risk-free borrowing.overpriced. Like risk-free borrowing.

Similar strategy for conversion, used when actual call Similar strategy for conversion, used when actual call overpriced.overpriced.


24

Summary

Software Demonstration 6.1, p. 257 shows the Excel spreadsheet stratlyz2.xls for analyzing option strategies.

Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 6: Basic Option Strategies A bird...

Documents

Transcript of Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 6: Basic Option Strategies A bird...