Bear Call Spread - Hull Chap 10

[3tac]

Having a problem understanding this concept. Similar to a Bull Spread, we should be able to create a spread using calls, but with a Bear Spread, we buy a call with a high strike price and sell a call with a low stock price. This is where I get stuck.

Consider the following example where we have S_0 = 45.

Suppose we look at a Bull Spread where we expect S_T = 50. We can buy a call w/ K=20 and sell a call w/ K=30.
The expected payoff then from this Bull Spread = (50-20)+(30-50)=10

Now, consider a Bear Spread where we expect S_T = 40. We can buy a call w/ K=30 and sell a call w/ K=20.
The expected payoff then from this Bear Spread = (40-30)+(20-40)= -10

:-?

[carrytheCrøss]

Not sure, and I'm not taking the exam, so I could be out of my league, but perhaps it has something to do with the expected profit, not payoff. For the Bull Spread at time 0, the expected payoff is 0 or positive, but we are buying the more expensive call. For the Bear Spread at time 0, the expected payoff is 0 or negative, but we are buying the less expensive call. Perhaps the concept of a Bear Spread, then, is based on a play on the option premiums, but really not sure; this is just a try.

[Scooterpye]

In your example, how much would you pay to put on a bull spread with a potential payoff of 10? Obviously, you would pay less than 10, say 9.

So, e.g., Call with strike of 30 + 9 = Call with strike of 20.

If instead you sell the call with strike of 20 and buy the call with the strike of 30, you will take in the 9 points. You're strategy is to hope that S falls so much that both calls are worthless and you can just keep the 9 points you took in. If S falls to 29, the call you own is worthless and the call you shorted is worth 9, so you would just breakeven. You would need the stock to go below 29 in order to make money.

Note that this bear call strategy is fairly similar to paying 1 point to buy a put with a strike of 30. (unless the stock price falls below 20, in which case owning the put outperforms the bear call spread).