Memorizing is for suckers.
Understanding is way better. Each strategy is just a combination of long/short calls/puts. Write out the formula, and you can easily deduce the min/max/BE for any strategy.
Bull Spread: Long Call at low strike, Short call at high strike. That’s all you need to know.
Profit = max(0, S_t - X_l) - C_l - [max(0, S_t - X_h) - C_h]
Note: l and h subscript corresponds to low and high call.
e.g., C_l = premium on low call
S_t = stock price at time t
Just look at it… how do you maximize it?
max(0, S_t - X_l) - C_l - [max(0, S_t - X_h) - C_h]
= max(0, S_t - X_l) - C_l - max(0, S_t - X_h) + C_h
You need to use some critical thinking to imagine how this could be maximized. Test some critical points in your head, plug in extreme and/or critical numbers if that helps you. Like, try with a S_t of 1,000, waaay above any of your strikes.
= S_t - X_l - S_t + X_h - C_l + C_h
= X_h - X_l + C_h - C_l
How would you minimize it? Use more imagination and critical thinking.
If you are stuck, plug in “critical numbers,” like, try plugging in different strike prices in place of S_t. Plug in 0 in place of S_t, or extremely high numbers in place of S_t.
You should just know the objective of each strategy, and that will lead you to good guesses about how to maximize or minimize the calculation. You should know a bull spread is designed to profit from increased stock price. That should give you a ton of clues.