Master covered call — Stock-Market notes

WHAT is a covered call?

Long stock: you own it, you profit if price rises.
Short call: you sold someone the right to buy your stock at strike $K$ before expiry. You received premium $c$ .

WHY would anyone do this?

The trade-off in plain words:

You gain: cash now (premium), a lower break-even, income in flat markets.
You lose: the big upside above the strike is capped.

HOW does the payoff work? (Derive from scratch)

Let:

$S_0$ = stock price today (when you buy shares)
$K$ = strike price of the call you sold
$c$ = premium received per share
$S_T$ = stock price at expiry

Step 1 — Profit from the stock leg. You bought at $S_0$ , it's worth $S_T$ : $\text{Stock P/L} = S_T - S_0$ Why this step? Owning stock just tracks price change, nothing fancy.

Step 2 — Profit from the short call leg. You received $c$ . The call buyer exercises only if $S_T > K$ , and then it costs you $(S_T - K)$ to honor it. A short call's payoff: $\text{Call P/L} = c - \max(S_T - K,\ 0)$ Why this step? If $S_T \le K$ the call expires worthless — you keep all of $c$ . If $S_T > K$ you must sell at $K$ something worth $S_T$ , losing the difference.

Step 3 — Add the two legs. $\boxed{\ \Pi(S_T) = (S_T - S_0) + c - \max(S_T - K,\ 0)\ }$

Step 4 — Split into the two regimes.

Below the strike ( $S_T \le K$ ): the $\max$ term is 0: $\Pi = S_T - S_0 + c$ This is a rising line — you still gain if the stock rises, plus the premium.

Above the strike ( $S_T > K$ ): $\max = S_T - K$ : $\Pi = (S_T - S_0) + c - (S_T - K) = K - S_0 + c$ The $S_T$ terms cancel → profit is a flat cap. That's the "capped upside."

Why break-even is $S_0 - c$ : the premium acts like a discount on your purchase price. You only start losing once the stock falls below what you effectively paid.

Worked Examples

Common Mistakes

Recall Feynman: explain to a 12-year-old

Imagine you own a bike. A friend pays you $5 today for a promise: "if I want, next month I can buy your bike for $110." You already think your bike is worth about $100 and won't jump much. So the $5 is nice pocket money! But if the bike suddenly becomes super trendy and worth $130, your friend will buy it for just $110 — you must sell, and you miss the extra value. That $5 was the "rent" for lending out that maybe-future sale. That's a covered call: you own the thing, and you sell someone the choice to buy it later at a fixed price.

Flashcards

What two positions make a covered call?

Long 100 shares + short 1 call (same underlying).

Why is it called "covered"?

Because you own the shares that back your obligation to deliver — no naked/unlimited risk.

Formula for max profit of a covered call?

K - S_0 + c

(reached at or above the strike).

Formula for break-even of a covered call?

S_0 - c

(cost basis reduced by premium).

Formula for max loss of a covered call?

c - S_0

(stock falls to zero, cushioned only by premium).

Above the strike, why does profit go flat?

Because

(S_T - S_0) + c - (S_T-K)

has the

S_T

terms cancel, leaving constant

K-S_0+c

Market outlook where covered calls shine?

Neutral to mildly bullish (sideways or slightly up).

Is a covered call downside protection?

No — it only cushions by the premium; big crashes still hurt a lot.

Why avoid strikes far below your cost basis?

Max profit

K-S_0+c

can lock in a loss.

What do you give up when selling the call?

All upside above the strike price.

Connections

Options Strategies
Naked Call — the uncovered, unlimited-risk cousin
Protective Put — the true downside-protection strategy
Cash-Secured Put — mirror-image income strategy on the put side
Call Option Payoff
Option Premium and Time Decay (Theta)
Covered Call vs Collar

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Covered call ka matlab simple hai: aapke paas already 100 shares hain (long stock), aur aap uske upar ek call option bech dete ho. Bechne ke badle turant premium (cash) milta hai. Isko "covered" isliye kehte hain kyunki jo shares deliver karne ka risk hai, wo aapke paas already maujood hain — naked call ki tarah unlimited risk nahi.

Yeh strategy tab best hai jab market sideways ya thoda upar jaane ka scene ho. Agar stock flat rehta hai, toh poora premium aapki jeb mein — free income jaisa. Lekin catch yeh hai: agar stock rocket ban ke strike ke upar chala gaya, toh aapko shares strike price pe hi bechne padenge, aur upar ka bada profit chhoot jayega. Isliye kehte hain: upside "cap" ho jaata hai.

Teen important numbers yaad rakho: Max profit = $K - S_0 + c$ , Break-even = $S_0 - c$ (premium ne aapki cost thodi sasti kar di), aur Max loss = $c - S_0$ (agar stock zero ho jaye — yaani yeh downside protection nahi hai, sirf chhota cushion hai). Mantra: "Own it, rent it, cap it" — apna stock rakho, upside kiraye pe do, aur profit strike pe cap ho jaayega.

Test yourself — Options Strategies

Connections