Topic 9 Trading Strategies for Options

1
Topic 9Trading Strategies for Options
2
Introduction

• The purpose of this lecture it to introduce you
  to some of the basic strategies that an options
  trader might use.
• Keep in mind that although we are examining these
  strategies in isolation, in reality you normally
  would execute them as part of a larger hedging or
  investment process. Only rarely would you simply
  implement these strategies for speculative
  purposes.
• Also, this lecture is a blend of Hulls chapter 9
  and McDonalds chapter 3.

3
Elementary Trading Strategies

• We can examine trading strategies relatively
  simply by examining the payoff diagrams to
  various option positions.
• Combining these payoff diagrams is a very useful
  tool for understanding not only more complex
  positions, but also more complex options.
• Lets begin with call and put options with a
  strike of 100, and three months to maturity.
  Lets assume that the premium paid for these
  options is 2 and 1.80, respectively, at time 0.
• Our profit, therefore is the terminal payoff less
  the premium (assuming we are long), or the
  premium less terminal payoff if we are short.

4
Elementary Trading Strategies
5
Elementary Trading Strategies

• As McDonald notes, the long call position allows
  us to cap our exposure to future price increases.
  
• If we knew we wanted to purchase the stock at
  some point in the future (perhaps to cover a
  short position!), then one way we could insure
  that we would not get creamed by a rise in the
  price of the stock would be to purchase a long
  call, in which case we have capped our price risk.

6
Elementary Trading Strategies
7
Elementary Trading Strategies
8
Elementary Trading Strategies

• McDonald points out that a long put position
  establishes a floor for the value of our stock.
• If we own the stock and are worried that the
  price might fall, then by buying a put option we
  are establishing the minimum value that our net
  portfolio can take.
• In this sense this is nothing more than an
  insurance policy.
• Indeed, insurance companies are basically in the
  business of writing put options on various
  things like lives, health, cars, houses, etc.
• McDonald has a really neat notion about the
  relationship between insurance and puts. He
  points out that if you own the asset then buying
  a put reduces risk since the put pays off when
  the asset decreases in price. If you dont own
  the asset, however, it increases your risk since
  you wind up adding volatility to your portfolio.
• The really cool example is like buying homeowners
  insurance on your house versus buying homeowners
  insurance on your neighbors house.

9
Elementary Trading Strategies
10
Covered Positions

• If you are going to write a call, frequently you
  will also hold the underlying asset to protect
  yourself against downside losses. This is called
  a covered call.
• Frequently people holding a stock will write out
  of the money calls to enhance the income from
  the portfolio. Note that this gives you a net
  position that is very similar to that of a put
  option!
• Buying a put on a stock that you hold (with a
  lower strike price) will give you some measure of
  insurance if the stock price goes down.
• This is the basic idea of portfolio insurance!
• It is called a protective put, and it has a
  payoff pattern very reminiscent of the payoff to
  the long call.

11
Covered Positions
12
Covered Positions
13
Spreads and Combinations

• A spread is a strategy where you buy or sell
  positions in the same type of option.
• A combination is a strategy where you buy or sell
  position in different types of options.
• A bull strategy is one that is designed to make
  money when the market rises, and a bear strategy
  makes money when the market falls.
• A volatility play makes money when there are
  large price swings in the market, regardless of
  the direction.

14
Spreads

• Bull Spread It is called this because the
  investor is hoping that the stock price will
  rise.
• To construct
• Buy low strike call
• Sell high strike call
• Initial cash flow is negative to investor
• Payoffs
• if terminal stock price
• If low strike price ST - Klow.
• If high stock price - Klow.
• Example An investor buys a 3 call with a strike
  of 30 and sells a 1 call with a strike of 35.
  The payoff from this bull spread strategy is 5
  if the stock price is above 35 and zero when it
  is below 30, and ST-30 when between 30 and 35.
  The cost of the strategy is 2.

15
Spreads

• It is worth considering a payoff diagram to a
  bull spread constructed with call options.

0
16
Spreads

• Bull Spread using puts
• To construct
• Buy low strike
• sell high strike
• initial cash flow is positive to investor
• Payoffs
• if terminal stock price
• If low strike price ST - Klow.
• If high stock price - Klow.

17
Spreads

• Bear Spreads
• With this strategy, the investor is hoping the
  stock price will fall.
• To construct
• buy call option at high strike price
• sell call option at low strike price.
• Initial cash flow is positive to investor
• Payoffs
• ST
• Klow
• STKhigh, 0

18
Spreads

• Real World Example of a bull spread.
• We will actually look at several examples of
  types of spreads. For all of these we will use
  options on IBM.
• The following graph shows IBMs stock price last
  year (well, at least through September 22, 2003.)

19
Spreads
20
Spreads
21
Spreads

• So lets say that we were fortunate on August 19,
  2003 to decide to put on a bull spread using IBM
  options.
• IBM was selling for 83.52 per share.
• Remember how to construct bull spread buy a low
  strike option and sell a high strike option.
• Lets say that we decided to construct this
  spread using the September options with strike
  prices of 80 and 85, respectively.
• The September 80 option had a price of
  4.20/share.
• The September 85 option has a price of
  1.20/share.

22
Spreads

• So we buy 1 options contract at 4.20 per share,
  and then we sell 1 options contract at 1.20 per
  share.
• Net cashflow 100(-4.20 1.20) -300.
• We note that on September 4, IBM was selling at
  86.33/share, so we decide to close our position.
  So we sell our holdings of the September 80 and
  then buy a September 85 option contract (to
  cancel the short September 85 contract we
  have.)
• September 80 price 6.6/share.
• September 80 price 2.45/share.
• Net cash flow on September 4 100(6.60 2.45)
  415.

23
Spreads

• So we invested 300 on August 19, and received
  415 on September 4.
• Our simple, un-annualized return was
• (415-300)/300 38.33
• Annualizing (and using continuous compounding),
  the rate of return is 740.25!
• Compare this to if we had just purchased a share
  of the stock.
• Our simple, un-annualized return would have been
• (86.33 83.52)/83.52 3.36
• Our annualized return was (only) 75.48.

24
Spreads

• What if we had not closed out our position on
  September 4, but instead held them until the
  expiration of the contracts, which would have
  been on September 19?
• On that day IBM traded at a price of 92. So our
  payoff on the September 80 contract would have
  been 12/share, or 1200, and we would have had
  to pay 7/share or 700 on the September 85
  contract that we were short.
• Net effect is we would have received 500, for
  200 profit on a 300 investment!

25
Spreads

• Of course, it could have happened that the price
  of IBM could have fallen.
• What would have happened if the price of IBM had
  fallen to 75 on September 19?
• Both options would have expired worthless, so
  there would have been no cash flow on September
  19th.
• We could keep the 120 we earned from selling the
  September 85 option, but we would lose the 420
  we paid for the September 80 option.
• Net effect is that we would be out 300. An
  infinitely negative return!

26
Spreads

• When an investor puts on a Bull or Bear spread
  they are fundamentally taking a position on the
  direction of the stock.
• Sometimes an investor would rather take a
  position not on the direction of movement, but
  rather on whether the stock will move much at
  all.
• This is known as a volatility play.
• It is perhaps easiest to start by seeing what
  would happen if the investor felt that the stock
  was UNLIKELY to move very much and wanted a
  position that would pay off if the stocks price
  pretty much stayed the same
• One approach would simply be to write a call
  option that was deeply out of the money.
• The drawback to that approach is that if
  volatility turns out to be high, you could lose a
  potentially unlimited amount of money.

27
Spreads

• A commonly used approach in such cases is to
  implement a butterfly strategy.
• To implement this strategy
• Buy a call option at the relatively low strike of
  K1.
• Buy a call option at the relatively high strike
  of K3.
• Sell two call options at strike K2, which is
  halfway between K1 and K3.
• The two long positions are the wings of the
  butterfly and the short position is the body.
• The payoff diagram to a generic butterfly is
  shown on the following page.

28
Spreads
29
Spreads
30
Spreads

• Clearly, then you are taking a position the nets
  you money when there is very little volatility in
  the stock.
• You are generically said to be selling
  volatility when you have this type of position.
• Of course you could also take the opposite
  position, if you felt that volatility was likely
  to be high.
• Sell one call option at K1.
• Sell one call at K3.
• Buy two calls at K2.
• You will get an inverted butterfly pattern.

31
Spreads
32
Spreads
33
Spreads

• One issue that Hull points out on page 197, is
  that if you bring K1, K2, and K3 to be very close
  to each other, the hump of a butterfly spread
  becomes a spike. Indeed, you could actually set
  it up so that you will get a payout only if the
  stock ended at K2 exactly.
• This means that you could create pure state
  securities with a butterfly spread. What this
  means is that, given enough butterfly spreads,
  you could replicate any other security in the
  market.

34
Spreads

• There are other types of spreads available such
  as the calendar spread.
• Sell a call with strike K and maturity T1.
• Buy a call with strike K and maturity T2, where
  T1
• This spread will net cost money at time 0.
• Generically they allow you to either make a
  volatility play (as the pure calendar spread
  does), or they let you make a play on the
  direction of the market.
• The key to the calendar spread is to realize that
  at time T1 the long call will have a higher value
  than will the short call (which matures at that
  day).

35
Spreads

• So, let us work an example. We begin with a stock
  with a price of 85 and we set the strike on the
  two options at 85. Let T11 month, and let T2 3
  months.
• Also, we assume volatility is 25, r10.
• The price for option 1 will be 2.62, and the
  price for option 2 will be 4.75 (using
  Black-Scholes).
• We short option 1, earning 2.62, and we go long
  option 2, so we have to pay 4.75, thus at time 0
  we must pay (2.62-4.75-2.13)
• One month later, the option we are short expires,
  generating the following payoffs to us

36
Spreads
37
Spreads
38
Spreads
39
Spreads

• There is another type of spread that McDonald
  discusses, the Box spread.
• The idea behind the Box spread is that you use
  options to synthetically create a long forward at
  one price and to synthetically create a short
  forward at a different price.
• This can actually guarantee a positive cash flow
  in the future (but obviously at a cost today).
  The net effect is that you are simply borrowing
  or lending money.
• Example 3-3 from McDonald
• Buy a 40-strike call and sell a 40-strike put,
  and also
• Sell a 45-strike call and buy a 45 strike put.

40
Spreads

• First, lets graph the long call and short put
  written at 40

41
Spreads
42
Spreads
43
Spreads

• Next, let us add in the 45 strike positions
  (remember, that is a short call at 45 and a long
  put at 45).

44
Spreads
45
Spreads
46
Spreads

• So we can see that the net effect is that we are
  always earning 5 at termination

47
Spreads
48
Spreads

• Finally, there is another type of spread that
  McDonald mentions, known as the ratio spread.
• In this type of spread you buy m calls at one
  strike and sell n calls at a different strike.
  (You could also work out equivalent positions
  using puts.)
• What is neat is that you can work this out to
  provide a position that is initially costless and
  will generate positive cash flows for in some
  circumstances.
• To see this, consider if a stock were selling
  today at 85, and had volatility of 25, and r
  were 10. According to the Black-Scholes, the
  price of a call option with a strike of 90 would
  be 2.66, and the price of a call with a strike
  of 95 would be 1.36.

49
Spreads

• Assume now that you bought 1 call at 90, for
  2.66, and sold 1.952 calls at 95 for 1.36 each.
• At time 0 your cash out would be
• 1.9521.36 2.66 0
• At maturity, if the stock ended at less than 90,
  your two options would each expire worthless, in
  which case you would have 0 cash flow.
• If the stock ended between 90 and 95, you would
  exercise your long position, but the short would
  expire worthless, so you have a positive cash
  flow.
• Above 95, the short call would come into play,
  but as long as the stock remained below (roughly)
  100, you make a positive return.
• Above 100, however, and your losses quickly
  become large.

50
Spreads
51
Spreads
52
Spreads
53
Spreads

• What you are doing with the ratio spread (as
  illustrated here) is you are trading off the
  upside potential of your call option to get rid
  of the time 0 cost.
• This illustrates one of the most useful, and
  dangerous, features of options you can trade off
  different risks for cash. In this case you are
  being paid to bear the risk that the stock will
  wind up being worth more than 100 to avoid the
  cost of buying your option today.
• Remember there is NEVER a free lunch if you
  costlessly put on an option position, you are
  trading risk (of some form) for that cost of the
  option position.

54
Combinations

• A combination is simply a trading strategy that
  involves using puts and calls on the same stock.
• There are four major combinations that Hull
  discusses
• Straddles
• Strips
• Straps
• Strangles

55
Combinations

• A straddle is simply a position where you take a
  long position in a call and a long position in a
  call usually at the same strike price.
• This is a form of a volatility play since you
  will make money when the stock finishes deeply in
  the money for either the call or the put (they
  both cannot make money).
• The following graph shows a straddle entered into
  at a strike of 85.

56
Combinations
57
Combinations
58
Combinations

• Of course, since we are taking two long
  positions, we have to pay something up front for
  these positions.
• Using our standard 25 volatility, 10 risk-free
  rate, and assuming these are 3 month options, the
  value of each option will be
• Call 5.32
• Put 3.22
• Thus, our net cost to construct the position will
  be 8.54.
• Factoring that into our payoff diagram gives us

59
Combinations
60
Combinations

• So you only make money if the strike is less than
  76.46 (85-8.54) or greater than 93.54 (858.54).
• So again, you only make money if the stock is
  relatively volatile after you buy the options.
• If you take short positions in the call and the
  put, you wind up creating an inverted straddle,
  sometimes called a top straddle or a straddle
  write.
• You make money from the premium but lose money if
  the stock ends up out of the money.

61
Combinations
62
Combinations

• Related to the strangle are the strip and strap.
• A strip consists of one call and two puts, each
  at the same strike.
• A strap consists of two calls and one put, each
  at the same strike.
• Each gives the same basic payoff as a straddle,
  just with a tilt toward either a downward price
  movement (in the case of a strip) or an upward
  price movement (in the case of a strap).
• The following two charts show the net for a strip
  and a strap on the 85 stock on which we formed
  the straddle.

63
Combinations
64
Combinations
65
Combinations

• Of course you can also take inverted strips and
  straps as well.
• Finally, we want to consider the Strangle. In
  this strategy, you are making a play for a very,
  very large increase in the stock price.
• Normally what you will do is buy a put at K1 and
  buy a call at K2, where K1
• The following chart demonstrates a strangle with
  K180 and K290. The put price would be put1.49
  call3.06.

66
Combinations
67
Combinations

• And, of course, you could take an inverted
  strangle, where you will make money if there are
  not large stock movements, but run the risk of
  very large losses if there are.

68
Combinations
69
Trading Positions

• The purpose of this lecture has been to examine
  some of the more common trading strategies that
  are used in the market.
• You should make sure that you are familiar with
  how to create and analyze all of these different
  types of strategies.