Hedging Options

HEDGING STRATEGIES USING OPTIONS
PROTECTIVE PUTS

Someone who owns shares of stock has a long position 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
S
T
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 price
is 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
'
"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
or
Loss
0 S
T

610


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
Fig.10.2: 2on# Put Position
Rs.
569
Profit
Or
loss
0 S
T

569 590
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.*:'.
:
Table 10.1 : Protective Put )orksheet
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Stock Price at Option Expiration
0 90 190 290 390 490 590 690 90
Lon! Stock
" Rs.610 #610 #520 #410 #320 #290 #120 #20 $%0 $1%0
Lon! Rs.590
P&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.
6
Fig. 10.3: Protective Put
Rs.
Profit
or
Loss

0 S
T
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. <orma""y they buy somethin# first an% se"" it "ater.
Tra%es %o not have to be ma%e in this or%er. )ith a short sa"e the
4
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. <ote that
with a short sa"e potentia" "osses are theoretica""y un"imite%. Prices
can rise to any "eve" an% the short se""er is ob"i#e% eventua""y to
rep"ace borrowe% shares.
Fig.10.4: Short Stock Position
Rs.

610 )axi*&* !ain
Profit or
Loss

0 S
T

610


*
)ax. loss is &nli*ite+
It is usefu" to compare the profit an% "oss %ia#ram for a short
sa"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.
7
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
Profit
or 00
loss
0 S
T
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
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
#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 loss
0 S
T
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
'(
/ 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
or
loss
0 -
1
-
2
S
T
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 C' is the strike price of the ca"" option
bou#ht C3 is the strike price of the ca"" option so"% an% ST 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.
''
Tab"e A.: Payoff from a 8u"" Sprea%
Stock Pa.off fro* Pa.off fro* Total
Price lon! call option s,ort call option
S
T
≥ -
2
S
T
/ -
1
-
2
/ S
T
-
2
/-
1
-
1
0S
T
0-
2
S
T
/ -
1
0 S
T
#-
1
S
T
≤ -
1
0 0 0
If the stock price %oes we"" an% is #reater than C3 the payoff is the %ifference between
the two strike prices C3 9 C' . If the stock price on the e+piration %ate "ie between the two strike
prices the payoff is ST D C' . If the stock price on the e+piration %ate is be"ow C' 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%erEs 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 C' an% has chosen to #ive some upsi%e
potentia" by se""in# a ca"" option with strike price C3 -C3 F C'.. In return for #ivin# the upsi%e
potentia" the tra%er #ets the price of the option with strike price C3 .
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 1S
T
2 Profit 1loss2
''''''''''''''''''''''''''''''''''''''
S
T
≥ 15 15
1500S
T
015 S
T
/ 160
S
T
≤ 150 #10
''''''''''''''''''''''''''''''''''''''
'3
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 S
T
-
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.
':
Profit
or
loss 0
-
1
-
2
S
T
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 C3 the payoff is ne#ative. If the stock price is
"ess than C' the payoff is ,ero. If the stock price is between C' an% C3 the payoff is D -ST D C' ..
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 Pa.off fro* Pa.off fro* Total
Price lon! call option s,ort call option
S
T
≥ -
2
S
T
/ -
2
-
1
/ S
T
#1-
2
/-
1
2

-
1
0S
T
0-
2
0 -
1
# S
T
#1S
T
#-
1
2
S
T
≤ -
1
0 0 0
'(.4 CO=8I</TIO<S
/ combination is a strate#y in which the investor is simu"taneous"y "on# or short options
of %ifferent types. There are many possib"e option combinations the popu"ar ones are1 stra%%"es
an% stran#"es.
1. Sraddles
The stra%%"e is the best9known option combination. If any investor owns both a put an% a
ca"" option with the same strike price the same e+piration %ate on the same un%er"yin# security
he is "on# a stra%%"e.
'6
Suppose the investor buys a <ovember9'76( stra%%"e on I<& stock . Tab"e '(.4 is a profit
an% "oss worksheet for various stock prices at option e+piration. / "on# stra%%"e becomes
profitab"e if prices rise or fa"" provi%e% they rise or fa"" substantia""y. &i#. '(.'( shows the
resu"ts.
Table 10.5 1 2on# Stra%%"e Payoffs
Stock price at option expiration
0 200 %00 140 2500 4000
Lon! 140 call " Rs.%0 #%0 #%0 #%0 #%0 6%0 21%0
Lon! 140 p&t " Rs.32 10% 150% 90% #32 #32 #32
(et 162% 142% 2% #112 64% 214%
The profit an% "oss %ia#ram for a "on# stra%%"e is simp"y the #raphic combination of a
"on# ca"" an% a "on# put. The worst outcome for the stra%%"e buyer is when both options e+pire
worth"ess. This happens on"y when they e+pire at9the9money. In this e+amp"e if I<& stock is
e+act"y Rs.'76( at <ovember e+piration both options are worth"ess.
/t any other price one -an% on"y one. of the options wi"" have some intrinsic va"ue. If the
stock rises the put e+pires worth"ess but the ca"" becomes va"uab"e. Converse"y if the stock fa""s
the put is va"uab"e but the ca"" e+pires worth"ess. &rom the %ia#ram it is apparent that there wi""
be two break9even points with the stra%%"e one correspon%in# to a price rise an% one to a price
%ec"ine. Each break9even point is Rs.''3 away from the Rs.'76( strikin# price.
Fig.10.10 1 2on# Stra%%"e
Rs.
162% T3o 4reak#e5en points
Profit
or
loss 140
0 162% 1%52
S
T
'4
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""Es 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
or
loss
112 162% 1%52 S
T

140
'*
162%
Losses are
potentiall.
&nli*ite+
&i#.'(.'3 Shows "on# stran#"e constructe% by buyin# an Infosys <ovember '*A( put an%
buyin# Infosys <ovember 'A(( ca"" the correspon%in# option prices bein# Rs.'A an% Rs.65
respective"y. The ma+imum "oss of Rs.:' -compare% to Rs.''3 un%er "on# stra%%"e. occurs when
the stock price %ec"ines to Rs.'*A(.
/n opposite of the "on# stran#"e is the short stran#"e. / short stran#"e invo"ves writin#
options the ma+imum #ain occurs if both options e+pire worth"ess an% this happens within the
strike price ran#e of Rs.'*A( an% Rs.'A((.
In the short stran#"e the ma+imum profit occurs at a sin#"e point the strikin# price. The
short stran#"e invo"ves a s"i#ht"y re%uce% ma+imum profit but it is earne% over a broa%er price
ran#e.
Fig.10.12: 2on# Stran#"e
Rs.
1649
Profit
or
loss
0 1649 16%0 169 S
T
'7
31

'(.* BE2T/ @EBII<I
The delta of a stock option is the ratio of the chan#e in the price of a stock option to the
chan#e in the price of the un%er"yin# stock. It is the number of units of the stock the investor
shou"% ho"% for each option written in or%er to create a risk"ess he%#e. The si,e of investment in
stock %epen%s on how the option price an% stock price are re"ate%. Suppose for e+amp"e the
investor estimates that percenta#e chan#es in the price of option are re"ate% in the fo""owin# way
to percenta#e chan#es in the price of stock.
E+pecte% chan#e in G a J δ chan#e in the
the price of option price of stock
Be"ta -δ. measures the sensitivity of option price to chan#es in the stock price. It is a"so e>ua" to
the he%#e ratio D that is the number of units of stock which shou"% be purchase% to he%#e the
e+posure.
The option %e"ta summarises the "ink between the option price an% the price of the
un%er"yin# asset. &or e+amp"e if an investor owns an option to buy a share of =aruthi stock the
chan#e in the va"ue of his investment wi"" be the same as if he he"% %e"ta stock of =aruthi.
Suppose that an investment %ea"er has written ca"" option on '((( shares of =aruthi. The option
price is Rs.3( the option %e"ta is (.* an% the stock price is Rs.6((. The investorEs position cou"%
be he%#e% by buyin# (.*+'(((G*(( shares. The #ain-"oss. on the option position wou"% ten% to
be offset by the "oss-#ain. on the stock position. &or e+amp"e if the stock price #oes up by Rs.'(
-pro%ucin# a #ain of Rs.*((( on the shares purchase%. the option price wi"" ten% to #o up by
(.*+Rs.'(GRs.* -pro%ucin# a "oss of Rs.*((( on the option written.0 if the stock price #oes %own
by Rs.'( -pro%ucin# a "oss of Rs.*((( on the shares purchase%. the option price wi"" ten% to #o
%own by Rs.* -pro%ucin# a #ain of Rs.*((( on the options written.
'A
In this e+amp"e the %e"ta of the investorEs 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 investorEs 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 @EBII<I CURRE<CK RISC
/ny transaction of the company in a currency other than the ba"ance9sheet currency "ea%s
to forei#n e+chan#e e+posure. Recent economic "ibera"isation has mu"tip"ie% these e+posures.
Currencies are fast becomin# commo%ities. Currency options #rants the ho"%er the ri#ht to buy or
se"" the specifie% currency at a specifie% price known as the e+ercise price. /n e+porter %ue to
receive US %o""ars three months from now can he%#e a#ainst the risk of its %epreciation by
buyin# a three9month rupee ca"" option -or %o""ar put option.. If contrary to e+pectations the
%o""ar appreciates the e+porter wi"" not be %enie% the win%fa"" #ains since the option %oes not
have to be e+ercise%. Effective"y the put sets a f"oor on the %o""ar to be receive%. Converse"y a
company that has to make a %o""ar payment can insure a#ainst its appreciation by purchasin#
rupee put option -or %o""ar ca"" option.. This caps the cost of the %o""ar to be pai%.
Currency Option Payoffs
Pa.#off
To ,e+!er Strike price 162
7pfront pre*i&* Rs.86
'5
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 @EBII<I I<TEREST R/TE RISC
Interest rate risk can be he%#e% usin# interest rate options -IRO. contracts. /n IRO is a
contract between the business firm an% its bank wherein the bank a#rees to #uarantee a specifie%
rate of interest for a notiona" principa" when re>uire% by the customer for a premium. The chief
merit of an IRO is that the risk of a%verse interest movement is e"iminate% whi"e at the same time
the buyer retains the potentia" to benefit from favourab"e rate movements by a""owin# ri#ht of
option to "apse if interest rates move in his favour. Suppose the treasurer of a company has a
number of "oans on variab"e rate basis "inke% to =I8OR. @e anticipates that interest rates wi""
fa"" but the finance %irector be"ieves otherwise. /n IRO can ba"ance both the possibi"ities an%
cover the e+posure. If rates increase IRO he"ps #et the refun% %ifference0 if interest rates fa"" the
treasurer wi"" aban%on the option an% the "oan wi"" be transacte% at a "ower =I8OR.
Suppose a Rs.4mi""ion "oan has a ro"" over in si+ monthsE time -on '
st
Sept.. when the
=I8OR wi"" be re9fi+e% for the ne+t si+ months. &urther assume that1
* D month =I8OR is current"y 5.34L
* D '3 &R/ is >uote% 1 5.'( D 5.((
On '
st
=arch the treasurer asks for a borrowerEs option to protect the present =I8OR
"eve" of 5.34L. The bank >uotes an in%ication rate of '* bps p.a. / basis point is (.(' percent.
In this e+amp"e the "oan ro"" over is si+ ca"en%ar months away. /ssume there are 'A( %ays in the
perio% after this the "oan rate wi"" be confirme%. Therefore the premium payab"e is1
Rs. 4(((((( M (.'* N'(( M 'A( N :*4 G Rs. : 564.3'
The treasurer be"ieves that the un%er"yin# si+ month interest rate cou"% increase or %ecrease by '
pc in the si+ month perio% before the =I8OR is re9fi+e%. In which case there is a "ist of possib"e
outcomes the e+tremes of which are1
-'. =I8OR is '(.34 L
3(
-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'
( '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
<et 9*( 9*( 9*( 9*( 964 '4 ''4
Rs.
Profit
1loss2
425
0 S
T
4%5
#60
"r#blem 2
/n investor is short stocks of TP2 2t%. at Rs.4'( per share to be %e"ivere% in two months
time. @e anticipates appreciation in TP2 stock price an% hence %eci%es to buy a ca"" option on the
same share at Rs.43 per contract with a strike price of Rs.46( per share. Show the payoff an%
%raw a #raph in%icatin# the resu"ts if possib"e price ran#e on e+piration %ate happens to be1
Rs. Oero Rs.46(
Rs.3(( Rs.*4(
33
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
<et 64A 34A ( 9A3 9A3 9 A3
Rs.
45%
Profit1loss2
540
0 S
T
45%
#%2
"r#blem 3

/ tra%er buys for Rs.63 a ca"" with a strike price of Rs.*'( an% se""s for Rs.3* a ca"" with
a strike price of Rs.*5(. The possib"e price ran#e of the un%er"yin# stock is1
Rs.64( Rs.*A(
Rs.4*( Rs.74(
Rs.*3( Rs.A4(
3:
-a. )hat is the cost of the strate#yP
-b. )hat is the net payoff for each of the possib"e price ran#eP
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 <et
Price "on# ca"" short ca"" Payoff
option option
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
64( ( ( 9'*
4*( ( ( 9'*
*3( '( ( 9 *
*A( 7( ( 46
74( '6( 9*( *6
A4( 36( 9'*( *6
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
"r#blem 4
The ca"" option on a stock are >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
/ 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 <et
Price "on# ca"" short ca"" PayoffQ
option option
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
'7( ( ( 37
34( ( ( 37
:(( ( 9'( 9'7
:6( ( 94( 93:
6(( 4( 9''( 9::
'''''''''''''''''''''''''''''''''''''''
Q Rs.37 -Rs.449Rs.3A. is the cash f"ow #enerate% by the investment up front
"r#blem 5
/ ca"" option with an e+ercise price of Rs.6( is avai"ab"e at a premium of Rs.:. / put
with same maturity an% e+ercise price can be purchase% at a premium of Rs.3. If you create a
stra%%"e show the payoff for the fo""owin# possib"e price ran#e an% %raw a #raph in%icatin# the
resu"ts.
Rs.,ero
Rs.:( Rs.64
Rs.:4 Rs.4(
Rs.6( Rs.44
S#lui#!
2on# Stra%%"e Payoff
Stock price at option e+piration
( :( :4 6( 64 4( 44
2on# 6( ca"" ? Rs.: 9: 9: 9: 9: 3 7 '3
2on# 6( Put ? Rs.3 :A A : 93 93 93 93
<et :4 4 ( 94 ( 4 '(
34
35
Profit-"oss2
35 40 45
0 S
T

#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 positionP
-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#htP
S#lui#!
-a. <o. of shares to be bou#ht G (.*+3((( G'3((
-b. Iain on shares purchase% Rs.J'3(((
-'3((+'(.
2oss on ca"" option written Rs.9'3(((
--(.*+'(G*+3((( shares.
<et resu"t (;;;
-c. <o. of a%%itiona" shares to be
8ou#ht -(.*49(.*(G(.(4+3(((.G '((
3*
'(.'( 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
$e%ie& 'uesi#!s a!d "r#blems
'. )hat is meant by a protective putP )hat position in ca"" options is e>uiva"ent to a protective
putP 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%%"eP 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%P
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#"eP
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 companyEs 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 priceP
3A
/. Rs.4*4 8. Rs.43(
C Rs.*'( B. Rs. 4((
4. In prob"em : above the ma+imum potentia" "oss is 1
/. Rs. 4*4 8. Rs. (
C Rs.*4 B. Rs. ':4
*. / tra%er is with a "on# position in a stock at a price of Rs.*(( an% is simu"taneous"y with "on#
ca"" at Rs.3( for a strike price of Rs.45(. what wi"" be the ma+imum potentia" "ossP
/. Rs.*(( 8. Rs. 3(
C Rs.:( B. Rs. 45(
7. / tra%er buys for Rs.'4 a ca"" with a strike price of Rs.'4( an% se""s for Rs.4 a ca"" with a
strike price of Rs.'74. The net pay off from the sprea% if ST G Rs.'64 wi"" be1
/. Rs. '( 8. Rs. '4
C 9 Rs.'4 B. D Rs.'(
A. In >uestion 7 above if ST G Rs.9'A4 the net pay off wi"" be1
/. Rs.'4 8. Rs. 34
C Rs. '( B. D Rs.'4
5. / bu"" sprea% can be create% by buyin# a ca"" with a "ower strike price an% se""in# a RR with
RR strike price.
/. Ca"" hi#her 8. Put hi#her
C Put "ower B. Ca"" "ower
'(. / bear sprea% can be create% by buyin# a ca"" with a hi#her strike price an% se""in# a RR
with RR strike price.
/. Ca"" hi#her 8. Put hi#her
C Put "ower B. Ca"" "ower
''. /n investor ownin# both a ca"" an% put option with the same strike price the same e+piration
%ate on the same un%er"yin# security is ca""e%RRR
/. 8u"" sprea% 8. Stran#"e
C Stra%%"e B. 8ear sprea%
'3. / 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 "ess than Rs.'76( at
e+piration the net pay off wi"" be
/. <e#ative 8. Oero
35
C Positive B. Oero 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
/. <e#ative 8. Oero
C Positive B. Oero or ne#ative
'6. In >uestion '3 above the break even va"ue of un%er"yin# stock wi"" be1
/. Rs. '76( 8. Rs. '*3A
C Rs. 'A43 B. 8oth 8 an% C
'4. In >uestion '3 above the ma+imum "oss occurs when the stock price is1
/. Rs. '76( 8. Rs. ,ero
C Rs. 6((( B. <one of these
)ase Sud*
=r. Ca%amba has been recent"y appointe% as the mana#er of /pe+ &un%. The /pe+ &un% was
starte% on San. 3((A with a tota" corpus of Rs.34 crore which was main"y investe% in the e>uity
stocks tra%e% on the In%ian stock market. The fun%s performance since be#innin# is as fo""ows1
Perio% Return on Return on
8enchmark In%e+ /pe+ &un%
3((A '* '5
3((5 '6 '*
3('( '* '4
3('' 3' 3(
3('3 '5 '5
3(': 3( '7
The &un%Es performance in recent years is be"ow the return on 8enchmark in%e+. The net asset
va"ue of the fun% has %ecrease% by '6 pc between San '' to Bec. 3(':. =r. Ca%amba foun% that
the ear"ier fun% mana#er %i% not use options market for he%#in# to protect the net asset va"ue
:(
-</V. of the fun%. @e wants to fo""ow some strate#ies that wi"" protect the unit ho"%ers of /pe+
&un%. Since the market has been hi#h"y vo"ati"e in the past 3 year perio% he %eci%es to
concentrate on his portfo"io on a month9to9month basis. @e wants to use options to protect the
</V of the fun% from %roppin# an% provi%e a%%itiona" #ains.
Ca%amba has co""ecte% %ata about various options contracts avai"ab"e on the 8enchmark
In%e+. There were 5 ca"" options an% 5 put options avai"ab"e with e+ercise price varyin# from
Rs.4A(( to Rs.*3((. Tab"e be"ow shows ca"" an% put options prices for various e+ercise prices
with the e+piry %ate of =arch :( 3('6.
E+ercise Price Ca"" Price Put Price
Rs. Rs. Rs.
4A(( 3(:.4 '6'.*
4A4( '5A.* '6A.4
45(( '76.4 '*'.3
454( '4A.3 '74.3
*((( '64.6 'A6.'
*(4( '3'.6 '5A.3
*'(( ''3.* 3'(.'
*'4( '('.3 33'.3
*3(( 54.: 3:(.4
Biscussion Tuestions
'. If he wants to enter into covere% ca"" writin# which of these options shou"% he chooseP
3. Since the market is e+pecte% to be bearish Ca%amba wants to enter into a bearish money
sprea%. @ow can this be accomp"ishe% usin# ca"" options an% what wou"% be the #ain
from this money sprea% transaction if the in%e+ is at 453( on =arch :(
th
P
:'
:. Since the market is e+pecte% to be bearish Ca%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
P
6. @ow can Ca%amba use a stra%%"e strate#y an% what wou"% be the #ain if the in%e+ is at
453( on =arch :(
th
.
:3