Learn hedging basics for protection — Stock-Market notes

WHAT is hedging?

The key word is offset. A hedge is not a separate bet — it is negatively correlated with what you already own.

Main position (long stock): wins if price ↑, loses if price ↓.
Hedge (e.g. put option): wins if price ↓.
Combined: the down-side is softened.

WHY hedge at all?

So we hedge to:

Protect gains you don't want to give back.
Stay in the game — avoid the account-ending drawdown.
Sleep — reduce emotional, panic-driven mistakes.

The trade-off: every hedge reduces expected return a little. Protection is never free.

HOW to hedge — the core methods

1. Protective Put (the classic)

You own the stock. You buy a put option giving you the right to sell at a fixed strike $K$ .

Formula Payoff of stock + protective put

Let $S_T$ = stock price at expiry, $S_0$ = price paid, $P$ = premium paid, $K$ = strike. Stock alone at expiry: value $= S_T$ . Put payoff at expiry: $\max(K - S_T,\ 0)$ (worth something only if price falls below $K$ ).

Combined P/L relative to what you paid: $\Pi = \underbrace{(S_T - S_0)}_{\text{stock P/L}} + \underbrace{\max(K - S_T,0)}_{\text{put payoff}} - \underbrace{P}_{\text{premium}}$

Deriving the floor: if $S_T \le K$ , then $\max(K-S_T,0) = K - S_T$ , so $\Pi = (S_T - S_0) + (K - S_T) - P = K - S_0 - P$ The $S_T$ cancels! Below $K$ your loss is frozen at $K - S_0 - P$ . That's your maximum loss — a hard floor. Above $K$ the put expires worthless and you just paid $P$ , so you ride the upside minus the premium.

2. Covered Call (a partial hedge / income)

You own the stock and sell a call at strike $K$ , collecting premium $C$ .

3. Diversification & Inverse positions

Diversify: hold assets that don't move together (low correlation) so one crash doesn't sink all.
Short / inverse ETF / index futures: sell futures against a portfolio to neutralize market ( $\beta$ ) risk.

Figure — Learn hedging basics for protection

The cost of protection (80/20 core)

The 20% that gives 80% of the benefit:

Protective put on your biggest position before known risk events (earnings, elections).
Position sizing so no single loss is fatal (this is a hedge against yourself).
Beta-hedging the index when you're bullish on stocks but scared of the whole market.

Common mistakes

Flashcards

What is a hedge in one line?

A position taken to offset the risk of an existing position; insurance for your portfolio.

What is a protective put?

Owning a stock and buying a put option, giving a hard floor on your maximum loss.

Derive the max loss of a protective put (S0, K, P).

For

S_T \le K

\Pi = (S_T-S_0)+(K-S_T)-P = K - S_0 - P

; the

S_T

cancels so loss is frozen at

K-S_0-P

Why does a

50\%

loss need a

100\%

gain to recover?

Recovery

=1/(1-L)-1 = 1/0.5-1 = 1 = 100\%

; losses compound harder than gains.

What does a covered call cap, and what does it give?

It caps the upside at strike

K

but collects premium now, giving small downside cushion.

Formula for number of futures to beta-hedge a portfolio?

N = \beta \cdot V_P / V_F

Why is a hedge never free?

Reducing variance costs expected return (premium paid); removing all risk leaves only the risk-free return.

When is portfolio insurance most expensive?

During panic/high volatility — buy protection in calm markets instead.

What is the core trade-off of hedging?

Lower variance / capped downside in exchange for reduced expected return.

Recall Feynman: explain to a 12-year-old

Imagine you love your bike and worry it might get stolen. You pay a small amount to a friend who promises: "If your bike is stolen, I'll give you money to buy a new one." Most days nothing happens and that money is "gone." But the day your bike vanishes, you're saved. Hedging is the same for money you invested in stocks — you pay a little now so a bad day can't wipe you out. The catch: if nothing bad happens, you're a tiny bit poorer for the safety. That's the price of not being scared.

Connections

Options Basics — Calls and Puts
Position Sizing and the 2% Rule
Beta and Systematic Risk
Diversification and Correlation
Volatility and Option Pricing
Risk-Reward and Drawdown Recovery

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Hedging ka matlab hai apne portfolio ke liye insurance kharidna. Jaise aap apni bike ya ghar ka insurance lete ho — thoda premium bharo, aur agar kuch bura ho jaye to bada loss cover ho jaata hai. Stock market mein bhi same cheez: aap ek chhota fixed cost accept karte ho, taaki koi bada aur uncertain loss aapko wipe out na kar de. Yaad rakho — hedge se aap paisa banane nahi jaate, aap "survive" karne jaate ho bure din mein.

Sabse common tool hai protective put. Aapke paas stock hai, aur aap ek put option kharidte ho jo aapko fixed strike price $K$ par bechne ka right deta hai. Agar market crash ho jaye, put profit deta hai jo stock ke loss ko offset karta hai. Maths ismein simple hai: agar price $K$ ke neeche gir jaye, aapka maximum loss freeze ho jaata hai at $K - S_0 - P$ . Matlab neeche kitna bhi gire, aapka nuksaan fixed hai — yahi hai "floor".

Ek important baat: hedging kabhi free nahi hoti. Har protection thoda expected return kam karti hai (premium jo aap bharte ho). Isliye smart traders partial hedge karte hain — sirf utna protection lo jitna zaroori hai badi tabaahi rokne ke liye, upside ko bahut zyada mat maaro. Aur ek trap: crash shuru hone ke baad insurance mat kharido — us waqt volatility high hoti hai aur premium mehenga ho jaata hai. Shaant market mein sasta hedge lena samajhdari hai.

80/20 rule: apni sabse badi position par put lo important events (earnings, election) se pehle, position size chhota rakho taaki ek trade tumhe barbaad na kare, aur agar poore market se darte ho to index futures se beta-hedge kar lo ( $N = \beta \cdot V_P / V_F$ ). Bas itna hi 80% protection de dega.

Test yourself — Risk & Money Management

Connections