Strategy of Bull Spread

Question

State when market is expected to go up then what is the Strategy of Bull Spread?

Answer 1

The bull spread strategy is deployed in cases when the investor has a strong perception that the markets would go up and he has bullish notions of the same. In order to implement this strategy, the investor acquires a long position in a call option (having a certain strike price) and correspondingly shorts another call option which is identical to the first call but this shorted call has a higher exercise price. As per general pricing rules, the call option that has the lower exercise price would have higher option premium than the identical call with higher strike price. Since the long position is acquired in the call with higher option premium, a net cash outflow would take place at the start which is expressed as the differences between the option premiums of the two call options.

To describe this strategy, certain notations are used. The call, whose exercise price K1 is lower is assumed to have an option premium equaling c1. On the other hand, the call option with the higher exercise price K2 is assumed to have the option premium c2. It is also assumed that the price at expiration is represented by ST. Thus, the value of the bull spread strategy at expiration would be:

V = max (0, ST – K1) – max (0, ST – K2).

There is a positive payoff which results from the long position in the call option when the prices of the asset in the market increase. Similarly, the short call has a negative payoff since the investor would be loosing from the short position in the call option when the prices of assets are unexpectedly high. The initial cost of the position is represented by c1 – c2 and accordingly the profit from this above stated strategy is expressed as:

Profit = max (0, ST – K1) – max (0, ST – K2) – (c1 – c2).

The various payoffs as well as the net profits from the bull spread strategies that would result in various situations have been depicted in the graph below:

It is clear that losses are maximum loss when the price of the stock at expiration of the option lower than K1 and this maximum loss is capped at the levels of the initial net premium paid. The gains that accrue from this strategy are also limited. The maximum gain can be realized only when the short position of the investor on the call option expires worthless and profits are realized from the long call. In other words, the stock prices at expiration should be less than K2 to yield profits, but at the same time, it should also be higher than K1. The maximum profit  can be expressed as K2 – K1 – c1 + c2. Profits can be realized only in the case of the difference between the exercise prices of the options being higher than the net premium outflow. Therefore, these spreads should be used by investors who hold a strong belief that that the stock prices would increase in the short run, but the increase in the prices of the assets would not be significant (Sinclair, 2010). The cover in this strategy is the shorted call which helps to minimize the net premium outflow that would have occurred only when the investor was long the option. Though this strategy provides limited upside potential on the upside in contrast to naked options, it also helps to minimize the maximum loss which could occur in the event of the investor going wrong and the asset price in the spot market actually declines (this is because the premium received due to the shorted call would be used to partly cover the option premium paid on the position of long call).