PART

1

• PART VI
• Options Strategies
• Profit Diagrams

2
Introduction

• Using options, we can create many different
  strategies.
• These can be tailored to suit the individual
  investors risk preferences and price
  expectations.
• The strategies may be bullish, bearish, or
  neutral.

3
Introduction (Cont)

• They may be aggressive, defensive, or virtually
  risk-less.
• For every strategy, we will show the cost of
  setting it up, the payoffs and the profit/loss
  at expiration, and the breakeven price(s).

4
Long Stock

• We will consider a Long Stock position because it
  is a very basic position, although it does not
  entail the use of options.
• Let the prevailing stock price be St.
• We will denote the stock price at expiration by
  ST, which is obviously a random variable.

5
Long Stock (Cont)

• A person who buys the stock at time t and holds
  it till time T is said to be long in the stock.
• The initial investment is St.
• The profit diagram may be depicted as follows.

6
?
ST?
St
-St
7
Long Stock (Cont)

• The X-axis denotes the stock price at expiration,
  and the Y-axis denotes the profit.
• The profit diagram is a 45? line passing through
  the X-axis at ST St.
• Why is the diagram a 45? line?

8
Long Stock (Cont)

• For every rupee increase in the terminal stock
  price, the profit will be Rs 1 more.
• And every rupee decrease, it will be Rs 1 less.
• If the terminal stock price is equal to the
  initial stock price, the profit will be zero.
• The maximum profit is unlimited, because the
  terminal stock price has no upper bound.

9
Long Stock (Cont)

• The maximum possible loss is equal to the price
  paid at the outset, because the terminal stock
  price cannot go below zero due to limited
  liability.
• This strategy is appropriate for investors who
  are bullish about the market, because the
  investor makes money if the market moves up.

10
Long Stock (Cont)

• It is an aggressive strategy, because the
  investor can make substantial losses, if his
  forecast of the market is wrong.

11
Numerical Illustration

• Assume that you buy a share of Colgate Palmolive
  for Rs 100.
• If the terminal stock price is also equal to Rs
  100, then the profit will be zero.
• Since there is no upper bound on the terminal
  stock price, the maximum profit, ST 100, is
  unlimited.
• The lowest possible value of ST is zero. So the
  maximum loss is Rs 100.

12
Short Stock

• This too is a basic position in the underlying
  asset.
• The strategy entails short selling the stock at
  the initial price of St, and buying it back later
  at a price of ST.
• The profit diagram can be depicted as follows.

13
St
?
ST?
St
14
Short Stock (Cont)

• The profit diagram is a line with a slope of
• -1, passing through the X-axis at ST St.
• Why is the slope of the line 1?
• For every rupee increase in the terminal stock
  price, the profit will be Rs 1 less.
• And for every rupee decrease in the terminal
  price, the profit will be Rs 1 more.

15
Short Stock (Cont)

• If the price at which the stock is bought back is
  equal to the price paid at the outset, then the
  profit will be zero.
• The minimum price at which the share can be
  bought back is zero.
• Therefore the maximum possible profit is the
  initial share price.

16
Short Stock (Cont)

• The terminal stock price has no upper bound, so
  consequently the maximum possible loss is
  unlimited.
• The strategy is appropriate for bearish
  investors, because if the market were to fall,
  they would benefit.
• It is a very aggressive strategy, because losses
  can be substantial.

17
Numerical Illustration

• Assume that a share of Colgate Palmolive is sold
  short at Rs 100.
• If the price at which the share is bought back
  subsequently is also Rs 100, then the profit will
  be zero.
• Since the lowest possible price at the time of
  purchase is zero, the maximum possible profit is
  Rs 100.

18
Numerical Illustration (Cont)

• Since the terminal stock price has no upper
  bound, the maximum possible loss, which is 100
  ST, is unlimited.

19
Long Call

• A long position in the call means that the
  investor has bought the call option.
• Let the exercise price be X, and the call premium
  be Ct.
• If the terminal stock price is less than the
  exercise price, the option will expire worthless,
  and the investors loss will be equal to the
  premium paid at the outset.

20
Long Call (Cont)

• So for the price range, 0 ? ST ? X, the profit
  is
• ? -Ct.
• As the terminal stock price rises beyond X, the
  profit will increase rupee for rupee.
• Thus for the price range, ST gt X
• ? ST X - Ct

21
Long Call (Cont)

• The breakeven price is given by
• ST X Ct
• The maximum possible loss is equal to the premium
  paid for the option.
• The maximum profit is unlimited.
• The strategy is meant for bullish investors
  because it makes money when prices rise.

22
Long Call (Cont)

• It is a defensive strategy, because the maximum
  possible loss is limited to the premium paid, if
  the market were to fall.
• The profit diagram may be depicted as follows.

23
?
X
ST?
X Ct
-Ct
24
Numerical Illustration

• Assume that you buy a call option with an
  exercise price of Rs 100, on Colgate Palmolive,
  for a premium of Rs 8.
• If the terminal stock price is less than
• Rs 100, the option will not be exercised, and
  the entire premium of Rs 8 will be a loss.

25
Numerical Illustration (Cont)

• If ST gt Rs 100, the profit will increase rupee
  for rupee.
• The breakeven stock price is
• Rs 100 Rs 8 Rs 108
• The maximum profit is unlimited.

26
Writing a Naked Call

• Writing a call means selling a call option.
• Writing a naked call means selling a call option
  without owning the underlying stock.
• Let us consider a call option with an exercise
  price of X.
• We will denote the corresponding premium by Ct.

27
Naked Calls (Cont)

• If the stock price at expiration is less than the
  exercise price, then the other party will not
  exercise the option, and the writer will get to
  keep the entire premium.
• That is, if 0 ? ST ? X, then
• ? Ct

28
Naked Calls (Cont)

• As the stock price rises above X, the writer will
  lose rupee for rupee, because the other party
  will now exercise.
• So while the maximum gain for the writer is
  limited to the premium paid at the outset, the
  maximum loss is unlimited because the terminal
  stock price has no upper limit.

29
Naked Calls (Cont)

• The position will breakeven when
• ST X Ct.
• The strategy is suitable for bearish investors,
  for they stand to make money if the market were
  to fall.
• It is an aggressive strategy, for while profits
  are limited, losses are unlimited.
• The profit diagram may be depicted as follows.

30
Ct
?
X
ST?
X Ct
31
Numerical Illustration

• Consider a call with an exercise price of
• Rs 100 on Colgate Palmolive.
• Let the premium be Rs 8.
• If the terminal stock price is less than or equal
  to Rs 100, the profit for the writer is Rs 8.
• As the terminal stock price rises above Rs
  100 the profit will fall rupee for rupee.

32
Numerical Illustration (Cont)

• The breakeven stock price is
• Rs 100 Rs 8 Rs 108.
• The maximum loss is unlimited.

33
Long Put

• A long position in a put means buying a put
  option.
• If the terminal stock price were to be greater
  than the exercise price then the put will expire
  worthless, and the investor will lose the entire
  premium.
• So, if ST ? X, ? -Pt

34
Long Put (Cont)

• As the terminal stock price declines below X, the
  profit will increase rupee for rupee.
• The breakeven stock price is given by
• X ST Pt 0 ? ST X Pt.
• The maximum profit is also X Pt, because the
  minimum stock price is zero.
• The maximum possible loss is limited to the
  initial premium paid.

35
Long Put (Cont)

• This strategy will be preferred by bearish
  investors.
• It is a defensive strategy because the maximum
  possible loss is limited.
• The profit diagram may be depicted as follows.

36
X - Pt
?
X - Pt
X
ST?
37
Numerical Illustration

• Consider a put option on Colgate Palmolive with
  an exercise price of Rs 100.
• Let the premium be Rs 6.
• If the terminal stock price were to be greater
  than Rs 100, the investor will let the option
  expire worthless, and the loss will be Rs 6.
• If the stock price dips below Rs 100, the profit
  will increase rupee for rupee.

38
Numerical Illustration (Cont)

• The breakeven stock price is
• Rs 100 Rs 6 Rs 94.
• The maximum profit is also Rs 94.

39
Writing a Put

• Writing a put means selling a put option.
• When you sell a put, the best thing that can
  happen is that the option will not be exercised,
  in which case the profit is equal to the premium
  received.
• So if ST ? X, ? Pt.
• As the stock price dips below X, the profit will
  decline rupee for rupee.

40
Writing a Put (Cont)

• The breakeven price is X Pt.
• The maximum loss is also X Pt, because the
  lowest possible stock price is zero.
• The maximum profit is of course Pt.
• The strategy is suitable for bullish investors
  because it makes money if the market rises.

41
Writing a Put (Cont)

• It is an aggressive strategy because there can be
  substantial losses.
• The profit diagram may be depicted as shown below

42
Pt
?
X
ST?
X - Pt
-(X Pt)
43
Numerical Illustration

• Assume that an investor writes a put with an
  exercise price of Rs 100 on Colgate Palmolive.
• Let the premium be Rs 6.
• If the terminal stock price is greater than
• Rs 100, then the other party will not exercise,
  and the profit for the investor is
• Rs 6.

44
Numerical Illustration (Cont)

• If the terminal stock price goes below
• Rs 100, the profit will decline rupee for rupee.
• The breakeven stock price is
• Rs 100 Rs 6 Rs 94.
• The maximum loss is Rs 94.

45
Writing a Covered Call

• When an investor writes a covered call, he writes
  a call option for every share in his possession.
• If we denote the initial share price as St and
  the terminal share price as ST, then the profit
  when the share is sold is
• ST - St

46
Covered Call (Cont)

• Profit from the call may be expressed as
• Ct Max0, ST X
• The overall profit is
• ST St Ct Max0, ST X
• If ST ? X, ? ST St Ct
• Because in this price range, the call will not be
  exercised by the other party.

47
Covered Call (Cont)

• As the stock price goes below X, the profit will
  decline rupee for rupee.
• The maximum loss will occur when ST 0, and is
  equal to St Ct.
• The position will breakeven when
• ST St - Ct

48
Covered Call (Cont)

• If ST gt X, ? X St Ct
• In this price range therefore, the profit is a
  constant.
• This also happens to be the maximum possible
  profit.
• The profit diagram may be depicted as follows.

49
X St Ct
?
X
ST?
St - Ct
-St Ct
50
Covered Call (Cont)

• The maximum profit that can be earned is limited
  because the stock will be called away if ST gt X.
• The maximum return is called the if-called return
  because it is the return earned if the call is
  exercised by the other party, and the stock is
  called away.

51
Covered Call (Cont)

• The maximum profit from the covered call is X
  Ct St.
• Let us compare it with the profit from a long
  stock position which is ST St.
• The profit from the covered call will be greater
  as long as ST lt X Ct
• X Ct is called the point of regret.

52
Covered Call (Cont)

• If the stock price goes higher than this, then
  the investor will regret writing the options.
• The objective of writing the call is to generate
  some extra income in a neutral to down market.
• This is because in a neutral to down market the
  call will not be exercised and the investor will
  retain the call premium.

53
Covered Call (Cont)

• Thus in such a market he will get an additional
  income compared to what he would have gotten had
  he chosen to just hold the stock.
• The call provides a cushion if the stock price
  falls.
• The position is said to be neutral to mildly
  bullish.

54
Covered Call (Cont)

• This is because the investor makes money for any
  price above the breakeven price of
• St Ct.
• However it is not suitable for a very bullish
  investor, because if the stock price were to rise
  too far and pass the point of regret, then the
  investor would have been better off not writing
  the call.

55
Covered Call (Cont)

• If the market were to decline substantially, then
  too the investor would make large losses.
• Is this a risky strategy?
• The answer is that it depends on the motive of
  the investor who is writing the call options.

56
Over-Writing

• Investors who implement such a strategy write
  calls against stocks which they are already
  holding in their portfolios.
• For them, overwriting is an opportunity to earn
  extra income at a time when the expectation is
  that the asset will not appreciate significantly
  in the short run.

57
Over-Writing (Cont)

• Since the investor any way owns the underlying
  stock, he is already exposed to the risk of a
  decline in the stock price.
• Thus, writing covered calls under such
  conditions, cannot be perceived as risky.

58
Buy-Write Strategies

• Investors who implement this strategy, buy the
  stock and write calls simultaneously.
• In this case we cannot compare the covered call
  position with a long stock position.
• The buy-write should be viewed as a single
  investment.

59
Buy-Write (Cont)

• If so, it is a risky strategy, because if the
  stock price were to decline sharply, there would
  be major losses.
• The profit diagram for a covered call resembles
  that for a short put.
• This is not surprising if one considers put call
  parity.

60
Covered Call

• From put-call parity

61
Covered Call (Cont)

• Therefore

Thus, a long position in a stock plus a short
position in a call, is equivalent to a short put
position, plus an investment in the risk-less
asset.
62
Numerical Illustration

• Assume that the current price of a share of
  Colgate Palmolive is Rs 100 and that call options
  with an exercise price of Rs 100 are trading at a
  price of Rs 8.
• Consider an investor who owns one share and has
  written a call option.

63
Illustration (Cont)

• If the share price is less than Rs 100, the call
  will not be exercised.
• The profit from the share ST 100
• The call premium Rs 8
• So total profit ST 92
• The maximum possible loss is Rs 92, which will
  occur if ST 0.

64
Illustration (Cont)

• The breakeven point is given by ST 92.
• If ST gt 100, the profit is
• X St Ct 100 100 8 8
• If the terminal stock price were to exceed
• Rs 108, the investor will regret writing the
  call.
• Thus Rs 108 is the point of regret.