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Chapter 11
Trading Strategies
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Trading Strategies
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What can be achieved when an option is traded in
conjunction with other assets?
Examine the properties of portfolios consisting of
positions in:
(1) an option and a zero-coupon bond
(2) an option and the asset underlying the option
(3) two or more options on the same underlying asset
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(a) of the same type (spread)
(b) in a mixture of calls & puts (combination)
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(i) Straddle
(ii) Strips and Straps
(iii) Strangles
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Principal Protected Note
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Allows investor to take a risky position
without risking any principal
Example: $1000 instrument consisting of
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3-year zero-coupon bond with principal of $1000
3-year at-the-money call option on a stock
portfolio currently worth $1000
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Principal Protected Note
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1. ST > K :
 + 1000 from the bond
 - 1000 pay strike price to buy the stock
 + ST (> 1000) sell the stock
2. ST =< K
 0 from the option
 + 1000 from the bond
The $ 1,000 principal can be received for certain
What is the cost?
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Writing Covered Calls
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Covered call
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Writing a call option against securities you already own
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If call owner exercises the option
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Cover the writer’s exposure to potential loss
Option-writer delivers the already owned securities without
having to buy them in the market
Not all covered call positions are profitable
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If stock price falls
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Long position in underlying stock decreases
However, receive call premium income
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Writing Covered Calls
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Naked call writing
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Occurs when call writer does not own the underlying
security
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Risky if the price of the underlying security increases
Initial margin of 15% or more required
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Whereas a covered option writer does not have to put
up extra margin to write a covered call
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Writing Covered Calls
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Covered call writers
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Gain the most when stock price remains at exercise
price and option expired unexercised
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If stock price increases significantly would have been
better off not having written the option
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Receive premium income and get to keep the stock
Will have to give security to exerciser
Protective put: buying a European put on a stock and
the stock it self.
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For strategies
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Covered call: short call, long stock
Reverse of covered call: long call, short stock
Protective put: long put, long stock
Reverse of protective put: short put, short
stock
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Positions in an Option & the Underlying
Profit
Profit
K
K
ST
ST
(b) Covered call (reverse)
(a)Covered call
K
ST
(c)Protective put
K
ST
(d) Protective put (reverse)
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Spreads
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Taking a position in two or more options of the
same type
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Can be either puts or calls but not puts and calls
Spread can occur based on
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Different strike prices (vertical spreads)
Different expirations (horizontal spreads)
Time spreads, calendar spreads
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Bull Spread Using Calls:
Buy a call with K1; sell a call with K2
Profit
ST
K1
K2
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Payoff from a bull spread using calls
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c1 > c2 : require an initial investment
Stock price
range
Payoff from
long call
Payoff from
short call
option
Total payoff
ST <= K1
0
0
0
K1 <ST<K2
ST – K1
0
ST – K1
ST >= K2
ST – K1
-(ST – K2)
K2 – K1
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Bull Spread Using Puts:
Buy a put with K1; sell a put with K2
Profit
K1
K2
ST
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Payoff from a bull spread using puts
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p1 < p2 : have a positive up-front cash flow
Stock price
range
Payoff from
long put
Payoff from
short put
Total payoff
ST <= K1
K1 - ST
-(K2 - ST)
K1 – K2
K1 <ST<K2
0
-(K2 – ST )
ST - K2
ST >= K2
0
0
0
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Bear Spread Using Calls:
Sell a call with K1; buy a call with K2
Profit
K1
K2
ST
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Payoff from a bear spread using calls
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c1 > c2 : have an initial cash inflow
Stock price
range
Payoff from
short call
Payoff from
long call
Total payoff
ST <= K1
0
0
0
K1 <ST<K2
-(ST – K1 )
0
-(ST – K1 )
ST >= K2
-(ST – K1 )
ST – K2
K1 – K2
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Payoff from a bear spread using puts

p1 < p2 : require an initial investment
Stock price
range
Payoff from
long put
Payoff from
short put
Total payoff
ST <= K1
K2 - ST
-(K1 – ST )
K2– K1
K1 <ST<K2
K2 - ST
0
K2 - ST
ST >= K2
0
0
0
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Box Spread
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A combination of a bull call spread and a
bear put spread with same two prices
If all options are European a box spread is
worth the present value of the difference
between the strike prices
If they are American this is not necessarily so
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Payoff from a box spread
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Cost: (K2-K1)e-rt
Stock price Payoff from bull
range
call spread
Payoff from
Total
bear put spread payoff
ST <= K1
0
K2 -K1
K2 -K1
K1 <ST<K2
ST-K1
K2 -ST
K2 -K1
ST >= K2
K2 -K1
0
K2 -K1
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Butterfly Spread Using Calls: Buy a call with
K1, buy a call with K3, Sell two calls with K2 : appropriate if an
investor feels that large stock price moves are unlikely
Profit
K1
K2
K3
ST
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Payoff from a butterfly spread
Stock price
range
Payoff from
Payoff from
first long call second long
call
Payoff from
short calls
Total payoff
ST <= K1
0
0
0
0
K1 <ST =<K2
ST – K1
0
0
ST – K1
K1 <ST =< K3
ST – K1
0
-2(ST – K2 )
K3 - ST
ST >=K3
ST – K1
ST – K3
2(ST – K2 )
0
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Butterfly Spread Using Puts: Buy a put with
K1, buy a put with K3, Sell two puts with K2
Profit
K1
K2
K3
ST
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Spreads and Combinations
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Spread: taking a position in two ore more
options of the same type
Combination: taking a position in both calls
and puts on the same stock.
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Straddle
Strips and Straps
Strangles
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A Straddle Combination: buying a
European call and put with the same
K and T
Profit
K
ST
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Straddles
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Straddle occurs when
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Equal number of puts and calls are bought on the same
underlying asset
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Long straddle position
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Profit if optioned asset either
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Must have same maturity and strike price
Experiences a large increase in price
Experiences a large decrease in price
Experiences large increases and decreases in price
Useful for a stock experiencing great deal of volatility
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Straddle Position
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Bottom Straddle: Downside limit
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Sum of put and call prices
Top Straddle ( or straddle write): Upside limit
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Sum of put and call prices
Selling a call and a put with the same exercise price and expiration
data
Highly risky
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Strips and Straps
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Strip: buying one European call and two
European puts with the same K and T
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Bet on a big price move; a decrease is more likely
Strap: buying two European call and one
European puts with the same K and T
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Bet on a big price move; an increase is more likely
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Strip & Strap
Figure 11.11, page 248
Profit
Profit
K
Strip
ST
K
ST
Strap
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A Strangle Combination (or bottom vertical
combination):buying a European call with T and K2, sell a put
with T and K1
Profit
K1
K2
ST
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Quiz
1.
What, to the nearest cent, is the lower bound for the price
of a six-month European put option on a stock when the
stock price is $30, the strike price is $35 and the risk-free
interest rate with continuous compounding is 5%?______
What is the answer if the option is American? _ _ _ _ _
2.
ABCD stock is trading at $26.00 on May 13, 2004. You
create a Bear Put Spread by selling the January 2005 put
for $0.35 (strike=20), and buying the January 2005 put for
$1.80 (strike=25). Provide the maximum loss, maximum
reward, and the breakeven price for this strategy.
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Quiz
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A three-month call with a strike price of $35 costs $2. A
three-month put with a strike price of $30 and costs $3.
A trader uses the options to create a strangle (buying a
European put and a European call with the same strike
price and expiration date). For what two values of the
stock price in three months does the trader breakeven
with a profit of zero? (Taking into account the initial cash
flow)
_ _ _ _ _ _ _ and _ _ _ _ _ _
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Quiz solution: Bound for European
Options (No Dividends )
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Put
p  Ke
 rT
 S0
P  K  S0
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Solution: p<=35-30e-0.05*0.5=5.74
P<=35-30=5
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Quiz solution: Payoff from a bear
spread using puts
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Initial cost:1.8-0.35=1.45
Stock price
range
Payoff from
long put
Payoff from
short put
Total payoff
ST <= 20
25 - ST
-(20 – ST )
25– 20=5
20<ST<25
25 - ST
0
25- ST
ST >= 25
0
0
0
Max loss: 1.45
Mas gain: 5-1.45=3.55
Breakeven price: 25-S-1.45=0: S=23.55
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Quiz solution: Strangle
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Initial cost: 2+3=5
Stock price
range
Payoff from
long call
Payoff from
long put
Total payoff
ST <= 30
0
30 – ST
30 – ST
30<ST<35
0
0
0
ST >= 35
ST -35
0
ST -35
Breakeven prices:
30-ST – 5=0: S=25
ST-35 – 5=0: S=40
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