Bull Put Spread Break even

The formula for BE I found is: Xh + pL - pH
How come it starts with Xh?? I am long the put with lower X ie logically I would start with Xl and then adjust for the premiums, or am I missing here something?

The same for BE under Bear Call Spread: Xl + cl - ch
Why do we start with Xl and not with Xh (which would be my trigerring point under long posiiton)??

Explanation in super plain language would be much appreciated :slight_smile:

The breakeven price is between the strike prices of the puts. Only the short put (with higher strike price) will be in the money

V_T = max(0, X_L - S_T) - max(0, X_H - S_T) - (p_L - p_H)

When the strategy is at breakeven point, V_T = 0 and X_L < S_T^* < X_H

0 = 0 - (X_H - S_T^*) - (p_L - p_H)

0 = -X_H + S_T^* - p_L + p_H

X_H + p_L - p_H = S_T^*

That´s a tough one to understand

You buy X(h) put premium P
You sell X(l) put premium p

You need the stock to drop X(h) to make money but you paid P and you received p
X(h) -P +p

I’m not sure why you think that logically you would start with X_L.

In a bull put spread you receive money today (i.e., your net cost is negative), and your payoff is zero or negative (i.e., you may have to give back some of the money you received today). Specifically, your payoff is zero when the price at expiration is greater than or equal to X_H, declines linearly between X_H and X_L to a value of X_L - X_H, and is X_L - X_H when the price at expiration is less than or equal to X_L.

To break even, you have to pay back the amount you received. To determine the price at which that occurs, you have to start at the lowest price at which your payoff is zero – X_H – and move to the left by the amount you received at the outset: P_H - P_L. Thus, the breakeven price is:

X_H - \left(P_H - P_L\right) = X_H + P_L - P_H

I find it much easier to think about the payoff diagram and work out (logically) the breakeven price than to try to memorize the formula for the breakeven price.

Thanks Magician!

My pleasure.