Question

Consider the following option portfolio whose components have the same maturity:

• A long call option with a strike of $25 and a premium of $5

• A short call option with a strike of $30 and a premium of $3

a. What is the name of this option strategy?

b. Why would you use such a strategy?

c. Draw the profit graph of this portfolio at expiration as a function of the spot price of the underlying asset (label as much as you can to ensure the diagram is to scale)

d. Considering only the total profit, identify when this strategy does better and when it does worse than simply buying the underlying asset

Answer 1

a) A Bull Call Strategy uses 2 call options to create a range. It involves buying a call option at lower exercise price and selling a call option at higher exercise price.
Since we are long the call option at strike price of $25 and short call option at exercise price of $30, the strategy used is Bull Call Spread.

b) The strategy is used when the expectation is for share price to rise but a limited rise is expected. The investor expects share price to rise so he buys call option at a lower exercise price. However, he expects share price to rise upto a particular level and to eat away the premium he sells call option at higher share price. By going short at higher price the strategy becomes less costly, however it limits the upside profitability.

c)

d) The strategy will result in profit when stock price exceeds lower exercise price by minimum of net premium paid such that profit = 0. This is the breakeven point also.
Here,
Premium paid on C+ at exercise price of 25 = $5
Premium received on C- at exercise price of 30 = $3
Net Premium paid = Premium paid on C+ - Premium received on C-
                                     = $5 – $3
                                   = $2
So this strategy will does better when Share price exceeds = 25 + 2 = 27
$ 27 is the breakeven point.
The maximum profit will be Difference of Strike Price – Net Premium Paid
Maximum Profit = $30 - $25 - $2
Maximum Profit = $3
This is achieved when the share price reaches the higher exercise price or above it. This is when the strategy yields highest profit.

In compare to buying the stock the standalone strategy will limit the downside to maximum of net premium paid. In case of stock maximum loss can be purchase price. However in bull call spread maximum loss will be limited to net premium paid. This is when the strategy will perform best compare to buying the underlying asset.

In compare to buying the stock the standalone strategy will also limit the upside. In case of stock maximum profit can be infinite. However in bull call spread maximum profit will be limited to Difference in higher and lower exercise price minus net premium paid.
That is in case of bull call spread profit will be limited when share price exceeds higher exercise price as payoff from C- will offset payoff from C+. This is when the strategy will perform worse compare to buying the underlying asset.