Learn collar strategy

HOW the payoff is built — derivation from scratch

Let's build the total payoff at expiry $S_T$ leg by leg. Let $S_0$ = purchase price of stock, $P$ = put premium paid, $C$ = call premium received.

Net premium paid up front: $N = P - C$ (negative if you collect more than you pay).

Leg 1 — Long stock. You bought at $S_0$ , now worth $S_T$ : $\text{Stock P\&L} = S_T - S_0$

Leg 2 — Long put, strike $K_p$ . A put pays $\max(K_p - S_T, 0)$ at expiry: $\text{Put P\&L} = \max(K_p - S_T,\,0) - P$ Why this step? The put only has value when $S_T < K_p$ ; below that it pays out the difference. You already paid $P$ .

Leg 3 — Short call, strike $K_c$ . You sold it, so you keep $C$ but owe $\max(S_T - K_c, 0)$ : $\text{Call P\&L} = C - \max(S_T - K_c,\,0)$ Why this step? If stock ends above $K_c$ , the buyer exercises and you must deliver at $K_c$ , losing $S_T - K_c$ .

Total payoff — add them all: $\boxed{\Pi(S_T) = (S_T - S_0) + \max(K_p - S_T,0) - \max(S_T - K_c,0) - (P - C)}$

Formula

Three regions (since $K_p < K_c$ ):

If $S_T \le K_p$ (crash): put is in the money, $\max(K_p - S_T,0)=K_p-S_T$ , call worthless. $\Pi = (S_T - S_0) + (K_p - S_T) - N = K_p - S_0 - N \quad(\text{constant floor})$
If $K_p < S_T < K_c$ (middle): both options expire worthless. $\Pi = S_T - S_0 - N \quad(\text{moves 1:1 with stock})$
If $S_T \ge K_c$ (rally): call in the money, $\max(S_T-K_c,0)=S_T-K_c$ . $\Pi = (S_T - S_0) - (S_T - K_c) - N = K_c - S_0 - N \quad(\text{constant ceiling})$

Max profit $= K_c - S_0 - N$ • Max loss $= K_p - S_0 - N$ (can be negative = a real loss) Breakeven: in the middle region, $\Pi=0 \Rightarrow S_T = S_0 + N$ .

Worked Examples

Common Mistakes

Recall

Recall Active recall (hide and answer)

What are the three legs of a collar? → long stock, long OTM put, short OTM call.
Formula for max loss? → $K_p - S_0 - N$ .
Formula for max profit? → $K_c - S_0 - N$ .
Where's breakeven? → $S_T = S_0 + N$ .
What makes it "zero-cost"? → call premium ≈ put premium so $N \approx 0$ .

Recall Feynman: explain to a 12-year-old

You have a bike you might sell later. You're scared it'll get scratched and lose value, so you pay a friend a little money for a promise: "If it drops below ₹95, you buy it from me at ₹95." That's the put — a safety net. But you don't want to pay from your pocket, so you make another deal: "If someone offers more than ₹108, I'll sell it to you at ₹108, and you pay me now." That's the call. So you can't lose much (safety net at 95) and can't win huge (you must sell at 108), but you got the safety almost for free. That fenced-in range is a collar.

Connections

Protective Put — the collar is a protective put plus selling a call to fund it.
Covered Call — the collar is a covered call plus buying a put for downside safety.
Options Payoff Diagrams — the flat-slope-flat shape is the visual signature.
Zero-Cost Structures — general idea of funding one option by selling another.
Put-Call Parity — explains why call and put premia relate to the collar's cost.
Risk Reversal — a collar without the underlying stock is just short put + long call (or reverse).

What are the three legs of a collar strategy?

Long 100 shares, long 1 OTM put (floor), short 1 OTM call (ceiling).

In a collar, why do you sell the call?

To collect premium that finances (pays for) the protective put, ideally making it zero-cost.

Collar max profit formula?

K_c - S_0 - N

, where

N = P - C

is net premium paid.

Collar max loss formula?

K_p - S_0 - N

(a floor set by the put strike).

Collar breakeven price at expiry?

S_T = S_0 + N

What does "zero-cost collar" mean and what risk remains?

Call premium ≈ put premium so net premium ≈ 0; you still risk loss from

S_0

down to

K_p

(the deductible).

Above the call strike

K_c

, how does collar P&L behave?

It flattens — profit is capped, because the short call loss cancels further stock gains.

Below the put strike

K_p

, how does collar P&L behave?

It flattens — loss is floored by the long put.

A collar equals a protective put plus what?

A short (covered) call sold to fund the put.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, collar strategy ka idea simple hai: tumhare paas ek stock hai jo tumhe pasand hai, par crash ka dar bhi hai. Toh tum do kaam karte ho — ek protective put kharidte ho (jo neeche gir jaane par tumhe bachata hai, ek floor deta hai), aur ek OTM call bech dete ho (jisse tumhe premium milta hai, par upar ka profit cap ho jata hai). Put ki insurance ka paisa call bech ke nikal aata hai, isiliye ise kai baar zero-cost collar kehte hain.

Formula yaad rakho: net premium $N = P - C$ . Max loss hoti hai $K_p - S_0 - N$ aur max profit hoti hai $K_c - S_0 - N$ . Breakeven simple $S_0 + N$ par hota hai. Matlab tumhara P&L do deewaron ke beech "collar" ho jata hai — neeche put floor, upar call ceiling. Beech mein stock ke saath 1:1 chalta hai.

Sabse badi galti jo log karte hain: sochte hain "stock hai toh unlimited profit hoga." Nahi bhai — short call tumhare upar ka gain kaat deta hai $K_c$ ke upar. Doosri galti: "zero-cost matlab zero risk." Galat — zero sirf premium ka hai, loss abhi bhi $S_0$ se $K_p$ tak ho sakta hai, jaise insurance mein deductible hota hai.

Kab use karo? Jab tum bullish-to-neutral ho, thoda protection chahte ho, aur thoda upside chhodne ko taiyaar ho. Yeh conservative investor ke liye badhiya hai jo already profit mein baitha hai aur usse lock karna chahta hai bina zyada paisa kharch kiye.

WHAT is a Collar?

WHY do traders build it?

HOW the payoff is built — derivation from scratch

Worked Examples

Common Mistakes

Recall

Connections

Concept Map

Hinglish (regional understanding)

Test yourself — Options Strategies

Connections