Risk of Bull Spread

[Adam]

In section 12.3 of Hull's book (9th global), it mentions 3 types of bull spreads as below.

• Both calls are out of money;
• One in one out;
• Both in.

Then it says the most aggressive is the first one since it is cheap to set up and has a low chance of giving a payoff. My question is how come this is the most aggressive type. In what way?
Thanks.

 

[radex]

They are aggressive in the sense that probability of a positive payoff is lower than other two strategies....but the amount of positive payoff is higher.

So for a lower initial investment...one can gain significant gains but only in a lower number of future scenarios

 

[mugono]

In section 12.3 of Hull's book (9th global), it mentions 3 types of bull spreads as below.

• Both calls are out of money;
• One in one out;
• Both in.

Then it says the most aggressive is the first one since it is cheap to set up and has a low chance of giving a payoff. My question is how come this is the most aggressive type. In what way?
Thanks.

In addition to the articulation given by radex, you can also think of the OTM bull spread through the lens of delta, which is lower compared with the other examples given.

 

[Adam]

In addition to the articulation given by radex, you can also think of the OTM bull spread through the lens of delta, which is lower compared with the other examples given.

Thank you both for your explanation.
However, if we consider in the usual risk-return trade-off argument here, it appears that case one has very low risk (or very low variation of outcome). This because the first case has an almost certain loss (premium paid/received for/from the two calls; if extremely out of money). If this is certain or semi-certain, then it has lower risk, then not aggressive.
Also if think in terms of delta, if calls are deeply out of money, then delta is almost 0. That is, small change in price will not affect option price much. Hence, almost certain no exercise of the calls, which again leads to a certain loss.
Is what I wrote above correct? Why not?
Thank you.

 

[mugono]

Thank you both for your explanation.
However, if we consider in the usual risk-return trade-off argument here, it appears that case one has very low risk (or very low variation of outcome). This because the first case has an almost certain loss (premium paid/received for/from the two calls; if extremely out of money). If this is certain or semi-certain, then it has lower risk, then not aggressive.
Also if think in terms of delta, if calls are deeply out of money, then delta is almost 0. That is, small change in price will not affect option price much. Hence, almost certain no exercise of the calls, which again leads to a certain loss.
Is what I wrote above correct? Why not?
Thank you.

An OTM bull spread is relatively risky (for the buyer) and is reflected in the lower price (relative to the reward on offer; eg risking 1 for a maximum reward of 4). The markets are generally priced fairly otherwise there would be an arbitrage opportunity.