Chapter 11 Trading Strategies

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

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

Principal Protected Note 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 The $ 1,000 principal can be received for certain What is the cost?

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

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

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.

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

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)

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

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

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

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

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

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

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

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

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

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

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

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 )

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

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

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

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

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

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

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

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

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, 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.

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 _ _ _ _ _ _

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

Quiz solution: Payoff from a bear spread using puts Initial cost:1.8-0.35=1.45 Max loss: 1.45 Mas gain: 5-1.45=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

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