Learn iron condor — Stock-Market notes

WHAT is an Iron Condor?

WHY the four legs?

The two short options ( $K_2, K_3$ ) collect premium — this is your income.
The two long options ( $K_1, K_4$ ) cap your loss on each side — this is what makes it defined risk (unlike a naked strangle, which has unlimited loss).

HOW to build the payoff — from first principles

We never memorize the profit formula. We derive it by adding the payoffs of the four legs at expiry. Let $S$ = stock price at expiry, $C$ = net credit received per share.

Payoff of a single long option at expiry:

Long call struck $K$ : $\max(S-K,\,0)$
Long put struck $K$ : $\max(K-S,\,0)$

A short option is just the negative of a long one.

Why add $C$ ? Because you received $C$ up front when you opened the trade; it is real cash in the account.

Now evaluate $V(S)$ region by region — Why this step? Because each $\max$ turns "on" only in its own region, so the piecewise structure appears naturally.

Region A — stock stays in the middle ( $K_2 \le S \le K_3$ ): All four $\max$ terms are 0 → $V=0$ → Profit $= C$ . This is the max profit zone, and it's flat. Why? Every option expires worthless; you keep the whole credit.

Region B — big drop ( $S \le K_1$ ): Short put pays $-(K_2-S)$ , long put pays $+(K_1-S)$ . Sum $= K_1-K_2$ (a constant negative). Profit $= (K_1-K_2)+C$ . Why constant? Below $K_1$ both puts move dollar-for-dollar and cancel their changes, leaving a fixed loss = spread width minus credit.

Region C — big rise ( $S \ge K_4$ ): By symmetry, Profit $= (K_3-K_4)+C = -(K_4-K_3)+C$ .

WHY only one side loses: the stock can't finish both below $K_1$ and above $K_4$ at the same expiry, so you're never assigned on both spreads.

Worked Examples

Worked example Example 1 — Symmetric condor (the standard case)

Stock at $100. You trade: Buy 90 put / Sell 95 put / Sell 105 call / Buy 110 call. Net credit $C = \$ 1.50 $per share (\$ 150 per contract).

Step 1 — wing widths: $w_p = 95-90 = 5$ , $w_c = 110-105 = 5$ . Why? Determines max loss.
Step 2 — max profit $= C = \$ 1.50 $(\$ 150). Why? Stock finishing in $95–$105 kills all options.
Step 3 — max loss $= w - C = 5 - 1.50 = \$ 3.50 $(\$ 350). Why? Widest a breached spread can go is $5; you keep $1.50.
Step 4 — break-evens $= 95 - 1.50 = \$ 93.50 $and$ 105 + 1.50 = $106.50$. Why? Below/above these your spread loss exceeds the credit.
Profit zone: any close between $93.50 and $106.50. Reward:risk $= 150:350 \approx 1:2.3$ .

Common Mistakes

Forecast-then-Verify

Recall Forecast before reading the answer

Stock at $50. Sell 45 put / Buy 42 put / Sell 55 call / Buy 58 call. Credit $1.00. Predict: max profit? max loss? break-evens? Then check.

Answer: wings $= 3$ each. Max profit $=\$ 1 $. Max loss$ = 3-1 = $2 $. Break-evens$ = 45-1=44 $and$ 55+1=56 $. Profit if it closes between \$ 44 and $56.

Flashcards

What four legs make an iron condor?

Sell OTM put, buy further-OTM put, sell OTM call, buy further-OTM call — all same expiry.

Is an iron condor a debit or credit trade?

Credit — you receive net premium up front.

What market view does an iron condor express?

Neutral / range-bound; you profit if the stock stays between the short strikes.

Max profit of an iron condor?

The net credit received,

C

Max loss of an iron condor (equal wings width

w

w - C

Why isn't max loss the sum of both wings?

At one expiry only one side can be breached; you can't be past both short strikes at once.

Break-even formulas?

K_2 - C

(lower) and

K_3 + C

(upper).

Does rising implied volatility help or hurt an iron condor?

Hurts — it's a short-volatility position.

Which Greek is your friend in an iron condor?

Theta (time decay) works in your favour.

For unequal wings, which width sets the max loss?

The wider wing,

\max(w_p, w_c) - C

In Example 1 (90/95/105/110, credit 1.50) what is max loss?

5 - 1.50 = \

3.50$ per share.

Recall Feynman: explain it to a 12-year-old

Imagine you bet your friend the temperature tomorrow will be "somewhere normal" — not freezing, not boiling. You take a little money from two other friends: one who bets it'll be super cold, one who bets super hot. If tomorrow is just a normal day, both of them lose and you keep their money. But to be safe, you make small side-bets so that even if it IS super cold or super hot, you only lose a little, not everything. The iron condor is exactly that: you win when the stock is boring, and your losses are capped on both extreme days.

Connections

Short Strangle — same neutral view but undefined risk; the condor adds long wings to cap it.
Bull Put Spread — the lower half of the condor.
Bear Call Spread — the upper half of the condor.
Iron Butterfly — same idea but short strikes at the SAME price (higher credit, narrower zone).
Theta Decay — the engine that earns you money over time.
Implied Volatility — the risk you're short.
Options Break-even Analysis — how the credit shifts break-evens outward.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Iron condor ka core idea simple hai: aap bet kar rahe ho ki stock boring rahega, yaani ek range ke andar hi ghoomta rahega. Iske liye aap ek OTM put bechte ho aur uske neeche ek aur put khareedte ho (protection), aur ek OTM call bechte ho aur uske upar ek aur call khareedte ho. Dono short options se aapko premium (credit) milta hai — yahi aapki kamai hai. Long wings sirf isliye lete ho taaki agar stock zyada gir jaaye ya zyada chadh jaaye, to aapka loss capped rahe, unlimited na ho.

Formula ratne ki zaroorat nahi — bas socho. Agar stock beech mein (short strikes ke beech) close hua, sabhi options bekaar ho gaye, aur aapne poora credit $C$ rakh liya — max profit = C. Agar ek taraf zyada move ho gaya, to sirf ek spread breach hota hai, aur us wing ki width minus credit aapka max loss hota hai. Yaad rakho: dono side ek saath loss nahi de sakti, kyunki expiry par stock ek hi jagah hoga.

Break-even nikaalna easy hai: neeche wala $K_2 - C$ , upar wala $K_3 + C$ . Matlab credit aapke safe zone ko thoda widen kar deta hai. Yeh trade short-volatility hai — aap chahte ho ki market shaant rahe. Theta (time decay) aapka dost hai, aur badhti hui implied volatility aapka dushman. Beginners aksar galti karte hain ki "zyada credit hamesha achha", lekin zyada credit ke liye strikes price ke paas laane padte hain, jisse profit zone chhota ho jaata hai aur loss ka chance badh jaata hai. Balance banana hi asli skill hai.

Test yourself — Options Strategies

Connections