econ 141 (winter, 2016) - lecture 5

7/25/2019 Econ 141 (Winter, 2016) - Lecture 5

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Chapter 3

(continued)

Insurance,Collars, and

Other Strategies


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2013 Pearson Education, Inc., publishing as Prentice Hall. ll rights reser!ed.

Spreads and Collars

An option spread is a position consisting ofonly calls oronly puts, in which some optionsare purchased and some written

Why? A lower cost way to speculate on price increase

Examples !ull spread, !ear spread, !ox spread

A collar is the purchase of a put option and thesale of a call option with a higher stri"e price,

with !oth options ha#ing the same underlyingasset and ha#ing the same expiration date

Example $ero%cost collar


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Spreads

A !ull spread is a position, in which you !uya call and sell an otherwise identical callwith a higher stri"e price

&t is a !et that the

price of the underlyingasset will increase

'ull spreads canalso !e constructedusing puts

Figure 3.7

Figure 3.7shows a %*'ull spread, !uying a %stri"e call and selling a *%stri"e call


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Spreads (continued)

Example 3.2 A !ull spread Suppose we want to speculate on the stoc" price rising+

'uy a %stri"e call with 3 months to expiration for -+./+

We can reduce the cost of this position (and also our potential pro0t !y)!y selling the *%stri"e call

1he initial cost 2 -+/. % +. 2 4+/4

1he cost at expiration (3 months)2 4+/45(4+/33)6+-* 2 4+/*

for 3 months 2 374- 2 +-*years


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Example 3.2 A !ull spread 1a!le 3+* shows the 8ayo9s, Costs, and total 8ro0t for this 'ull spread 1his is plotted in :igure 3+. on the next page

Spreads (continued)

ProftCostPayo Payo


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Spreads

Figure 3.7shows a %* 'ull spread,!uying a %stri"e call and selling a *%

stri"e call

We give up proft in this region

To reducecosts


7/24 2013 Pearson Education, Inc., publishing as Prentice Hall. ll rights reser!ed.

Spreads (continued)

A !ear spread is a position in which one sells a call and !uysan otherwise identical call with a higher stri"e price this is simply the exact opposite of Example 3+-, 1a!le 3+*, :igure 3+.

A !ox spread is accomplished !y using options to create asynthetic long forward at one price and a synthetic short

forward at a di9erent price+ Why !uy a !ox spread?A !ox spread is a means of !orrowing or lending money

A !ox spread has no stoc" price ris"

1hus a !ox spread is an alternati#e to !uying or selling a !ond

see Example 3+3

A ratio spread is constructed !y !uying mcalls at one stri"eand selling ncalls at a di9erent stri"e, with all options ha#ingthe same time to maturity and same underlying asset;atio spreads can also !e constructed using puts



Collars

A collar represents a !et that the price of theunderlying asset will decrease and resem!les ashort forward, !ut with a range !etween stri"es inwhich the payo9 is una9ected !y the underlyingasset #alue

Collars are used to implement insurance strategies A $ero%cost collar can !e created when the premiums of

the call and put exactlyo9set one another



Collars (continued)

Example 3.4 A !asic collar Suppose we sell a *%stri"e

Call with a +. premiumand !uy a %stri"e 8ut with a4+ premium

1his creates the collar shown

in :igure 3+/ 'ecause the purchased 8ut

has a higher premium thanthe written call, the positionre


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Collars (continued)

Example 3.5 A collar used as insurance for a long stoc" 1his is called a collared stock ==ou own >= stoc" and then you

!uy insurance #ia a collar (i+e+ !uy a put and sell a call as done inexample 3+)

Actually, the put gi#es you insurance and the call is used toreduce the cost of the insurance

1he pro0t calculations for this set of transactions (!uy the stoc", !uy

a %stri"e 8ut, sell a *%stri"e Call) are show in 1a!le 3+@


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Collars (continued)

Example 3.5 A collar used as insurance for a long stoc" 1he collared stoc" loo"s li"e a !ull spread and in fact, 1a!le 3+@

and 3+* ha#e the same total pro0t+

1he collared stoc" !egins with owning the stoc" initially, andthen the need for insurance leads to purchasing the collar, asshown in :igure 3+ (this happens to !e a $ero%cost collar)


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Collars (continued)

Example 3.5

1his collar exposes you tostoc" price mo#ements!etween + % 4+.-(i+e+ !etween the two stri"eprices)


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Collars (continued)

Example 3.5

1his collar exposes you tostoc" price mo#ements!etween + % 4+.- (i+e+!etween the two stri"eprices)

=ou also getdownside protection

!elow +


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Collars (continued)

Example 3.5

1his collar exposes you tostoc" price mo#ements!etween + % 4+.- (i+e+!etween the two stri"eprices)

=ou also getdownside protection

!elow +

=ou pay for thisprotection !y gi#ingup gains should thestoc" mo#e a!o#e4+.-


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Speculating on olatility

Bptions can !e used to create positions that arenondirectionalwith respect to the underlying asset

Who would use nondirectional positions?

&n#estors who do not care whether the stoc" goes up or down,

!ut only how much it moves, i+e+, who speculate on #olatility

Examples

Straddles

Strangles

'uttery spreads


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Straddles

'uying a call anda put with thesame stri"e priceand time toexpiration

A straddle is a !et

that #olatility will!e high relati#e tothe mar"etDsassessment

if the stoc" priceat expiration isnear the stri"eprice (i+e+ low#olatility) thenyou loosemoney+

if the stoc" price at expiration isfar from the stri"e price (i+e+ high

#olatility) then you ma"e money+

Figure 3.10


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Strangles

Straddles are expensi#e =ou can reduce the cost

!y !uying out%of%the%money options, ratherthan at%the%moneyoptions

Strangles reduce yourcost and maximumloss, !ut they alsoincrease the #olatilityre


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Strangles (continued)

uestio!% which is!etter, a straddle or astrangle?

"!s#er% nless youha#e a particularprediction on themar"et mo#ement,you can say one is!etter than the other

Figure 3.11


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Written Straddles

Selling a call and put with

the same stri"e price andtime to maturity

Why? A written straddleis a !et that #olatility will!e low relati#e to the

mar"etDs assessment uestio!% what if you

want insurance againstpossi!le large losses?

"!s#er% 'uttery

spreads

Figure 3.12

8ro0t with small stoc"mo#ements (i+e+ low#olatility)

Foss with highstoc" mo#ements(i+e+ high#olatility)


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'uttery Spreads

Write a straddle Gadd a strangle 2insured writtenstraddle

A !uttery spread

insures against largelosses on a straddle

Figure 3.13


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'uttery Spreads (continued)

i!sura!eagainst largelosses at high #olatility

=our proftisfocused only in the

low #olatilityregion

Compared to the writtenstraddle, the 'uttery has alower max pro0t (due to thecost of insurance) near (low #olatility) and lower loss

for large stoc" mo#ements(high #olatility) due to theinsurance Figure 3.13


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Asymmetric 'uttery Spreads

Write a straddle Gadd a strangle 2insured writtenstraddle

A !uttery spread

insures against largelosses on a straddle


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Summary of arious Strategies

Strategies dri#en !y the #iew of olatility (i+e+ themar"etDs direction)


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Figure 3.1%

Summary of arious Strategies

1here are numerous

strategies which permitspeculating on thedirection of the stoc" orthe si$e of stoc" price

mo#es (#olatility) So"e are su""ari#ed in

$igure 3.1%

econ 141 (winter, 2016) - lecture 5

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