4.7.8
Intuition Ek-sentence ideaHedging ka matlab hai apne portfolio ke liye insurance khareedna : tum abhi ek chhoti, certain cost accept karte ho taaki baad mein koi bada, uncertain loss cap ho sake. Tum hedge se paisa banana nahi chahte — tum us bure din survive karna chahte ho.
Hedge ek aisi position hoti hai jo deliberately existing position ke risk ko offset (kam) karne ke liye li jaati hai. Agar main position loss mein jaaye, toh hedge gain karti hai, isliye combined outcome kam swing karta hai.
Key word hai offset . Hedge koi alag bet nahi hai — yeh us cheez ke saath negatively correlated hoti hai jo tumhare paas already hai.
Main position (long stock): jeetegi agar price ↑, haaregi agar price ↓.Hedge (e.g. put option): jeetegi agar price ↓.Combined: down-side soft ho jaata hai.
Intuition "Insurance" sahi mental model kyun haiGhar ki insurance: tum har saal ek chhota premium bharate ho. Zyaadatar saalon mein tum ise "waste" karte ho. Lekin jis saal ghar jal jaaye, payout tumhe bachata hai. Hedge bilkul waisi hi hoti hai — premium protection ki cost hai, aur tum umeed karte ho ki tumhe kabhi payout ki zaroorat na pade.
Intuition Barbadi ka ganitLosses, barabar ke gains se zyaada takleef dete hain. Ek − 50% + 100% recovery = 1 − L 1 − 1 L = 0.5 = 0.5 1 − 1 = 1 = 100% downside cap karna payment ke kabil hai .
Toh hum hedge karte hain:
Gains protect karne ke liye jo tum wapas nahi dena chahte.Game mein bane rehne ke liye — account khatam karne wala drawdown avoid karna.Neend aane ke liye — emotional, panic-driven galtiyon ko kam karna.
Trade-off yeh hai: har hedge expected return thoda kam kar deti hai. Protection kabhi free nahi hoti.
Tumhare paas stock hai. Tum ek put option khareedते ho jo tumhe ek fixed strike K sell karne ka right deta hai.
Worked example Protective put, worked exampleTumhare paas 100 shares hain jo S_0 = \ 100m e ink ha r i d i t hi . T u m s t r ik e w a l i p u t
Agar price crash karke S_T = \ 70$ ho jaaye:
Stock P/L = 70 − 100 = − 30 Kyun? Stock par 30 ka loss hua.
Put payoff = max ( 95 − 70 , 0 ) = 25 Kyun? Tum ab bhi 95 par sell kar sakte ho.
Total = − 30 + 25 − 3 = − 8 − 8 = K − S 0 − P = 95 − 100 − 3 = − 8 30 nahi , s i r f
Agar price badh kar S_T = \ 120$ ho jaaye:
Stock P/L = + 20 = 20 − 3 = + 17 Kyun? Upside milta hai, minus insurance cost.
Tumhare paas stock hai aur tum strike K call sell karte ho, premium C
Worked example Covered callS 0 = 100 K = 110 C = 4
S T = 105 + 5 = 5 + 4 = + 9 S T = 130 + 30 max ( 130 − 110 , 0 ) = 20 = 30 − 20 + 4 = + 14 S T = 96 − 4 = − 4 + 4 = 0 Kyun? Premium ne chhoti drop ko exactly offset kar diya.
Diversify: aisi assets rakho jo saath move na karein (low correlation) taaki ek crash sab kuch na dooba de.Short / inverse ETF / index futures: market (β
Intuition Koi free lunch nahi hotaEk perfect hedge sari risk hata deti hai — lekin sara expected return bhi jo risk-free rate se upar hota hai. Art hai partial hedge mein: sirf itna premium pay karo jo sach mein damaging outcomes cap kare, jabki zyaadatar upside bana rahe.
Woh 20% jo 80% benefit deta hai:
Protective put apni sabse badi position par, known risk events se pehle (earnings, elections).Position sizing taaki koi single loss fatal na ho (yeh apne aap ke against ek hedge hai).Beta-hedging index ko jab tum stocks par bullish ho lekin pure market se dare ho.
Common mistake "Hedging ka matlab hai market gire toh main paisa banaunga."Kyun sahi lagta hai: hedge actually gain karti hai jab market girta hai, toh yeh profit machine lagti hai.
Fix: hedge sirf tumhara existing loss offset karti hai. Net mein, tum aksar tab thoda bura hi karate ho jab markets uthte hain (tumne premium pay kiya tha). Hedge expected return ko lower variance ke liye trade karta hai, free profit nahi.
Common mistake "Main crash shuru hone ke baad hedge kar lunga."Kyun sahi lagta hai: tum calm times mein premium bachana chahte ho.
Fix: jab fear spike karta hai, option premiums (volatility) explode ho jaati hai — insurance exactly tab sabse expensive hoti hai jab tumhe zaroorat hoti hai. Protection tab kharido jab sasta ho (calm ho), aag ke dauran nahi.
Common mistake "Over-hedging sabse safe hai."Kyun sahi lagta hai: zyaada protection = zyaada safety, toh max kar lo.
Fix: fully hedged position ~risk-free rate kamaati hai lekin premiums pay karti hai, toh yeh dheere dheere paisa khho sakti hai. Excess hedging guarantee karta hai ek chhota certain loss, ek bade uncertain loss se bachne ke liye jo shayad kabhi aaye hi nahi. Hedge size ko real exposure se match karo.
Ek line mein hedge kya hai? Ek existing position ke risk ko offset karne ke liye li gayi position; tumhare portfolio ke liye insurance.
Protective put kya hoti hai? Stock hold karna aur put option khareedna, jo tumhare maximum loss par ek hard floor deta hai.
Protective put ka max loss derive karo (S0, K, P). S T ≤ K Π = ( S T − S 0 ) + ( K − S T ) − P = K − S 0 − P S T K − S 0 − P
50% 100% Recovery = 1/ ( 1 − L ) − 1 = 1/0.5 − 1 = 1 = 100%
Covered call kya cap karta hai, aur woh kya deta hai? Upside ko strike K
Portfolio ko beta-hedge karne ke liye futures ki sankhya ka formula? N = β ⋅ V P / V F
Hedge kabhi free kyun nahi hoti? Variance kam karne se expected return ki cost lagti hai (premium pay hota hai); sari risk hatane par sirf risk-free return bachta hai.
Portfolio insurance sabse expensive kab hoti hai? Panic/high volatility ke dauran — isliye protection calm markets mein kharido.
Hedging ka core trade-off kya hai? Lower variance / capped downside, reduced expected return ke badle mein.
Recall Feynman: 12-saal ke bacche ko samjhaoSocho tumhara apna cycle hai aur tumhe darr hai ki kahin chori na ho jaaye. Tum apne ek dost ko thodi si raqam dete ho jo promise karta hai: "Agar teri cycle chori ho gayi, toh main tujhe nayi khareedne ke liye paisa dunga." Zyaadatar din kuch nahi hota aur woh paisa "gone" ho jaata hai. Lekin jis din cycle gaayab ho, tum bach jaate ho. Stocks mein lagaye paise ke liye hedging bilkul waisi hi hai — tum thoda abhi dete ho taaki bura din tumhe tabah na kar sake. Pakda: agar kuch bura nahi hota, tum safety ke liye thoda poore hote ho. Yahi hai darr se bachne ki keemat.
P.A.I.D. — tumhe PAID protection milti hai:
P remium cost hai, A ccept karo chhota certain loss, I nsurance crash offset karti hai, D ownside ko floor milta hai.
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
Protect gains and survive
Max loss = K minus S0 minus P
