chapter 25 - options strategies · chapter 25 - options strategies 25-1: the value and profit of a...

ANSW ERS TO QUESTIONS & PROBLEMS

Chapter 25 - Options Strategies

25-1:

The value and profit of a $40

March written call option sold at

$2.50

If GE goes to $20 the option

expires out of the money. The

value is $0 and the profit to the

writer is $250. If GE goes to $60

the option is exercised by the

buyer. The value is -$2,000 and

the profit is -$1,750.

The value and profit on a long

position of 100 shares of GE

purchased at $40

If GE goes to $20 the value of

the long position is $2000 and

the profit is -$2,000. If GE goes

to $60 the value is $6000 and

the profit is $2000.

To combine the two add

vertically.

If GE goes to $20 the value of

the portfolio is $0+$2000 =

$2000 and the profit is $250-

$2000 = -$1750. If GE goes to

$60 the value of the portfolio is -

$2000+$6000 = $4000 and the

profit is $-1750+$2000 = $250

OLTHETEN & WASPI 2012

25-2:

If HR

goes to

Shares or Unhedged Portfolio Put Options Hedged Portfolio

Value Profit Value Profit Value Profit

$30 $30,000 ($20,000) $20,000 $19,000 $50,000 ($1,000)

$40 $40,000 ($10,000) $10,000 $9,000 $50,000 ($1,000)

$50 $50,000 $0 $0 ($1,000) $50,000 ($1,000)

$60 $60,000 $10,000 $0 ($1,000) $60,000 $9000

$70 $70,000 $20,000 $0 ($1,000) $70,000 $19,000

You should see from the pattern of returns that the hedged portfolio would appeal to the more risk averse investor.

In essence buying the put option is like buying insurance against losses in the portfolio: you pay a premium, but if losses

occur then you are compensated at the stated rate. Once again we buy lower risk with lower return; paying the

premium on the put option reduces the rate of return if disaster does not strike.


25-3:

If GE

goes to

Long $30 Put @ 0.40 Long $50 Call @ 0.15 Portfolio


$20 $1,000 $960 $0 ($15) $1,000 $945

$30 $0 ($40) $0 ($15) $0 ($55)

$40 $0 ($40) $0 ($15) $0 ($55)

$50 $0 ($40) $0 ($15) $0 ($55)

$60 $0 ($40) $1,000 $985 $1,000 $945

There are two breakeven points in a strangle: one just below $30 and one just above $50

If GE goes below $30 we exercise the put.

So at a price P (below $30) the value of the option is:

Value = ($30 - P) * 100 shares

and the breakeven price is given where profit is $0

($30 - P) * 100 - $55 = $0

$30 - P - $0.55 = $0

P = $29.45

If GE goes to $29.45 the value of our strangle is $55 and

our profit is $0.

If GE goes above $50 we exercise the call.

So at a price P (above $50) the value of the option is:

Value = (P - $50) * 100 shares


(P - $50) * 100 - $55 = $0

P - $50 -$0.55 =$0

P = $50.55

If GE goes to $50.55 the value of our strangle is $55 and

out profit is $0


25-4:

If GE

goes to

Short $30 Call @ 10.20 Short $50 put @ 12.30 Portfolio


$20 $0 $1,020 ($3,000) ($1,770) ($3,000) ($750)

$30 $0 $1,020 ($2,000) ($770) ($2,000) $250

$35 ($500) $520 ($1,500) ($270) ($2,000) $250

$40 ($1,000) $20 ($1,000) $230 ($2,000) $250

$45 ($1,500) ($480) ($500) $730 ($2,000) $250

$50 ($2,000) ($980) $0 $1,230 ($2,000) $250

$60 ($3,000) ($1,980) $0 $1,230 ($3,000) ($750)

There are two breakeven points in a strangle: one just below $30 and one just above $50. What makes this a

convoluted strangle is that if the price of GE stays between $30 and $50 then both the call and the put are

exercised.


If GE goes below $30 only the $50 put is exercised..

So at a price P (below $50) the value of the option is:

Value = ($50 - P) * - 100 shares


- 100 * ($50 - P) + $2250 = $0

- $50 - P + $22.50 = $0

P = $27.50

If GE goes to $27.50 the $30 call expires, the $50 put is

exercised and the value of our strangle is -$2,250. Our

profit is $0.

If GE goes above $50 only the $30 call is exercised.


Value = (P - $30) * - 100 shares


-100 * (P - $30) + $2250 = $0

- P + $30 + $22.50 =$0

P = $52.50

If GE goes to $52.50 the $50 put expires, the $30 call is

exercised, and the value of our strangle is - $2,250. Our

profit is $0

We could do a similar write strangle by using a $30 put and a $50 call. Note that with this strategy each option is $10

out-of-the-money rather than $10 in-the-money. This tends to be an easier strategy to analyze because between $30

and $50 neither option is exercised, whereas in the in-the-money strangle between $30 and $50 both options are

exercised.

If GE

goes to

Short $30 put @ 0.40 Short $30 call @ 0.15 Portfolio


$20 ($1,000) ($985) $0 $40 ($1,000) ($945)

$30 $0 $15 $0 $40 $0 $55

$35 $0 $15 $0 $40 $0 $55

$40 $0 $15 $0 $40 $0 $55

$45 $0 $15 $0 $40 $0 $55

$50 $0 $15 $0 $40 $0 $55

$60 $0 $15 ($1,000) ($985) ($1,000) ($970)


There are two breakeven points in a strangle: one just below $30 and one just above $50

If GE goes below $30 only the $30 put is exercised..

So at a price P ( below $30) the value of the option is:

Value = ($30 - P) * - 100 shares


- 100 * ($30 - P) + $55 = $0

- $30 + P + $0.55 = $0

P = $29.45

If GE goes to $29.45 the $50 call expires, the $30 put is

exercised, and the value of our strangle is -$55 and our

profit is $0.

If GE goes above $50 only the $50 call is exercised.


Value = (P - $50) * - 100 shares


-100 * (P - $50) + $55 = $0

- P + $50 + $0.55 =$0

P = $50.55

If GE goes to $50.55 the $30 put expires, the $50 call is

exercised, and the value of our strangle is - $55. Our

profit is $0

Note that the in-the-money write strangle ($30 call and $50 put) dominates the out-of-the-money write strangle ($30

put and $50 call); at every possible price for GE the profit is greater with the in-the-money write strangle.


25-5:

If GE

goes to

Long $40 Call @ 2.50 Short $30 Call @ 10.20 Portfolio


$20 $0 ($250) $0 $1,020 $0 $770

$30 $0 ($250) $0 $1,020 $0 $770

$35 $0 ($250) ($500) $520 ($500) $270

$40 $0 ($250) ($1,000) $20 ($1,000) ($230)

$50 $1,000 $750 ($2,000) ($980) ($1,000) ($230)

Between $30 and $40 the buyer of our $40 call exercises, forcing us to sell at a loss. So at a price P between $30 and

$40 the value of the option is:

Value = - (P - $30) * 100 shares

To break even, this value must offset the premium we collected of $770 ($1020 collected on the $30 written call less

$250 paid on the $40 call)

- 100 * (P - $30) + $770 = $0

- P + $30 + $7.70 = $0

P = $37.70

If GE goes to $37.70 the value of our bear spread is -$770 and our profit is $0.

This is a bear spread because we make money when the price of GE falls.


25-6:

Write one $30 March Put at $0.40 and buy one $50 March Put at $12.30. The option contracts are both puts and the

strike prices are given as $30 and $50.

To determine weather we need to buy or write begin with both puts out of the money. Both puts are out of the money

when the price of GE is above $50. The puts expire worthless and the value line is horizontal at zero.

When the price of GE is between $30 and $50 the $30 put expires but the $50 put is exercised. To make sure that we

make a profit of the exercise we need to buy the $50 put. So we buy one $50 put at $12.30

When the price of GE is below $30 the $30 put is exercised and must offset the profit we make on the $50 put. To

generate this offset we write the $30 put.

The strategy incurs an initial investment of $1,190

If GE

goes to

Short $30 Put @ 0.40 Long $50 Put @ 12.30 Portfolio


$20 ($1,000) ($960) $3,000 $1,770 $2,000 $810

$30 $0 $40 $2,000 $770 $2,000 $810

$35 $0 $40 $1,500 $270 $1,500 $310

$40 $0 $40 $1,000 ($230) $1,000 ($190)

$50 $0 $40 $0 ($1,230) $0 ($1,190)


25-7:

If GE

goes to

Long $40 Call @ 2.50 Short $50 Call @ .15 Portfolio


$20 $0 ($250) $0 $15 $0 ($235)

$30 $0 ($250) $0 $15 $0 ($235)

$40 $0 ($250) $0 $15 $0 ($235)

$50 $1,000 $750 $0 $15 $1,000 $765

$60 $2,000 $1,750 ($1,000) ($985) $1,000 $765

Between $40 and $50 we exercise the $40 call. So at a price P between $40 and $50 the value of the option is:

Value = - (P - $40) * 100 shares

To break even, this value must offset the premium we paid of $235 ($250 paid on the $40 call less $15 collected on the

$50 call)

(P - $40) * 100 = $235

P - $40 = $2.35

P = $42.35

If GE goes to $42.35 the value of our bear spread is $235 and our profit is $0.

This is a bull spread because we make money when the price of GE rises.


25-8:Buy one $30 March Put at $0.40 and write one $50 March Put at $12.30. The options contracts are both puts and the

strike prices are given as $30 and $50.

To determine weather we need to buy or write begin with both puts out of the money. Both puts are out of the money

when the price of GE is above $50. The puts expire worthless and the value line is horizontal at zero.

When the price of GE is between $30 and $50 the $30 put expires but the $50 put is exercised. To make sure that we

make a loss on the exercise we need to write the $50 put. So we write one $50 put at $12.30 collecting $1,230.

When the price of GE is below $30 the $30 put is exercised and must offset the profit we make on the $50 put. To

generate this offset we buy the $30 put paying $40.

We collect a premium of $1,190 to put this strategy in place.

If GE

goes to

Long $30 Put @ 0.40 Short $50 Put @ 12.30 Portfolio


$20 $1,000 $960 ($3,000) ($1,770) ($2,000) ($810)

$30 $0 ($40) ($2,000) ($770) ($2,000) ($810)

$40 $0 ($40) ($1,000) $230 ($1,000) $190

$50 $0 ($40) $0 $1,230 $0 $1,190

$60 $0 ($40) $0 $1,230 $0 $1,190


25-9:

BUTTERFLY SPREAD premium investment The premium from writing the

two $40 call options does not

quite cover the premium for

buying the $35 and $45 call

options. So we must invest $85 to

set up this position.

Long 1 June $35 call option $6.70 ($670.00)

Short 2 June $40 call options $3.80 $760.00

Long 1 June $45 call option $1.75 ($175.00)

Net Investment ($85.00)

The graph of the payout to this strategy will have a kink or pivot point at each strike price: at $35, $40, and $45.

If GE

goes to

Buy 1 $35 call

@ 6.70

Write 2 $40 calls

@ 3.80

Buy 1 $45 call

@ 1.75

Portfolio

Value Profit Value Profit Value Profit Value Profit

$30 $0 ($670) $0 $760 $0 ($175) $0 ($85)

$35 $0 ($670) $0 $760 $0 ($175) $0 ($85)

$40 $500 ($170) $0 $760 $0 ($175) $500 $415

$45 $1,000 $330 ($1,000) ($240) $0 ($175) $0 ($85)

$50 $1,500 $830 ($2,000) ($1,240) $500 $325 $0 ($85)

From the graph and table we can see that in this strategy the graph has four straight-line segments. Each line segment

can be described by an equation that comes from the nature of the options exercised in the segment.

These equations pinpoint the breakeven prices; just set the profit to 0.


$35 $40 $45

All options expire exercise $35 option exercise $35 option

$40 options exercised

exercise $35 option

$40 options exercised

exercise $45 option

ð = -$85 ð = -85

+ 100 (P - $35)

ð = -$85

+ 100 (P - $35)

- 200 (P - $40)

ð = -$85

+ 100 (P - $35)

- 200 (P - $40)

+ 100 (P - $45)

ð = -$85 ð = 100P - $3,585 ð = $4,415 - 100P ð = -$85

ð = 0:

P = $35.85

ð = 0:

P = $44.15

Thus if the price of GE stays within $35.85 and 44.15 we will make a profit on this strategy.


25-10:

If GE

goes

to

Buy 1 $40 June call

@ 3.80

Buy 1 $40 June put

@ $3.90

Portfolio

Value Profit Value Profit Value Profit RETURN

$20 $0 ($380) $2,000 $1,610 $2,000 $1,230 $1230/$770 160%

$30 $0 ($380) $1,000 $610 $1,000 $230 $230/$770 30%

$40 $0 ($380) $0 ($390) $0 ($770) ($770) /$770 -100%

$50 $1,000 $620 $0 ($390) $1,000 $230 $230/$770 30%

$60 $2,000 $1,620 $0 ($390) $2,000 $1,230 $1230/$770 160%

The breakeven prices are $32.30 and $47.70

$0 < P < $40

exercise put

$40 < P

exercise call

100 ($40 - P) - $770 = $0

$40 - P - $7.70 = $0

P = $32.30

100 (P - $40) - $770 = $0

P - $40 - $7.70 = $0

P = $47.70


25-11:

If GE

goes

to

Write 1 $40 June call

@ 3.80

Write 1 $40 June put

@ $3.90

Portfolio

Value Profit Value Profit Value Profit RETURN

$20 $0 $380 ($2,000) ($1,610) ($2,000) ($1,230) ($1,230)/$2000 -61.5%

$30 $0 $380 ($1,000) ($610) ($1,000) ($230) ($230)/2000 -11.5%

$40 $0 $380 $0 $390 $0 $770 $770/$2000 38.5%

$50 ($1,000) ($620) $0 $390 ($1,000) ($230) ($230)/$2000 -11.5%

$60 ($2,000) ($1,620) $0 $390 ($2,000) ($1,230) ($1,230)/$2000 -61.5%

The breakeven prices are $32.30 and $47.70

$0 < P < $40

put exercised

$40 < P

call exercised

-100 ($40 - P) + $770 = $0

-$40 + P + $7.70 = $0

P = $32.30

-100 ( P - $40) + $770 = $0

P - $40 - $7.70 = $0

P = $47.70


25-12:

G June $45 6 the premium for the $45 call is $1.75 so we need to write 43 calls to cover the cost of the put.

Contract Premium Amount

buy 100. (10,000 shares) June $30 put $0.75 $7,500.00

write 43. (4,300 shares) June $45 call $1.75 $7,525.00

Total Premiums: $25.00

G June $50 6 the premium for the $50 call is $0.80 so we need to write 94 calls to cover the cost of the put.

Contract Premium Amount

buy 100. (10,000 shares) June $30 put $0.75 $7,500.00

write 94. (9,400 shares) June $50 call $0.80 $7,520.00

Total Premiums: 20.00

The advantage of the $45 call is that we risk having 4,300 shares called away rather than the 9,400 shares that will be

called away with the $50 option, but that risk comes $5 sooner.

If GE

goes

to

June $45 call options June $50 call options

Action Value Profit Action Value Profit

$20exercise put@$30 $300,000.00 ($99,975.00) exercise put@ $30 $300,000.00 ($99,980.00)

$30$300,000.00 ($99,975.00) $300,000.00 ($99,980.00)

$40$400,000.00 $25.00 $400,000.00 $20.00

$45$450,000.00 $50,025.00 $450,000.00 $50,020.00

$50

4,300 @ $45 $193,500.00

5,700 @ $50$285,000.00

$478,500.00 $78,525.00 $500,000.00 $100,020.00

$55

4,300 @ $45 $193,500.00 9,400 @ $50 $470,000.00

5,700 @ $55$313,500.00

600 @ $55$33,000.00

$507,000.00 $107,025.00 $503,000.00 $103,020.00

$60

4,300 @ $45 $193,500.00 9,400 @ $50 $470,000.00

5,700 @ $60$342,000.00

600 @ $60$36,000.00

$535,500.00 $135,525.00 $506,000.00 $106,020.00

$70

4,300 @ $45 $193,500.00 9,400 @ $50 $470,000.00

5,700 @ $70$399,000.00

600 @ $70$42,000.00

$592,500.00 $192,525.00 $512,000.00 $112,020.00


From the graph we can see that if GE comes in at anything less than $45 the two strategies differ by the $5

difference in premium. At prices between $45 and $54.2147 the $50 call strategy dominates. At prices above

$54.2147 the $45 call strategy dominates.

Which strategy we recommend depends on the probability that GE goes over $54.2147 between now and June.

(4300 * $45) + (5,700 * P) - $400,000 + 25

5,100P

P

= (9,400 * 50) + (600 * P) - $400,000 + 20

= 276,495

= $54.2147

25-13:

A. $58.75

B. Kevin pays a premium of 10 contracts * 100 shares per contract * 4.40 = $4,400.00

C. Joe collects a premium of 10 contracts * 100 shares per contract * 14.10 = $14,100.00

D. Since we haven't been given the parameters for the payout graphs lets be thorough and use $10 increments

spanning from $20 less than the call option strike price to $20 more than the put option strike price.


HR Price Kevin's $60 call options Joe's $70 put options

Value Profit Value Profit

$40 expire at $0 ($4,400) ($30,000) ($15,900)

$50 expire at $0 ($4,400) ($20,000) ($5,900)

$60 expire at $0 ($4,400) ($10,000) $4,100

$70 $10,000 $5,600 expire at $0 $14,100

$80 $20,000 $15,600 expire at $0 $14,100

$90 $30,000 $25,600 expire at $0 $14,100

Kevin’s and Joe’s profits are equal at two prices, one where Joe’s puts are exercised and one where Kevin exercises his

calls.

Although Joe’s profit is greater at prices between $51.50 and $78.50 he faces significant losses at prices below $51.50.

Kevin limits his losses to the premium he pays on the option. Thus Joe takes the greater risk.


25-14:

A. Intel is trading at $50 so you have a choice between the $40 and the $45 puts. However, at a premium of $1.50

for the $45 put, you would need to write a $55 call since that is the only July call with a premium high enough to

cover the cost of the put. This creates a fairly narrow margin for the collar. The $40 put at a premium of $0.50

reduces the cost of the protective put from $15,000 to $5,000 on the 10,000 shares of Intel so this seems like a

better bet.

B. We can either write 63 $60 calls or 100 $65 calls. The tradeoff here is between having 6,300 of 10,000 shares called

away at $60 or having all 10,000 shares called away at $65. At a stock price of $60 or less the $60 call generates

$40 more than the $65 call; at prices between $60 and $73.50 the $65 call dominates; and at prices above $73.50

the $60 call dominates. Your assessment of the risk should take into account your assessment of the probability

that Intel would move from its current price of $50 to $60 or $73.50


25-15:

DVC 100 shares DVC 10 $100 call options 1 $100 call + 6% CD*

Value Profit Return Value Profit Return Value Profit Return

$80 $8,000 ($2,000) -20.0% $0 ($10,000) -100.0% $9,270 ($730) -7.3%

$90 $9,000 ($1,000) -10.0% $0 ($10,000) -100.0% $9,270 ($730) -7.3%

$100 $10,000 $0 - $0 ($10,000) -100.0% $9,270 ($730) -7.3%

$110 $11,000 $1,000 10.0% $10,000 $0 0.0% $10,270 $270 2.7%

$120 $12,000 $2,000 20.0% $20,000 $10,000 100.0% $11,270 $1,270 12.7%

* a CD that pays 3% over a six month period must be described as a 6% CD. Describing it as a 3% CD would imply that

it paid 1.5% over the six month period.

chapter 25 - options strategies · chapter 25 - options strategies 25-1: the value and profit of a...

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