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I don't grasp the blue difference below. If $P \ge 48$, isn't the investor's

Maximum loss = spread credit + $\color{red}{\text{Loss from his sold 44C}} - \color{limegreen}{\text{profit from his purchased 48C}}$. = spread credit + $\color{red}{P - 44} - \color{limegreen}{(P - 48})$
= spread credit + $\color{limegreen}{48} - \color{red}{44}$.

= The last line is wrong anyways, because $3 -4 = -1$.

Bear Call Spread Example

Investor is bearish on stock XYZ when it is trading at \$50 per share and believes the stock price will decrease over the next month. The investor sells (writes) \$44 call and buys a \$48 call for a net credit of \$3. Best case scenario is if the stock price ends up at or below \$44 then the options expire worthless and the trader keeps the spread credit. Worst case scenario is if the stock price ends up at or above \$48 then the trader is down the spread credit minus (\$44 - \$48) amount.

Break even point = 44 strike + spread credit = \$44 + \$3 = \$47

Maximum Profit = Spread credit = \$3

Maximum Loss = Spread credit $\color{CornflowerBlue}{- (\$48 - \$44)}$ = \$3 - \$4 = \$1

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You have your minus signs mixed up for buying and selling the underlying. When your short call is exercised, you sell the stock for 44 (credit). When your long call is exercised, you buy the stock for 48 (debit). So in your terminology, the maximum loss is:

  • (-P + 44) + (P - 48) + spread credit = 44 - 48 + 3 = -1

A much easier way to remember this is that with vertical spreads:

  • If it's a credit spread, the maximum gain is the credit received and the maximum loss is the difference in strikes less the credit received.

  • If it's a debit spread, the maximum gain is the difference in strikes less the debit paid and the maximum risk is the debit.

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