hedging options

8/12/2019 Hedging Options

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HEDGING STRATEGIES USING OPTIONS

PROTECTIVE PUTS

Someone who owns shares of stock has a longposition in the

security. In the investment business the term !"on#$ simp"y means

ownin# somethin#. It has nothin# to %o with time span.

&i#. '(.' is a profit an% "oss %ia#ram for the purchase of )IP

common stock at Rs.*'( per share. The stock price on e+piration

ST is %enote% on hori,onta" a+is an% profit -"oss on the vertica"

a+is. The ma+imum "oss occurs if the stock %ec"ines to ,ero whi"e

the potentia" profit is un"imite%. I#norin# commissions %ivi%en%s

an% opportunity costs the strate#y !breaks even$ if the stock priceis unchan#e% at a specific future time.

Investors occasiona""y anticipate a %ec"ine in the va"ue of an

investment but cannot convenient"y se"" it because of ta+

consi%erations or other reasons. In such a situation the investor

mi#ht consi%er usin# a protective put.

/ protective put is not a specia" kin% of put option0 it is a

%escriptive term #iven to a "on# stock position combine% with a

'


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"on# put position. If someone owns shares of )ip an% buys a )ip

put -re#ar%"ess of strikin# price or e+piration the put is a

protective put.

Fig.10.11 2on# Stock Position

Rs.

Profit

orLoss

0 ST610

610

&i#. '(.3 shows the profits an% "osses associate% with

various stock prices if someone buys a )ip Oct. Rs. 45( put at a

price of Rs.3'. To he"p in constructin# the combine% %ia#ram a

profit an% "oss worksheet "ike Tab"e '(.' he"ps.

3


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Fig.10.2: 2on# Put Position

Rs.

569

Profit Or

loss

0 ST569 590

21

The worksheet shows that the ma+imum "oss is Rs.6' an%

that it occurs at a"" stock prices of Rs.45( or be"ow. The strate#y

appears to break even at a stock price somewhere between Rs.45(an% Rs.7((. 8y checkin# a few more prices it can be foun% that

the break9even point is Rs.*:'.

:


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Table 10.1 : Protective Put )orksheet

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

Stock Price at Option Expiration0 90 190 290 390 490 590 690 90

Lon! Stock" Rs.610 #610 #520 #410 #320 #290 #120 #20 $%0 $1%0

Lon! Rs.590P&t " Rs.21 569 49 39 29 19 9 #21 #21 # 21

'''''''''''''''''''''''''''''''''''''''''''''''''''''

(et # 41 # 41 # 41 # 41 # 41 # 41 #41 $59 $159

/t this price the va"ue of the stock has risen by Rs.3'. The put

e+pires out9of9the9money so it is worth"ess. /t Rs.*:' the stock

rose e+act"y enou#h to offset the cost of the put. The ma+imum

#ain is un"imite% because the stock can rise to any va"ue. &i#. '(.:

shows the combine% positions.

In many respects a protective put is "ike a co""ision insurance

po"icy on an automobi"e. / car is va"uab"e an% its owner suffers if

it is %ama#e% in an acci%ent. To protect a#ainst this potentia" for

"oss peop"e buy insurance fu""y e+pectin# to !"ose$ a"" the money

they pay for it.

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Fig. 10.3: Protective Put

Rs.

Profit or Loss

0 ST

590 631

41

PROTECTIVE C/22S

The previous section showe% how put options can provi%e a

he%#e a#ainst "osses from fa""in# security prices. The same thin#

can be %one with ca"" options to provi%e a he%#e a#ainst "osses

resu"tin# from risin# security prices.

Investors make money when they se"" an asset for more than

they pay for it.


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first -or openin# transaction is a sa"e0 the secon% -or c"osin#

transaction is a purchase. Short se""ers borrow shares from their

brokers se"" them hope to buy i%entica" shares in the future at a

"ower price an% then return the borrowe% shares. C"osin# out a

short position is ca""e% !coverin# the short position$. Short se""ers

make a profit if security prices %ec"ine.

)hen &i#. '(.' -2on# Stock Position is rotate% it becomes

the %ia#ram for a short stock position as in &i#. '(.6.


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)ax. loss is &nli*ite+

It is usefu" to compare the profit an% "oss %ia#ram for a shortsa"e with that of a "on# put position. In buyin# a put the ma+imum

"oss is the option premium yet the profit potentia" is very simi"ar

to the more risky strate#y of se""in# short. =any informe%

in%ivi%ua" investors who are bearish fin% the purchase of a put

vast"y preferab"e to a short sa"e of the stock for this reason. In

a%%ition buyin# a put re>uires "ess capita" than the hefty mar#in

re>uirements necessary to open a short account with a brokera#e

firm.

/"thou#h short positions are %an#erous for the typica"

investor professiona" tra%ers he%#e fun%s an% portfo"io mana#ers

fre>uent"y use them. On the e+chan#e f"oor members routine"y

tra%e usin# short sa"es meanin# that they c"ose out the short

position before the market c"oses. They avoi% mar#in re>uirements

because the position is not he"% overni#ht an% the risk of a%verse

price movements stemmin# from overni#ht news is e"iminate%.

Even for such we""9financia" peop"e positione% on the front "ines of

the market p"ace however the potentia" for "ar#e "osses is

noteworthy.

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One way to he%#e this risk is to a%% a "on# ca"" position to the

short stock position. Combinin# the profit an% "oss %ia#rams for a

"on# ca"" an% a short stock position resu"ts in a p"ot "ike &i#.'(.4.

This fi#ure comes from a short sa"e of )IP ? Rs.*'( an% the

purchase of an Oct Rs.7(( ca"" ? 64. The important feature of

&i#.'(.4 is that there is no potentia" for un"imite%"osses.

Fig.10.5:Short Stock P"us 2on# Ca""

Rs.

565

Profitor 00

loss0 ST

565

#135

The most that the short se""er can "ose in this situation is

Rs.':4. )hi"e the stock price can keep risin# -resu"tin# in

increasin# "osses on the short position for every rupee the stock

rises above Rs.5( the ca"" is worth a rupee more. @ere the rupee

#ain on the ca"" e+act"y cance"s the rupee "oss on the short position.

A


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Table 10.2: Profit an% 2oss )orksheet

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;( '(( :(( 4(( 4*4 7(( 5((

S,ort stock" Rs.610 610 510 310 110 $45 #90 #290

Lon! call Rs.00" Rs.45 #45 #45 #45 #45 #45 #45 $155

''''''''''''''''''''''''''''''''''''''''''

(et 565 465 265 65 0 #135 #135

/nother way to "ook at a situation "ike this is via a profit an%

"oss worksheet "ike that in Tab"e '(.3. This presents the same

information as the &i#.'(.4. /t a stock price of ,ero the investor

#ains Rs.*'( on the short stock position. The e+pirin# ca"" is out9

of9the money so it is worth"ess an% the premium of Rs.64 is "ost.

The net #ain is Rs.4*4. /t a stock price of Rs.7(( the option is at9

the9money0 at any hi#her stock price the option wi"" be in9the

money. The "oss in the short position an% the #ain in the "on# ca""

position e+act"y cance" at any stock price above Rs.7(( so the

ma+imum "oss on the combine% position occurs at Rs.7((.

'(.: COVEREB C/22S

Sometimes an investor owns stock an% writes a ca"" a#ainst it #ivin# someone e"se the

ri#ht to buy the shares. Such a ca"" is a covere% ca"". &i#. '(.* shows the profit or "oss possibi"ities

for an October **( covere% ca"" on )IP stock. This #raph incorporates the profits an% "oss

%ia#ram for a "on# position in the stock an% a short position in the October **( ca"". Option writer

5


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#ets the premium ri#ht away an% he keeps it no matter what happens to the stock price. &i#.'(.*

shows that if the stock price were to %ec"ine the ca"" premium cushions the "oss by Rs.4(. Even if

the stock were to %rop to ,ero he keeps the option premium so his net "oss is on"y Rs.4*(

-instea% of Rs.*'( as in &i#.'(.'

Fig.10.6: Covere% Ca""

Rs.

100 Profit

or loss0 ST 560 660

560

Sometimes an investor owns stock an% fears a market %ownturn. @e mi#ht consi%er usin#

ca""s to provi%e some cushion a#ainst "osses from fa""in# market.

In &i#.'(.* the Rs.4( premium receive% from writin# the ca"" means that no actua" cash

"oss occurs unti" )IP stock fa""s be"ow the current price -Rs.*'( minus the premium receive%

-Rs.4( or Rs.4*(. )hi"e this strate#y provi%es some %ownsi%e protection it is not a particu"ar"y

effective he%#e. In #enera" an in%ivi%ua" who nee% protection a#ainst fa""in# stock prices is better

off buyin# put options.

'(.6 SPRE/BS

'(


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/ sprea% tra%in# strate#y invo"ves simu"taneous purchase an% sa"e of option contracts in

which there is an anticipate% re"ationship between the assets un%er"yin# the options.

1. Bull Spreads

One of the most popu"ar types of sprea%s is a bu"" sprea%. 8u"" sprea% strate#y is use% by

a tra%er anticipatin# increase in the price of the un%er"yin# asset. It can be create% by buyin# a

ca"" option on a stock with a certain strike price an% se""in# a ca"" option on the same stock with a

hi#her strike price. 8oth the options have the same e+piration %ate. The strate#y is i""ustrate% in

&i#. '(.7.

Fig. 10.7 : 8u"" Sprea%

Rs.

Profit

orloss

0 -1 -2 ST

The profits from the two options positions taken separate"y are shown by the %ashe% "ines an%

from the who"e strate#y is in%icate% by the so"i% "ine.

Since a ca"" price a"ways %ecreases as the strike price increases the va"ue of the option

so"% is a"ways "ess than the va"ue of option bou#ht. / bu"" sprea% when create% from ca""s

therefore re>uires an initia" investment. Suppose that ' is the strike price of the ca"" option

bou#ht 3 is the strike price of the ca"" option so"% an% S T is the stock price on e+piration %ate of

the options. Tab"e '(.: shows the tota" payoff that wi"" be rea"ise% from a bu"" sprea% in %ifferent

circumstances.

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Tab"e A.: Payoff from a 8u"" Sprea%

Stock Paoff fro* Paoff fro* TotalPrice lon! call option s,ort call option

ST -2 ST / -1 -2 / ST -2/-1

-1ST-2 ST / -1 0 ST#-1

ST -1 0 0 0

If the stock price %oes we"" an% is #reater than 3 the payoff is the %ifference between

the two strike prices 3 9 ' . If the stock price on the e+piration %ate "ie between the two strike

prices the payoff is STD ' . If the stock price on the e+piration %ate is be"ow ' the payoff is

,ero. The net profit is ca"cu"ate% by subtractin# the initia" investment from the payoff.

/ bu"" sprea% strate#y "imits the tra%ers upsi%e as we"" as %ownsi%e risk. It means that

the tra%er has a ca"" option with a strike price e>ua" to 'an% has chosen to #ive some upsi%e

potentia" by se""in# a ca"" option with strike price 3 -3 F '. In return for #ivin# the upsi%e

potentia" the tra%er #ets the price of the option with strike price 3 .

Example

/ tra%er buys for Rs.'4 a ca"" option on a stock with a strike price of Rs.'4( an% se""s for Rs.4 a

ca"" with a strike price of Rs.'74 on the same stock. The payoff from the bu"" sprea% is Rs.34 if

the stock price is above Rs.'74 an% ,ero if it is be"ow Rs.'4(. If the stock price is between Rs.'4(

an% Rs.'74 the payoff is the amount by which the stock price e+cee%s Rs.'4(. The cost of the

strate#y is Rs.'4 D 4 G Rs.'(. The profit is therefore1

;;;;;;;;;;;;;;;;;;;;;;;;;''''''''''''''''''

Stock Price ST Profit loss''''''''''''''''''''''''''''''''''''''

ST 15 15

150ST 15 ST / 160

ST 150 #10''''''''''''''''''''''''''''''''''''''

'3


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8u"" sprea% can a"so be create% by buyin# a put with a "ow strike price an% se""in# a put

with a hi#h strike price as i""ustrate% in &i#.'(.A. Un"ike the bu"" sprea% create% from ca""s bu""

sprea%s create% from puts invo"ve a positive cash f"ow to the tra%er upfront an% a payoff that is

either ne#ative or ,ero.

Fig.10.8: 8u"" sprea% usin# put options

Rs.

Profit or loss

0 ST

-1 -2

2. Bear Spreads

/ bu"" sprea% strate#y is use% by a tra%er anticipatin# that the stock price swi"" %ec"ine.

2ike a bu"" sprea% a bear sprea% can be create% by buyin# a ca"" with one strike price an% se""in#

a ca"" with another strike price. @owever in the case of a bear sprea% the strike price of the

option purchase% is #reater than the strike price of the option so"%. In &i#.'(.5 the profit from the

sprea% is shown by the so"i% "ine.

Fig.10.9:8ear Sprea% create% usin# ca"" option

Rs.

':


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Profit orloss 0

-1 -2 ST

Tab"e '(.6 shows the payoff that wi"" be rea"ise% from a bear sprea% in %ifferent

circumstances. If the stock price is #reater than 3 the payoff is ne#ative. If the stock price is

"ess than ' the payoff is ,ero. If the stock price is between ' an% 3 the payoff is D -STD ' .

The profit is ca"cu"ate% by a%%in# the initia" cash f"ow to the payoff.

Table 10.4 Payofff from a 8ear sprea%

Stock Paoff fro* Paoff fro* TotalPrice lon! call option s,ort call option

ST -2 ST / -2 -1 / ST #-2/-1

-1ST-2 0 -1 # ST #ST#-1

ST -1 0 0 0

'(.4 CO=8I


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Suppose the investor buys a


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112

&rom the above e+amp"e it is c"ear that it is better to buy a stra%%"e when it is "ike"y that a

stock wi"" move sharp"y one way or the other. If the investor writes both a put an% a ca"" with the

same strikin# price the same e+piration %ate on the same un%er"yin# security he is short a

stra%%"e. The stra%%"e buyer wants the stock price to move si#nificant"y in one %irection or the

other. The stra%%"e writer wants Hust the opposite1 "itt"e movement in the stock price.

&i#.'(.'' is the %ia#ram of a short stra%%"e. The ma+imum #ain in this strate#y occurs

when the options finish at9the9money an% therefore e+pire worth"ess. 2osses are potentia""y

un"imite% on the upsi%e because the short ca"" is uncovere%.

2. Sra!gles

Stran#"es are simi"ar to stra%%"es e+cept the puts an% ca""s have %ifferent strikin# prices.

The motivation for buyin# a stran#"e is simi"ar to the motivation for buyin# a stra%%"e1 the

investor e+pects a sharp price movement either up or %own in the un%er"yin# stock.

/ stran#"e has two strikin# prices. )ith a long strangle the most popu"ar version

invo"ves buyin# a put with a "ower strikin# price than the ca""s strikin# price. 8y %oin# so the

profit an% "oss characteristics are simi"ar to those of the "on# stra%%"e but the ma+imum "oss is

sma""er.

Fig.10.11: Short stra%%"e

Rs.

Profit

orloss

112 162% 1%52 ST

140

'*


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162%Losses arepotentiall

&nli*ite+

&i#.'(.'3 Shows "on# stran#"e constructe% by buyin# an Infosys


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31

'(.* BE2T/ @EBI


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In this e+amp"e the %e"ta of the investors option position is (.*+-9'((( G 9*((. In other

wor%s the investor "oses *(( S. The %e"ta of the stock is by %efinition '.( an% the "on# position

in *(( shares has a %e"ta of J*((. The %e"ta of the investors overa"" position is therefore ,ero.

The %e"ta of the asset position offsets the %e"ta of the option position. The construction of a

risk"ess he%#e is sometimes referre% to as delta hedging. The %e"ta of a ca"" option is positive

whereas the %e"ta of a put option is ne#ative.

'(.7 @EBI


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Options un"ike forwar%s re>uire the payment of a premium upfront. That is the reason

why few treasurers use these instruments. Premiums are fat because the banks that write such

options are face% with a paucity of a"ternatives to he%#e their e+posure.

Capita" account convertibi"ity wi"" a""ow corporates an% banks to access the forei#n

e+chan#e an% money markets abroa% increasin# the he%#in# possibi"ities. &urther as a proper

rupee yie"% curve be#ins to take shape the banks can price such options more appropriate"y.

'(.A @EBI


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-3 =I8OR is A.34L

'(.34 5.6'L worst case

*9month 5.34 Time

=I8OR

A.6'L 8est case

A.34

It can be observe% that if =I8OR touches the peak of '(.34L the treasurer wi"" pay an

effective rate of 5.6'L.

'(.5 I22USTR/TIVE PRO82E=S

"r#blem 1

/n investor has purchase% shares of TT2 2t%. at Rs.66( per share. /nticipatin# %ec"ine in

the share price he bou#ht a put option on TT2 stock at Rs.64 per share with a strike price of

Rs.634 per share. Show the payoffs an% %raw a #raph in%icatin# the resu"ts if the possib"e price

ran#e of stock on e+piration %ate is

Rs.,ero Rs.:4( Rs.4*(

Rs. '4( Rs.66(

Rs. 3'( Rs.4((

So"ution1

Protective put payoffs

Stock price at option e+piration -Rs.

3'


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( '4( 3'( :4( 66( 4(( 4*(

2on# stock at Rs.66( 966( 935( 93:( 95( ( *( '*(

2on# Rs.634 put at Rs.64 J:A( ':( '7( :( 964 964 964


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Rs.64A Rs.74(

S#lui#!

Payoff )orksheet

Stock price at option e+piration -Rs.

( 3(( 64A 46( *4( 74(

2on# stock at Rs.66( 4'( :'( 43 9:( 9'6( 936(

2on# Rs.634 ca"" ? Rs.43 943 943 943 943 4A 9'4A


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-a )hat is the cost of the strate#y

-b )hat is the net payoff for each of the possib"e price ran#e

S#lui#!

-a The cost of the strate#y

Rs.63 D 3* G '*

-b Payoff from a 8u"" sprea%

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;Stock Payoff from Payoff from uote% on a stock e+chan#e as1

Option Price Stock Price

3A :4(

4( :'(

44 35(

Construct a suitab"e sprea% strate#y from the view point of a tra%er who is anticipatin#

%ec"ine in the stock price an% workout the payoffs from the strate#y if the possib"e price of stock

on the e+piration %ate is in the ran#e of1

Rs.34( Rs.:(( Rs.6((

Rs.'7( Rs.:6(

S#lui#!

36


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/ bear sprea% strate#y can be create% by buyin# ca"" with a hi#her strike price i.e.

Rs.:4( an% se""in# a ca"" with "ower strike price i.e. Rs.35( to "imit the %ownsi%e risk.

Payoff from a 8ear Sprea%

''''''''''''''''''''''''''''''''''''''''Stock Payoff from Payoff from


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35

Profit-"oss

35 40 450 ST

#5

"r#blem 6

/n option has a %e"ta of (.*. The option price is Rs.'( an% the stock price is Rs.'((. The

investor has written a ca"" option -i.e. ob"i#e% to se"" on 3((( shares. The investor wishes to

he%#e his position.

-a @ow many shares shou"% he buy to he%#e his position

-b Show the resu"t if stock price #oes up by Rs.'(.

-c If after few %ays the %e"ta increases to (.*4 how many a%%itiona" shares to be

bou#ht

S#lui#!

-a


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'(.'( SU==/RK

@e%#in# is the act of transferrin# unwante% risk to someone who is wi""in# to bear it.

Options can be use% to he%#e a#ainst "osses resu"tin# from a%verse price movements. /

protective put is a "on# put position he"% in conHunction with a "on# position in the un%er"yin#

stock. This is "ike an insurance po"icy on stock. The most common use of stock options by both

in%ivi%ua"s an% institutions is writin# covere% ca""s which is the writin# of ca"" options a#ainst

stock a"rea%y owne%. This strate#y has risk an% return characteristics simi"ar to that of writin# put

options which as a strate#y much "ess fre>uent"y use%.

Options sprea%s are strate#ies in which someone is simu"taneous"y "on# an% short options

of the same type but with %ifferent strike prices. The popu"ar sprea%s are bu"" sprea%s an% bear

sprea%s. / bu"" sprea% can be create% by buyin# a ca"" -put with a "ow strike price an% se""in# a

ca"" -put with a hi#her strike price. / bear sprea% can be create% by buyin# a ca"" -put with a

hi#h strike price an% se""in# a ca"" -put with a "ow strike price.

Option combinations are strate#ies in which investor is simu"taneous"y "on# or short

options of %ifferent types. The best9known combination is a stra%%"e which is a "on# ca"" position

an% a "on# put position on the same un%er"yin# asset where the two options have the same

strikin# price. / stra%%"e is appropriate when anticipate% price movements are hi#h in either

%irection in the un%er"yin# security. Stran#"es are "ike stra%%"es e+cept that the two options have

%ifferent strike prices.

=ost options tra%ers use more sophisticate% he%#in# schemes such as %e"ta he%#in#. This

provi%es protection from sma"" chan#es in the price of the un%er"yin# asset in the ne+t sma""

interva" of time. The %e"ta he%#e is the number of units of the stock investor shou"% ho"% for each

option shorte% in or%er to create a risk"ess he%#e.

37


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$e%ie& 'uesi#!s a!d "r#blems

'. )hat is meant by a protective put )hat position in ca"" options is e>uiva"ent to a protective

put I""ustrate with a suitab"e e+amp"e.

3. E+p"ain two ways in which a bear sprea% can be create%. I""ustrate with a suitab"e e+amp"e.

:. )hat is the %ifference between a stran#"e an% a stra%%"e I""ustrate with a suitab"e e+amp"e.

6. E+p"ain how an a##ressive bear sprea% can be create% usin# put options.

4. Befine %e"ta he%#in#. E+p"ain how option %e"ta is compute%.

*. Suppose that options on a stock with strike prices Rs.'4( an% Rs.'74 cost Rs.3( an% Rs.:4

respective"y. @ow can the options be use% to create -a a bu"" sprea% an% -b a bear sprea%

Construct a tab"e that shows the profit an% "oss payoffs for both sprea%s.

7. / ca"" option with a strike price of Rs.4(( costs Rs.3(. / put option with a strike price of

Rs.64( costs Rs.:(. E+p"ain how a stran#"e can be crate% from these two options. )hat is

the pattern of profits from the stran#"e

A. The treasurer of a "ar#e manufacturin# company p"ans to borrow Rs.'(( mi""ion after *

months for a perio% of * months. The current =I8OR is A.5(L. The companys banker is

>uotin# an in%ication rate of (.3( pc per annum. It is be"ieve% that the un%er"yin# si+9month

interest rate cou"% increase or %ecrease by ' pc in the si+9month perio% before the =I8OR is

re9fi+e%. Biscuss how the IRO he"ps mana#e interest rate e+posure in the present case. &or

this purpose you can assume that interest rate reaches its e+treme point in either case.

()'s

'. The strate#y use% to #uar% a#ainst the risk of "on# position in the security is ca""e%1

/. Protective ca"" 8. Protective put

C Covere% ca"" B. Stra%%"e

3. The strate#y use% to #uar% a#ainst the risk of short position in the security is ca""e%1

/. Protective ca"" 8. Protective put

C Covere% ca"" B. Stra%%"e

:. / tra%er has a short position in stock at Rs.*'( an% buys a ca"" on stock at Rs.64 with a strike

va"ue of Rs.7((. If the stock price at e+piration is Rs.4(( the net profit -"oss wi"" be1

/. Rs.''( 8. 9 Rs. *4

C 9 Rs.''( B. Rs. *4

6. In >uestion : above what is the break9even "eve" of e+piration price

3A


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C Positive B. ero or ne#ative

':. / tra%er ho"%s a ca"" an% put option on the same stock -with a strike va"ue of Rs.'76( at

Rs.A( an% Rs.:3 respective"y. If the price of un%er"yin# stock is more than Rs.'76( at

e+piration the net pay off wi"" be

/. uestion '3 above the ma+imum "oss occurs when the stock price is1

/. Rs. '76( 8. Rs. ,ero

C Rs. 6((( B.


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:. Since the market is e+pecte% to be bearish a%amba wants to enter into a bearish money

sprea%. @ow can this be accomp"ishe% usin# put options an% what wou"% be the #ain

from this money sprea% transaction if the in%e+ is at 453( on =arch :( th

6. @ow can a%amba use a stra%%"e strate#y an% what wou"% be the #ain if the in%e+ is at

453( on =arch :(th.

:3

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