Profit and max profit for covered call

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lillilland

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On the topic of covered calls, on pg 43 of book 5 in Schweser it states:
(1) profit = -max(0, ST - X) + ST - S0 + C0
then it says
(2) max profit = X + C0 - S0
Can someone please explain the intuition behind (2)?
 
Think “what is the best thing that can happen to me with a covered call” -
Since you are long the stock and short the call, the best thing that can happen to you is to have the price of the stock go up just to the strike of the covered call, but not past it. That way you have received the premium for the call, but you don’t have to pay out AND you stock has gone up in price.
If you break it into the components using the information on page 43:
If you sold a call with a strike of 45 for 2.10 when the stock 43
profit = -max(0, ST - X) + ST - S0 + C0
profit = -max(0, 45 - 45) + 45 - 43 + 2.10
Since the first term is 0 it reduces to X - S0 + CO
Again this is because the best thing that can happen to you with this strategy is that the stock price rises to exactly the strike price.
I don’t know any of these formulas, I just think about each separate component to each strategy and figure it out from there. Once you understand the underlying positions you won’t have to memorize anything.
Hope this helps.
 
A covered call basically means that the security will be called away from you if the price goes over the strike price. When that happens, you will receive the strike price for your call, and you will hand over the underlying stock to your counterparty. Therefore, the highest price YOU can receive for the stock position is the strike price, X, no matter how high the underlying moves.
Profit from the call position: X - S0, because you bought at S0 and effectively sold it at X.
But that’s not your total profit, since you got paid a premium for selling the call. That premium is CO. Total profit is both from the sale of the security and from the premium.
Total Max Profit = (X - S0) + CO
If the call isn’t exercised, i.e. ST < X, then your profit (or loss) is the difference in the begin and end prices for the underlying, plus the premium for selling the option. The option premium is a realized gain, whereas the stock gain (or loss) does not have to be realized at option expiration if you don’t want to.
Total Profit if ST
 
for (1)
At the end of the day, you have stock St, you paid S0 and you collected C0 at the beginning, that is St - S0 + C0
now think about the guy who bought your call: his payoff is max(0, St -X). His payoff is your loss. so you add a minus sign in front of it.
Guess you won’t feel it is difficult any more.
for (2)
Once price increases past X (or equal), the guy who bought the call from you want to exercise it. His payoff is St - X, so yours is X - St, then add it with the other three items you got X - S0 + C0
This should be crystal clear now.
lillilland Wrote:
——————————————————-
> On the topic of covered calls, on pg 43 of book 5
> in Schweser it states:
>
> (1) profit = -max(0, ST - X) + ST - S0 + C0
>
> then it says
>
> (2) max profit = X + C0 - S0
>
> Can someone please explain the intuition behind
> (2)?
 
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