Learn protective put

WHAT is a protective put?

WHY does this feel like insurance?

• You pay a small premium $P$ upfront (like an insurance premium).
• If disaster strikes (stock crashes), the put "pays out" and covers your loss below $K$.
• If nothing bad happens (stock rises), the put expires worthless — you just "lost" the premium, exactly like an insurance policy you never claimed.

HOW to build the payoff — derive from scratch

Let:

• $S_0$ = price you paid for the stock (entry price)
• $S_T$ = stock price at expiry
• $K$ = strike price of the put
• $P$ = premium paid for the put

Step 1 — Payoff of the long stock at expiry. You bought at $S_0$, it is now worth $S_T$: $\text{Stock P/L} = S_T - S_0$ Why this step? Profit on a share is simply "what it's worth now minus what you paid."

Step 2 — Payoff of the long put at expiry. A put lets you sell at $K$. You only exercise if $S_T < K$ (selling high when market is low): $\text{Put value at expiry} = \max(K - S_T,\ 0)$ Why this step? If $S_T \ge K$ you'd sell in the open market instead, so the put is worthless. If $S_T < K$ you gain the difference $K - S_T$.

Step 3 — Subtract the premium you paid. $\text{Put P/L} = \max(K - S_T,\ 0) - P$ Why this step? You spent $P$ to buy the put; that's a sunk cost regardless of outcome.

Step 4 — Add both legs. $\boxed{\;\Pi = (S_T - S_0) + \max(K - S_T,\ 0) - P\;}$

Step 5 — Split into the two regimes to see the shape.

Case A: Stock falls below strike ($S_T < K$). Here $\max(K-S_T,0)=K-S_T$: $\Pi = (S_T - S_0) + (K - S_T) - P = K - S_0 - P$ Notice $S_T$ cancels out — the loss is constant no matter how low the stock goes. This is your floor.

Case B: Stock rises above strike ($S_T \ge K$). Here the put is worthless: $\Pi = S_T - S_0 - P$ This rises 1-for-1 with the stock — unlimited upside (minus the premium drag).

Deriving break-even: set $\Pi = 0$ in Case B: $S_T - S_0 - P = 0 \Rightarrow S_T = S_0 + P$. ✔

Worked Examples

Common Mistakes

Active Recall

Flashcards

Connections

• Covered Call — the mirror-image strategy (short option instead of long).
• Long Put — the standalone bearish option that forms the protective leg.
• Put-Call Parity — shows a protective put has the same payoff as a long call plus cash (synthetic call).
• Options Greeks — the put adds negative delta and positive vega, reducing net directional risk.
• Married Put — identical strategy when the put is bought at the same time as the stock.
• Hedging Basics — protective put is the classic hedge for a long equity position.

Concept Map

Hinglish (regional understanding)