The higher-strike put is the one that actually makes money as price falls — it's your engine.
The lower-strike put is sold to collect premium, reducing your cost. But it also gives up all gains below KL, because if the stock crashes far, your buyer of the lower put profits at your expense, cancelling your extra gains.
The value of a long put at expiry with strike K and stock price ST is its intrinsic value:
Long put=max(K−ST,0)
A short put (you sold it) is just the negative:
Short put=−max(K−ST,0)
WHY these? A put lets its holder sell at K. If ST<K, they sell high (worth K−ST); if ST≥K it's worthless. The seller has the mirror-image obligation.
Add the two legs (buy KH, sell KL) and subtract the net debit D you paid up front:
Now evaluate the three regions of ST (this is the derivation — do it yourself once):
Region 1: ST≥KH (price high, above both strikes)
Both puts expire worthless.
Payoff=0−0−D=−D(you lose the debit — MAX LOSS)
Region 2: KL≤ST<KH (between strikes)
Long put is in the money, short put still worthless.
Payoff=(KH−ST)−0−D=(KH−D)−ST
A downward-sloping line: profit grows as ST falls.
Region 3: ST<KL (price below both strikes)
Both puts in the money.
Payoff=(KH−ST)−(KL−ST)−D=(KH−KL)−D(MAX PROFIT, flat)
The −ST terms cancel — that's why profit is capped below KL.
What two legs make a bear put spread (same expiry)?
Buy a higher-strike put KH, sell a lower-strike put KL (KL<KH).
Is a bear put spread a debit or credit trade?
A debit — you pay net D=PH−PL>0.
Formula for max loss of a bear put spread?
D (the net debit), occurring when ST≥KH.
Formula for max profit?
(KH−KL)−D, occurring when ST≤KL.
Breakeven price?
STBE=KH−D (higher strike minus debit).
Why is profit capped below the lower strike?
Below KL both puts are ITM; the −ST terms cancel, leaving constant (KH−KL)−D.
Max profit + max loss equals what?
The strike width KH−KL.
Buy 100-put @6, sell 90-put @2: debit, max loss, max profit, breakeven?
D=4; loss=4; profit=6; BE=96.
When should you prefer this over an outright long put?
When moderately (not violently) bearish and you want lower cost + defined risk, accepting capped profit.
Recall Feynman: explain to a 12-year-old
Imagine you think a toy's price will drop a bit. You buy a coupon that pays you more the cheaper the toy gets (that's the higher put). But that coupon is pricey, so you sell a second, weaker coupon to someone else to get some cash back (the lower put). Now the trade costs you less. The catch: if the toy becomes super cheap, the coupon you sold makes the other person happy and eats your extra winnings. So you win a nice, but limited, amount — and you can never lose more than the small cost you paid.
Bear put spread ka matlab hai — aap maante ho ki stock thoda gireGa, crash nahi hoga, bas mild fall. Is bet ke liye aap ek higher strike ka put khareedte ho (jo girne par paisa banata hai) aur cost kam karne ke liye ek lower strike ka put bech dete ho. Kyunki higher-strike put mehenga hota hai, net mein aapko paisa dena padta hai — isko debit kehte hain. Yahi debit aapka maximum loss hai, isse zyada aap kabhi nahi haaroge.
Ab profit kaise banta hai? Jab stock KH (higher strike) se neeche girta hai, tab aapka long put paisa banane lagta hai. Lekin jab stock KL (lower strike) se bhi neeche chala jaaye, to aapne jo put becha tha wo bhi active ho jaata hai aur aapke extra profit ko cancel kar deta hai. Isliye profit cap ho jaata hai — max profit = (strike width) minus (debit). Example: 100-put @6 kharida, 90-put @2 becha, to debit = 4, max loss = 4, max profit = 6, aur breakeven = 96.
Yaad rakhne ka simple formula: "Buy High, Sell Low, Debit do, price Below aane do." Reward-to-risk yahan 6:4 = 1.5:1 tha. Iska fayda ye hai ki naked put se ye sasta padta hai aur risk fixed rehta hai. Nuksan ye ki agar bada crash aa gaya to extra profit nahi milta. Isliye jab aapko lagta hai stock mild-to-moderate gireGa (thoda niche KL tak), tab ye strategy best fit hai.
