DMCH15

David Dubofsky and 15-* Thomas W. Miller, Jr.Chapter 15Option Strategies and Profit DiagramsIn the diagrams that follow, it is important to remember that the diagrams that follow are based on option intrinsic value, at expiration.

Helpful Hint: In the diagrams that follow, the KINKS are at strike prices.

Throughout this chapter, bid-ask spreads and brokerage fees are assumed to be zero. CT = max(0, ST-K) and PT = max(0, K-ST)

David Dubofsky and 15-* Thomas W. Miller, Jr.Quick Quiz: Identify These Six Basic Derivative Positions:

STProfit

Sheet1

[A][B][C]

[D][E][F]

David Dubofsky and 15-* Thomas W. Miller, Jr.To These Six Basic Positions, add These Two Riskless Positions

Why are these positions riskless?What do they represent?Riskless Borrowing, [A], Receive money today, always pay money at expiration of the loan. (AKA: Short (sell) T-bills)Lending, [B], Pay money today, always receive money at expiration of the loan. (AKA: Long (buy) T-bills)

profit

ST

Sheet1

[A][B]

David Dubofsky and 15-* Thomas W. Miller, Jr.There are Three Basic Option Trading StrategiesTake a position in an option and the underlying.

Take a position in 2 or more options of the same type (This is called a spread)Same type means:Use only calls or-Use only puts

Take a position in a mixture of calls and puts (This is called a combination.)

*

David Dubofsky and 15-* Thomas W. Miller, Jr.Positions in an Option and the UnderlyingTry to identify the positions in the option, the underlying, and the net position.NB: The KINKS occur at strike prices.

Sheet1

[A] Covered Call[B]

[C] Protective Put[D]

David Dubofsky and 15-* Thomas W. Miller, Jr.How to construct a profit tableBegin by computing the initial outlay, CF0.Choose a range of day T prices for the underlying asset (begin at ~$2 below the lowest strike price and end at ~$2 above the highest strike price)Compute the expiration day payoffs for each position if they are offset on day TAdd up the expiration day payoffs from offsetting each position; this gives you CFT.Add CFT to the initial outlay, CF0, and you will have computed the strategy profit for each relevant value of ST.

David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Protective Put, I.Suppose you current own 100 shares of a stock, with a value of $86.38/share.You fear it may fall in value in the short run, but do not want to sell now.You see the following option data:

You decide to purchase an 85 put.The protective put strategy is long stock + long put.

Sheet1

StrikeCallPut

7511.500.75

807.001.38

854.253.25

902.256.13

950.818.88

David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Protective Put, IIThat is:

At time 0Buy stock -86.38Buy put- 3.25CF(0)-89.63{This is the range of S(T) that you really need

Sheet1

StockCF(0)+CF(T)

Price atP(T)SellPortfolio

Expiration85 PutstockCF(T)CF(0)Profit

78.007.0078.0085.00-89.63(4.63)

79.006.0079.0085.00-89.63(4.63)

80.005.0080.0085.00-89.63(4.63)

81.004.0081.0085.00-89.63(4.63)

81.753.2581.7585.00-89.63(4.63)

82.003.0082.0085.00-89.63(4.63)

83.002.0083.0085.00-89.63(4.63)

84.001.0084.0085.00-89.63(4.63)

85.000.0085.0085.00-89.63(4.63)

86.000.0086.0086.00-89.63(3.63)

86.380.0086.3886.38-89.63(3.25)

87.000.0087.0087.00-89.63(2.63)

88.000.0088.0088.00-89.63(1.63)

89.250.0089.2589.25-89.63(0.38)

89.630.0089.6389.63-89.630.00

90.000.0090.0090.00-89.630.37

91.000.0091.0091.00-89.631.37

92.000.0092.0092.00-89.632.37

David Dubofsky and 15-* Thomas W. Miller, Jr.Then, One Can Plot the Constituent Profits and the Portfolio Profits

Chart1

4.75-9.38-4.63

3.75-8.38-4.63

2.75-7.38-4.63

1.75-6.38-4.63

0.75-5.38-4.63

0-4.63-4.63

-0.25-4.38-4.63

-1.25-3.38-4.63

-2.25-2.38-4.63

-3.25-1.38-4.63

-3.25-0.38-3.63

-3.250-3.25

-3.250.62-2.63

-3.251.62-1.63

-3.253.250

-3.253.620.37

-3.254.621.37

-3.255.622.37

-3.256.623.37

-3.257.624.37

-3.258.625.37

-3.259.626.37

Long 85 Put

Long Stock

Portfolio Profit

Stock Price at Expiration

Portfolio Profit

Example: Protective Put

PPT 15.2

(A)(B)

(D)(E)(F)

PPT 15.3

(A)(B)

PPT 15.5

[A] Covered Call[B]


PPT 15.6

[A] Bull Call Spread

PPT 15.7

[B] Bull Put Spread

PPT 15.8

[C] Bear Call Spread

PPT 15.9

[D] Bear Put Spread

BC Spread Data

ValueValue

LongCostProfitShortProceedsProfitPosition

75 Call75 Call75 Call80 Call80 Call80 CallProfit (Loss)

730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

BC Spread Chart

ValueValue



730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

BC Spread Chart

Underlying Price at Expiration

Profit/Loss

Bullish Vertical Spread with Calls

Some Raw Data

StrikeCallPut

7511.500.75

807.001.38

854.253.25

902.256.13

950.818.88

StockValueLongLongStockValueLongValueLong

Price atLongCost85 PutStockStockPortfolioPrice atLongCost85 PutLongCost85 CallPortfolio

Expiration85 Put85 PutProfitCostProfitProfitExpiration85 Put85 PutProfit85 Call85 CallProfitProfit

72.0013.003.259.7586.38(14.38)(4.63)72.0013.003.259.750.004.25(4.25)5.50

73.0012.003.258.7586.38(13.38)(4.63)73.0012.003.258.750.004.25(4.25)4.50

74.0011.003.257.7586.38(12.38)(4.63)74.0011.003.257.750.004.25(4.25)3.50

75.0010.003.256.7586.38(11.38)(4.63)75.0010.003.256.750.004.25(4.25)2.50

76.009.003.255.7586.38(10.38)(4.63)76.009.003.255.750.004.25(4.25)1.50

77.008.003.254.7586.38(9.38)(4.63)77.008.003.254.750.004.25(4.25)0.50

78.007.003.253.7586.38(8.38)(4.63)78.007.003.253.750.004.25(4.25)(0.50)

79.006.003.252.7586.38(7.38)(4.63)79.006.003.252.750.004.25(4.25)(1.50)

80.005.003.251.7586.38(6.38)(4.63)80.005.003.251.750.004.25(4.25)(2.50)

81.004.003.250.7586.38(5.38)(4.63)81.004.003.250.750.004.25(4.25)(3.50)

81.753.253.250.0086.38(4.63)(4.63)81.753.253.250.000.004.25(4.25)(4.25)

82.003.003.25(0.25)86.38(4.38)(4.63)82.003.003.25(0.25)0.004.25(4.25)(4.50)

83.002.003.25(1.25)86.38(3.38)(4.63)83.002.003.25(1.25)0.004.25(4.25)(5.50)

84.001.003.25(2.25)86.38(2.38)(4.63)84.001.003.25(2.25)0.004.25(4.25)(6.50)

85.000.003.25(3.25)86.38(1.38)(4.63)85.000.003.25(3.25)0.004.25(4.25)(7.50)

86.000.003.25(3.25)86.38(0.38)(3.63)86.000.003.25(3.25)1.004.25(3.25)(6.50)

86.380.003.25(3.25)86.380.00(3.25)86.380.003.25(3.25)1.384.25(2.87)(6.12)

87.000.003.25(3.25)86.380.62(2.63)87.000.003.25(3.25)2.004.25(2.25)(5.50)

88.000.003.25(3.25)86.381.62(1.63)88.000.003.25(3.25)3.004.25(1.25)(4.50)

89.250.004.25(4.25)87.382.87(1.38)89.250.003.25(3.25)4.254.250.00(3.25)

89.630.003.25(3.25)86.383.250.0089.630.003.25(3.25)4.634.250.38(2.87)

90.000.003.25(3.25)86.383.620.3790.000.003.25(3.25)5.004.250.75(2.50)

91.000.003.25(3.25)86.384.621.3791.000.003.25(3.25)6.004.251.75(1.50)

92.000.003.25(3.25)86.385.622.3792.000.003.25(3.25)7.004.252.75(0.50)

92.500.003.25(3.25)87.386.122.8792.500.003.25(3.25)7.504.253.250.00

93.000.003.25(3.25)86.386.623.3793.000.003.25(3.25)8.004.253.750.50

94.000.003.25(3.25)86.387.624.3794.000.003.25(3.25)9.004.254.751.50

95.000.003.25(3.25)86.388.625.3795.000.003.25(3.25)10.004.255.752.50

96.000.003.25(3.25)86.389.626.3796.000.003.25(3.25)11.004.256.753.50

97.000.004.25(4.25)87.3810.626.3797.000.003.25(3.25)12.004.257.754.50

98.000.005.25(5.25)88.3811.626.3798.000.003.25(3.25)13.004.258.755.50

Pro Put Chart

(1)(2)(3)(4)

StockLongLong

Price atPutStockPortfolio

ExpirationProfitProfitProfit

77.004.75-9.38-4.63

78.003.75-8.38-4.63

79.002.75-7.38-4.63

80.001.75-6.38-4.63

81.000.75-5.38-4.63

81.750.00-4.63-4.63

82.00-0.25-4.38-4.63

83.00-1.25-3.38-4.63

84.00-2.25-2.38-4.63

85.00-3.25-1.38-4.63

86.00-3.25-0.38-3.63

86.38-3.250.00-3.25

87.00-3.250.62-2.63

88.00-3.251.62-1.63

89.63-3.253.250.00

90.00-3.253.620.37

91.00-3.254.621.37

92.00-3.255.622.37

93.00-3.256.623.37

94.00-3.257.624.37

95.00-3.258.625.37

Pro Put Chart

4.75-9.38-4.63

3.75-8.38-4.63

2.75-7.38-4.63

1.75-6.38-4.63

0.75-5.38-4.63

0-4.63-4.63

-0.25-4.38-4.63

-1.25-3.38-4.63

-2.25-2.38-4.63

-3.25-1.38-4.63

-3.25-0.38-3.63

-3.250-3.25

-3.250.62-2.63

-3.251.62-1.63

-3.253.250

-3.253.620.37

-3.254.621.37

-3.255.622.37

-3.256.623.37

-3.257.624.37

-3.258.625.37

-3.259.626.37

Long 85 Put

Long Stock

Portfolio Profit


Portfolio Profit


Straddle Chart

StockLongLong

Price at85 Put85 CallPortfolio


72.009.75-4.255.50

73.008.75-4.254.50

74.007.75-4.253.50

75.006.75-4.252.50

76.005.75-4.251.50

77.004.75-4.250.50

78.003.75-4.25-0.50

79.002.75-4.25-1.50

80.001.75-4.25-2.50

81.000.75-4.25-3.50

81.750.00-4.25-4.25

82.00-0.25-4.25-4.50

83.00-1.25-4.25-5.50

84.00-2.25-4.25-6.50

85.00-3.25-4.25-7.50

86.00-3.25-3.25-6.50

86.38-3.25-2.87-6.12

87.00-3.25-2.25-5.50

88.00-3.25-1.25-4.50

89.25-3.250.00-3.25

89.63-3.250.38-2.87

90.00-3.250.75-2.50

91.00-3.251.75-1.50

92.00-3.252.75-0.50

92.50-3.253.250.00

93.00-3.253.750.50

94.00-3.254.751.50

95.00-3.255.752.50

96.00-3.256.753.50

97.00-3.257.754.50

98.00-3.258.755.50

Straddle Chart

Long 85 Put

Long 85 Call

Position Profit


Profit

Example: Long 85 Straddle

PPT 15.13

Long Butterfly Using Calls

PPT 15.14

Long Butterfly Using Puts

PPT 15.18

Long Straddle Using a Call and a Put

PPT 15.19

Long Strangle Using a Call and a Put

PPT 15.20

[A] Long Strip[B] Long Strap

David Dubofsky and 15-* Thomas W. Miller, Jr.Writing a covered callBuy a stock for S(0) = 43Sell a call with K = 45 for C(0) = 1Initial outlay is -42

profitST45+342

Sheet1

StockoffsetCF(0)+CF(T)

Price atC(T)SellPortfolio

Expiration45 callstockCF(T)CF(0)Profit

40.000.0040.0040.00-42.00(2.00)

41.000.0041.0041.00-42.00(1.00)

42.000.0042.0042.00-42.000.00

43.000.0043.0043.00-42.001.00

44.000.0044.0044.00-42.002.00

45.000.0045.0045.00-42.003.00

46.00-1.0046.0045.00-42.003.00

47.00-2.0047.0045.00-42.003.00

48.00-3.0048.0045.00-42.003.00

David Dubofsky and 15-* Thomas W. Miller, Jr.Vertical Spreads, I.[A] Bullish Vertical Spread with Calls (AKA: A Bull Call Spread, or a bullish call money spread).Buy Call with lower strike.Sell Call with higher strike.

ProfitStIdentify the Strike Prices Using the kinksNote that there is an initial outlay with this strategy; the purchased call has a higher price than the written call

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Vertical Spreads, II.[B] Bullish Vertical Spread with Puts (AKA: A Bull Put Spread.)Buy Put with lower strike.Sell Put with higher strike.

ProfitStAgain: Identify the Strikes by the Kinks. Do they make sense?There is an initial cash inflow with this strategy.

Sheet1

[B] Bull Put Spread

David Dubofsky and 15-* Thomas W. Miller, Jr.Vertical Spreads, III.[C] Bearish Vertical Spread with Calls (AKA: A Bear Call Spread.)Buy call with higher strike.Sell call with lower strike.

ProfitStIs there an initial cash inflow or outflow?

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Vertical Spreads, IV.[D] Bearish Vertical Spread with Puts (AKA: A Bear Put Spread.)Buy put with higher strike.Sell put with lower strike.

ProfitStIs there an initial cash inflow or cash outflow?

Sheet1

[D] Bear Put Spread

David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Bullish Vertical Spread with Calls, I.Suppose you observe the following data from the CBOE:Price of Jan 80 Call: $3.75 ($375 per contract)Price of Jan 75 Call: $5.00 ($500 per contract)You decide to buy the Jan 75 call and sell the Jan 80 Call.Today, your outlay is $1.25, or $125 per contract.At expiration:At any price lower than $75, your payoff is $0 and your loss is $1.25 (your initial outlay).If the underlying price is $76 at expiration, your payoff is $1.00, and your loss (CF0 + CFT) is $0.25.If the underlying price is $77 at expiration, your payoff is $2.00, and your profit is $0.75.If the underlying price is $79 at expiration, your payoff is $4.00, and your profit is $2.75.At any price equal to or above $80, your payoff is $5.00, or $500, and your profit is 3.75.

David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Bullish Vertical Spread with Calls, II.Today: Buy Jan 75 call-5

Sell Jan 80 call +3.75CF(0)-1.25

Sheet1

C(T)C(T)Total

OffsetoffsetProfit

ST75 Call80 CallCF(T)CF(0)+CF(T)

730.000.000.00(1.25)

740.000.000.00(1.25)

750.000.000.00(1.25)

761.000.001.00(0.25)

772.000.002.000.75

783.000.003.001.75

794.000.004.002.75

805.000.005.003.75

816.00(1.00)5.003.75

827.00(2.00)5.003.75

838.00(3.00)5.003.75

849.00(4.00)5.003.75

8510.00(5.00)5.003.75

David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Bullish Vertical Spread with Calls, III.Then, one can plot the underlying price at expiration against the position profit or loss (note that the kinks are at the strike prices, 75 and 80):(Obviously, one could plot each elementary position as well.)

Chart1

-1.25

-1.25

-1.25

-0.25

0.75

1.75

2.75

3.75

3.75

3.75

3.75

3.75

3.75


Profit/Loss


PPT 15.2

(A)(B)

(D)(E)(F)

PPT 15.3

(A)(B)

PPT 15.5

[A] Covered Call[B]


PPT 15.6


PPT 15.7

[B] Bull Put Spread

PPT 15.8


PPT 15.9

[D] Bear Put Spread

PPT 15.11

ValueValue



730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

PPT 15.12

ValueValue



730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

PPT 15.12


Profit/Loss


David Dubofsky and 15-* Thomas W. Miller, Jr.Butterfly Spread Using CallsThis is a Long Call Butterfly: With equally spaced strikes:

Long 1 with lowest strike; Short 2 with middle strike; Long 1 with highest strikeProfitST

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Butterfly Spread Using PutsThis is a Long Put Butterfly: With equally spaced strikes:

Long 1 with lowest strike; Short 2 with middle strike; Long 1 with highest strikeWhat do you think a written butterfly would look like?

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Other Spreads, I.Calendar Spreads:Use the same strike, but with two different expiration dates.Can use either calls or puts.The resulting payoff is curved. This is because one option is still alive at the expiration date of the other.

Ratio Spreads (pg. 430)Can use either calls or puts.Same expiration, but with two different strikes.However, unlike other spreads, the number of options held in each position is not the same. For example, a one could buy 3 puts with a strike of 30, and sell one put with a strike of 35.

David Dubofsky and 15-* Thomas W. Miller, Jr.Other Spreads, II.

Condor Spread.

Uses four, equally spaced strikes.

For a long condor spread: Long 1 at the lowest and 1 at the highest strike; short 1 at both intervening strikes.

The resulting payoff resembles a butterfly spread, but with a flat spot between the middle two strikes. (The payoff for a long butterfly resembles a witches hat; the payoff for a long condor resembles a stovepipe hat.)

David Dubofsky and 15-* Thomas W. Miller, Jr.Other Spreads, III.Box Spread (Really, these are combinations)Use two equally spaced strikes, K1 and K2, where K1 < K2.Long Box: Long a call with strike K1; Long a put with strike K2. Short a call with strike K2; Short a put with strike K1.

A Long Box costs money today, but always has a value of K2 K1 at expiration. Therefore, a long box resembles riskless lending, I.e., long T-bill.

A Short Box is formed by reversing all the positions in a long box. As a result, a short box generates a cash inflow today, but has a value of (K2 K1) at expiration. Therefore, a short box resembles riskless borrowing, I.e., short T-bill.

David Dubofsky and 15-* Thomas W. Miller, Jr.Combinations, I.A Long Straddle is formed by a long call and a long put:Both have the same strike and expiration date.What is the worst possible value for the underlying at expiration?In a Short Straddle, one sells the call and sells the put.

ProfitST

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Combinations, II.A Long Strangle is formed by a long call and a long put:Both have the same expiration date.But, the call and put have different strike prices.In a Short Strangle, one sells the call and sells the put.(what does it look like?)

ProfitST

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Combinations, III.Strips and StrapsStrips and straps are formed by using a different number of calls and puts. However, all the options shareThe same strike price.The same expiration date.

Long 1 Call; Long 2 PutsLong 1 Put; Long 2 CallsWhat are the slopes of these lines?

Sheet1


David Dubofsky and 15-* Thomas W. Miller, Jr.Example: Long 85 StraddleYou see the following option data and decide to purchase an 85 call and an 85 put.

Using the steps to build a profit table, you construct the following table.

Sheet1

StrikeCallPut

7511.500.75

807.001.38

854.253.25

902.256.13

950.818.88

David Dubofsky and 15-* Thomas W. Miller, Jr.Long 85 Straddle, II. Time 0Buy C (K=85)-4.25Buy P (K=85)-3.25CF(0)-7.50

Sheet1

StockOffsetOffset

Price atP(T)C(T)Portfolio

Expiration85 Put85 CallCF(T)CF(0)Profit

75.0010.000.0010.00(7.50)2.50

76.009.000.009.00(7.50)1.50

77.008.000.008.00(7.50)0.50

78.007.000.007.00(7.50)(0.50)

79.006.000.006.00(7.50)(1.50)

80.005.000.005.00(7.50)(2.50)

81.004.000.004.00(7.50)(3.50)

81.753.250.003.25(7.50)(4.25)

82.003.000.003.00(7.50)(4.50)

83.002.000.002.00(7.50)(5.50)

84.001.000.001.00(7.50)(6.50)

85.000.000.000.00(7.50)(7.50)

86.000.001.001.00(7.50)(6.50)

86.380.001.381.38(7.50)(6.12)

87.000.002.002.00(7.50)(5.50)

88.000.003.003.00(7.50)(4.50)

89.250.004.254.25(7.50)(3.25)

89.630.004.634.63(7.50)(2.87)

90.000.005.005.00(7.50)(2.50)

91.000.006.006.00(7.50)(1.50)

92.000.007.007.00(7.50)(0.50)

92.500.007.507.50(7.50)0.00

93.000.008.008.00(7.50)0.50

94.000.009.009.00(7.50)1.50

95.000.0010.0010.00(7.50)2.50

David Dubofsky and 15-* Thomas W. Miller, Jr.Long 85 Straddle, III.Then, one can plot the profit data:

Chart2

9.75-4.255.5

8.75-4.254.5

7.75-4.253.5

6.75-4.252.5

5.75-4.251.5

4.75-4.250.5

3.75-4.25-0.5

2.75-4.25-1.5

1.75-4.25-2.5

0.75-4.25-3.5

0-4.25-4.25

-0.25-4.25-4.5

-1.25-4.25-5.5

-2.25-4.25-6.5

-3.25-4.25-7.5

-3.25-3.25-6.5

-3.25-2.87-6.12

-3.25-2.25-5.5

-3.25-1.25-4.5

-3.250-3.25

-3.250.38-2.87

-3.250.75-2.5

-3.251.75-1.5

-3.252.75-0.5

-3.253.250

-3.253.750.5

-3.254.751.5

-3.255.752.5

-3.256.753.5

-3.257.754.5

-3.258.755.5

Long 85 Put

Long 85 Call

Position Profit


Profit


PPT 15.2

(A)(B)

(D)(E)(F)

PPT 15.3

(A)(B)

PPT 15.5

[A] Covered Call[B]


PPT 15.6


PPT 15.7

[B] Bull Put Spread

PPT 15.8


PPT 15.9

[D] Bear Put Spread

BC Spread Data

ValueValue



730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

BC Spread Chart

ValueValue



730.005.00(5.00)0.003.753.75(1.25)

740.005.00(5.00)0.003.753.75(1.25)

750.005.00(5.00)0.003.753.75(1.25)

761.005.00(4.00)0.003.753.75(0.25)

772.005.00(3.00)0.003.753.750.75

783.005.00(2.00)0.003.753.751.75

794.005.00(1.00)0.003.753.752.75

805.005.000.000.003.753.753.75

816.005.001.00(1.00)3.752.753.75

827.005.002.00(2.00)3.751.753.75

838.005.003.00(3.00)3.750.753.75

849.005.004.00(4.00)3.75(0.25)3.75

8510.005.005.00(5.00)3.75(1.25)3.75

BC Spread Chart


Profit/Loss


Some Raw Data

StrikeCallPut

7511.500.75

807.001.38

854.253.25

902.256.13

950.818.88

StockValueLongLongStockValueLongValueLong

Price atLongCost85 PutStockStockPortfolioPrice atLongCost85 PutLongCost85 CallPortfolio

Expiration85 Put85 PutProfitCostProfitProfitExpiration85 Put85 PutProfit85 Call85 CallProfitProfit

72.0013.003.259.7586.38(14.38)(4.63)72.0013.003.259.750.004.25(4.25)5.50

73.0012.003.258.7586.38(13.38)(4.63)73.0012.003.258.750.004.25(4.25)4.50

74.0011.003.257.7586.38(12.38)(4.63)74.0011.003.257.750.004.25(4.25)3.50

75.0010.003.256.7586.38(11.38)(4.63)75.0010.003.256.750.004.25(4.25)2.50

76.009.003.255.7586.38(10.38)(4.63)76.009.003.255.750.004.25(4.25)1.50

77.008.003.254.7586.38(9.38)(4.63)77.008.003.254.750.004.25(4.25)0.50

78.007.003.253.7586.38(8.38)(4.63)78.007.003.253.750.004.25(4.25)(0.50)

79.006.003.252.7586.38(7.38)(4.63)79.006.003.252.750.004.25(4.25)(1.50)

80.005.003.251.7586.38(6.38)(4.63)80.005.003.251.750.004.25(4.25)(2.50)

81.004.003.250.7586.38(5.38)(4.63)81.004.003.250.750.004.25(4.25)(3.50)

81.753.253.250.0086.38(4.63)(4.63)81.753.253.250.000.004.25(4.25)(4.25)

82.003.003.25(0.25)86.38(4.38)(4.63)82.003.003.25(0.25)0.004.25(4.25)(4.50)

83.002.003.25(1.25)86.38(3.38)(4.63)83.002.003.25(1.25)0.004.25(4.25)(5.50)

84.001.003.25(2.25)86.38(2.38)(4.63)84.001.003.25(2.25)0.004.25(4.25)(6.50)

85.000.003.25(3.25)86.38(1.38)(4.63)85.000.003.25(3.25)0.004.25(4.25)(7.50)

86.000.003.25(3.25)86.38(0.38)(3.63)86.000.003.25(3.25)1.004.25(3.25)(6.50)

86.380.003.25(3.25)86.380.00(3.25)86.380.003.25(3.25)1.384.25(2.87)(6.12)

87.000.003.25(3.25)86.380.62(2.63)87.000.003.25(3.25)2.004.25(2.25)(5.50)

88.000.003.25(3.25)86.381.62(1.63)88.000.003.25(3.25)3.004.25(1.25)(4.50)

89.250.004.25(4.25)87.382.87(1.38)89.250.003.25(3.25)4.254.250.00(3.25)

89.630.003.25(3.25)86.383.250.0089.630.003.25(3.25)4.634.250.38(2.87)

90.000.003.25(3.25)86.383.620.3790.000.003.25(3.25)5.004.250.75(2.50)

91.000.003.25(3.25)86.384.621.3791.000.003.25(3.25)6.004.251.75(1.50)

92.000.003.25(3.25)86.385.622.3792.000.003.25(3.25)7.004.252.75(0.50)

92.500.003.25(3.25)87.386.122.8792.500.003.25(3.25)7.504.253.250.00

93.000.003.25(3.25)86.386.623.3793.000.003.25(3.25)8.004.253.750.50

94.000.003.25(3.25)86.387.624.3794.000.003.25(3.25)9.004.254.751.50

95.000.003.25(3.25)86.388.625.3795.000.003.25(3.25)10.004.255.752.50

96.000.003.25(3.25)86.389.626.3796.000.003.25(3.25)11.004.256.753.50

97.000.004.25(4.25)87.3810.626.3797.000.003.25(3.25)12.004.257.754.50

98.000.005.25(5.25)88.3811.626.3798.000.003.25(3.25)13.004.258.755.50

Pro Put Chart

(1)(2)(3)(4)

StockLongLong

Price atPutStockPortfolio


77.004.75-9.38-4.63

78.003.75-8.38-4.63

79.002.75-7.38-4.63

80.001.75-6.38-4.63

81.000.75-5.38-4.63

81.750.00-4.63-4.63

82.00-0.25-4.38-4.63

83.00-1.25-3.38-4.63

84.00-2.25-2.38-4.63

85.00-3.25-1.38-4.63

86.00-3.25-0.38-3.63

86.38-3.250.00-3.25

87.00-3.250.62-2.63

88.00-3.251.62-1.63

89.63-3.253.250.00

90.00-3.253.620.37

91.00-3.254.621.37

92.00-3.255.622.37

93.00-3.256.623.37

94.00-3.257.624.37

95.00-3.258.625.37

Pro Put Chart

4.75-9.38-4.63

3.75-8.38-4.63

2.75-7.38-4.63

1.75-6.38-4.63

0.75-5.38-4.63

0-4.63-4.63

-0.25-4.38-4.63

-1.25-3.38-4.63

-2.25-2.38-4.63

-3.25-1.38-4.63

-3.25-0.38-3.63

-3.250-3.25

-3.250.62-2.63

-3.251.62-1.63

-3.253.250

-3.253.620.37

-3.254.621.37

-3.255.622.37

-3.256.623.37

-3.257.624.37

-3.258.625.37

-3.259.626.37

Long 85 Put

Long Stock

Portfolio Profit


Portfolio Profit


Straddle Chart

StockLongLong

Price at85 Put85 CallPortfolio


72.009.75-4.255.50

73.008.75-4.254.50

74.007.75-4.253.50

75.006.75-4.252.50

76.005.75-4.251.50

77.004.75-4.250.50

78.003.75-4.25-0.50

79.002.75-4.25-1.50

80.001.75-4.25-2.50

81.000.75-4.25-3.50

81.750.00-4.25-4.25

82.00-0.25-4.25-4.50

83.00-1.25-4.25-5.50

84.00-2.25-4.25-6.50

85.00-3.25-4.25-7.50

86.00-3.25-3.25-6.50

86.38-3.25-2.87-6.12

87.00-3.25-2.25-5.50

88.00-3.25-1.25-4.50

89.25-3.250.00-3.25

89.63-3.250.38-2.87

90.00-3.250.75-2.50

91.00-3.251.75-1.50

92.00-3.252.75-0.50

92.50-3.253.250.00

93.00-3.253.750.50

94.00-3.254.751.50

95.00-3.255.752.50

96.00-3.256.753.50

97.00-3.257.754.50

98.00-3.258.755.50

Straddle Chart

Long 85 Put

Long 85 Call

Position Profit


Profit


PPT 15.13


PPT 15.14


PPT 15.18


PPT 15.19


PPT 15.20


David Dubofsky and 15-* Thomas W. Miller, Jr.Profit Diagrams for Positions Offset Prior to the Expiration DayAny strategy can be offset prior to expiration. To prepare a profit diagram (as a function of the price of the underlying asset on a given day prior to T), you must estimate the value of the options. For this, you need an option pricing model. You also have to guess what implied volatility () will exist in the option prices on that day.See pg. 434 for diagrams depicting how a bullish money spread and a long straddle evolve over time.

David Dubofsky and 15-* Thomas W. Miller, Jr.Expectations of StudentsYou should know what the following strategies are, and what their profit diagrams look like:Long stock, short stockLong call, short call, long put, short putCovered call, protective putBullish money spread and bearish money spreadLong and short straddle and strangleBUTI can give you any melange of elementary positions, and you should be able to prepare a profit table. See, for example, problem 15.10.

*

DMCH15

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