1. Chapter 11 Trading Strategies

2. Trading Strategies
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
(a) of the same type (spread)
(b) in a mixture of calls & puts (combination)
(i) Straddle
(ii) Strips and Straps
(iii) Strangles

3. Principal Protected Note
Allows investor to take a risky position without risking any principal
Example: $1000 instrument consisting of
3-year zero-coupon bond with principal of $1000
3-year at-the-money call option on a stock portfolio currently worth $1000

4. Principal Protected Note
1. ST > K :
from the bond
pay strike price to buy the stock
+ ST (> 1000) sell the stock
2. ST =< K
0 from the option
The $ 1,000 principal can be received for certain
What is the cost?

5. Writing Covered Calls Covered call If call owner exercises the option
Writing a call option against securities you already own
Cover the writer’s exposure to potential loss
If call owner exercises the option
Option-writer delivers the already owned securities without having to buy them in the market
Not all covered call positions are profitable
If stock price falls
Long position in underlying stock decreases
However, receive call premium income

6. Writing Covered Calls Naked call writing
Occurs when call writer does not own the underlying security
Risky if the price of the underlying security increases
Initial margin of 15% or more required
Whereas a covered option writer does not have to put up extra margin to write a covered call

7. Writing Covered Calls Covered call writers
Gain the most when stock price remains at exercise price and option expired unexercised
Receive premium income and get to keep the stock
If stock price increases significantly would have been better off not having written the option
Will have to give security to exerciser
Protective put: buying a European put on a stock and the stock it self.

8. For strategies 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

9. Positions in an Option & the Underlying
Profit
Profit K K ST ST
(a)Covered call
(b) Covered call (reverse) K ST K ST
(c)Protective put
(d) Protective put (reverse)

10. Spreads Taking a position in two or more options of the same type
Can be either puts or calls but not puts and calls
Spread can occur based on
Different strike prices (vertical spreads)
Different expirations (horizontal spreads)
Time spreads, calendar spreads

11. Bull Spread Using Calls: Buy a call with K1; sell a call with K2
Profit ST K1 K2

12. Payoff from a bull spread using calls
c1 > c2 : require an initial investment
Stock price range
Payoff from long call
Payoff from short call option
Total payoff
ST <= K1
K1 <ST<K2
ST – K1
ST >= K2
-(ST – K2)
K2 – K1

13. Bull Spread Using Puts: Buy a put with K1; sell a put with K2
Profit ST

14. Payoff from a bull spread using puts
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
-(K2 – ST )
ST - K2
ST >= K2

15. Bear Spread Using Calls: Sell a call with K1; buy a call with K2
Profit K1 K2 ST

16. Payoff from a bear spread using calls
c1 > c2 : have an initial cash inflow
Stock price range
Payoff from short call
Payoff from long call
Total payoff
ST <= K1
K1 <ST<K2
-(ST – K1 )
ST >= K2
ST – K2
K1 – K2

17. 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
ST >= K2

18. Box Spread
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

19. Payoff from a box spread
Cost: (K2-K1)e-rt
Stock price range
Payoff from bull call spread
Payoff from bear put spread
Total payoff
ST <= K1
K2 -K1
K1 <ST<K2
ST-K1
K2 -ST
ST >= K2

20. 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

21. Payoff from a butterfly spread
Stock price range
Payoff from first long call
Payoff from second long call
Payoff from short calls
Total payoff
ST <= K1
K1 <ST =<K2
ST – K1
K1 <ST =< K3
-2(ST – K2 )
K3 - ST
ST >=K3
ST – K3
2(ST – K2 )

22. Butterfly Spread Using Puts: Buy a put with K1, buy a put with K3, Sell two puts with K2
Profit K1 K2 K3 ST

23. Spreads and Combinations
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.
Straddle
Strips and Straps
Strangles

24. A Straddle Combination: buying a European call and put with the same K and T
Profit K ST

25. Straddles Straddle occurs when Long straddle position
Equal number of puts and calls are bought on the same underlying asset
Must have same maturity and strike price
Long straddle position
Profit if optioned asset either
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

26. Straddle Position Bottom Straddle: Downside limit
Sum of put and call prices
Top Straddle ( or straddle write): Upside limit
Selling a call and a put with the same exercise price and expiration data
Highly risky

27. Strips and Straps
Strip: buying one European call and two European puts with the same K and T
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
Bet on a big price move; an increase is more likely

28. Strip & Strap Figure 11.11, page 248
Profit
Profit K ST K ST
Strip
Strap

29. 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

30. Quiz
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? _ _ _ _ _
ABCD stock is trading at $26.00 on May 13, 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.

31. Quiz
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 _ _ _ _ _ _

32. Quiz solution: Bound for European Options (No Dividends )
Put
Solution: p<=35-30e-0.05*0.5=5.74
P<=35-30=5

33. Quiz solution: Payoff from a bear spread using puts
Initial cost: =1.45
Max loss: 1.45
Mas gain: =3.55
Breakeven price: 25-S-1.45=0: S=23.55
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
ST >= 25

34. Quiz solution: Strangle
Initial cost: 2+3=5
Breakeven prices:
30-ST – 5=0: S=25
ST-35 – 5=0: S=40
Stock price range
Payoff from long call
Payoff from long put
Total payoff
ST <= 30
30 – ST
30<ST<35
ST >= 35
ST -35