Learn loss aversion and disposition effect — Hinglish notes

6.6.8 · Stock-Market › Factor & Behavioral Finance

YEH TOPIC EXIST KYU KARTA HAI?

Classical finance assume karta hai ki log rational hain aur sirf final wealth levels ki parwah karte hain. Lekin real humans aisa nahi karte. Hum outcomes ko gains aur losses ke roop mein ek reference point ke relative evaluate karte hain (usually purchase price), aur hum ek matching gain ke pleasure se kahin zyada sharply loss ka dard feel karte hain. Yeh asymmetry, jo Kahneman & Tversky (Prospect Theory, 1979) ne discover ki, lakhon trading decisions ko quietly distort karti hai.

VALUE FUNCTION KAISE KAAM KARTI HAI? (Scratch se Derivation)

Hum chahte hain ki "koi outcome kitna achha/bura lagta hai" ke liye ek mathematical shape banayein, jise value function $v (x)$ kehte hain, jahan $x$ gain (positive) ya loss (negative) hai jo reference point se measure kiya gaya hai, na ki absolute wealth se.

Step 1 — Reference dependence. Kyun? Kyunki aap us cheez ke relative zyada/kam ameer feel karte hain jo aapne pay kiya, zero ke relative nahi. Isliye define karo $x = W - W_{r e f}$ .

Step 2 — Diminishing sensitivity. Kyun? ₹100 aur ₹200 ka fark ₹1100 aur ₹1200 ke fark se bada lagta hai. Isliye $v$ gains ke liye concave aur losses ke liye convex honi chahiye (axis ki taraf curve karti hui). Ek power law ise capture karta hai: $v (x) = x^{α}, x \geq 0, 0 < α < 1$

Step 3 — Loss aversion. Kyun? ₹100 ka loss ₹100 ke gain se zyada sting karta hai. Isliye loss branch ko ek factor $λ > 1$ se scale up karna hoga aur negative banana hoga: $v (x) = - λ (- x)^{β}, x < 0, λ > 1$

Sab mila kar:

Loss aversion ka coefficient size $x$ ke ek symmetric bet ke dard aur khushi ko compare karke define kiya jata hai: $λ = \frac{- v ( - x )}{v ( x )} = \frac{λ ( - ( - x ) ) ^{β}}{x ^{α}}$ Symmetric case $α = β$ ke liye yeh exactly constant $λ$ hai — dukh aur khushi ka ratio.

Figure — Learn loss aversion and disposition effect

LOSS AVERSION → DISPOSITION EFFECT KYU HOTA HAI?

Shape dekho. Loss region mein curve convex hai (risk-seeking): loss ke baad aap steep-then-flattening part par hote hain jahan aur zyada lose karne ka marginal dard chhota hota hai, isliye aap gamble karna prefer karte hain ("hold karo aur umeed karo ki recover hoga") bajaye dard lock in karne ke. Gain region mein curve concave hai (risk-averse): aap sure gain secure karne ki jaldi karte hain bajaye use risk mein daalne ke. Result:

Winner (gains mein, concave, risk-averse): abhi sell karo → gain bahut jaldi realize kiya.
Loser (losses mein, convex, risk-seeking): hold karo → loss defer kiya.

Common Mistakes (Steel-manned)

Forecast-then-Verify

Feynman

Recall 12-saal ke bacche ko explain karo

Socho tumhe road par ₹100 mila — tum khush ho. Ab socho tumhari pocket se ₹100 kho gaye — tum itne khush the usse do-gune se zyada dukhi ho. Bas yahi hai! Ab stocks ke saath: agar stock ne tum se paise kamaaye, tum jaldi bech dete ho taaki koi woh khushi ka feeling na le jaaye. Agar stock ne tum se paise khoye, tum bechne se mana kar dete ho kyunki bechne se dukh real ho jaata, isliye tum umeed karte rehte ho ki wapas aayega. Toh log acche wale bech dete hain aur bure wale rakh lete hain — usually smart ka ulta. Isko beat karne ka trick: pretend karo tumhare paas koi stocks nahi hain, sirf cash hai. Poochho "kya main aaj YEH stock kharidta?" Agar nahi, toh becho.

Flashcards

Loss aversion kya hai?

Ek loss ki disutility equal-sized gain ki utility se zyada hoti hai; losses "loom larger" hote hain (λ≈2.25×).

Disposition effect kya hai?

Winners ko bahut jaldi bechne aur losers ko bahut zyada der tak hold karne ki tendency.

Gains par kaun si value function branch apply hoti hai, aur uska risk attitude kya hai?

Concave branch

v (x) = x^{α}

0 < α < 1

→ risk-averse.

Losses par kaun si value function branch apply hoti hai, aur uska risk attitude kya hai?

Convex branch

v (x) = - λ (- x)^{β}

→ risk-seeking.

Log losers kyun hold karte hain?

Convex loss region mein woh risk-seeking ho jaate hain, recovery par gamble karte hain bajaye kink par dardnaak loss lock in karne ke.

Typical loss-aversion coefficient λ kya hai?

Lagbhag 2.25.

Prospect theory mein reference point usually kya hota hai?

Purchase price (ek sunk cost), ya recent high/expectation.

Kya ₹200 loss ₹100 loss se do-guna dardnaak hota hai?

Nahi — do-gune se kam, kyunki β<1 diminishing sensitivity deta hai:

20 0^{0.88} < 2 \cdot 10 0^{0.88}

Disposition effect ka ek practical fix

Poochho "kya main aaj is stock ko uski current price par kharidta?"; purchase price ignore karo.

Prospect theory / disposition effect ko kisne formalize kiya?

Kahneman & Tversky (1979) / Shefrin & Statman (1985).

Connections

Prospect Theory
Reference Points and Anchoring
Mental Accounting
Sunk Cost Fallacy
Momentum Anomaly (why holding losers hurts returns)
Tax-Loss Harvesting
Risk Aversion vs Risk Seeking
Behavioral Portfolio Theory