Learn loss aversion and disposition effect — Stock-Market notes

WHY does this topic exist?

Classical finance assumes people are rational and care only about final wealth levels. But real humans don't. We evaluate outcomes as gains and losses relative to a reference point (usually the purchase price), and we feel the pain of a loss far more sharply than the pleasure of a matching gain. This asymmetry, discovered by Kahneman & Tversky (Prospect Theory, 1979), quietly distorts millions of trading decisions.

HOW does the value function work? (Derivation from scratch)

We want a mathematical shape for "how good/bad an outcome feels", called a value function $v(x)$ , where $x$ is the gain (positive) or loss (negative) measured from the reference point, not absolute wealth.

Step 1 — Reference dependence. Why? Because you feel richer/poorer relative to what you paid, not relative to zero. So define $x = W - W_{ref}$ .

Step 2 — Diminishing sensitivity. Why? The difference between ₹100 and ₹200 feels bigger than between ₹1100 and ₹1200. So $v$ should be concave for gains and convex for losses (curving toward the axis). A power law captures this: $v(x) = x^{\alpha}, \quad x \ge 0, \qquad 0 < \alpha < 1$

Step 3 — Loss aversion. Why? A ₹100 loss stings more than a ₹100 gain pleases. So the loss branch must be scaled up by a factor $\lambda > 1$ and made negative: $v(x) = -\lambda\,(-x)^{\beta}, \quad x < 0, \qquad \lambda > 1$

Putting it together:

The coefficient of loss aversion is defined by comparing the pain and pleasure of a symmetric bet of size $x$ : $\lambda = \frac{-v(-x)}{v(x)} = \frac{\lambda (-(-x))^{\beta}}{x^{\alpha}}$ For the symmetric case $\alpha=\beta$ this is exactly the constant $\lambda$ — the ratio of hurt to joy.

Figure — Learn loss aversion and disposition effect

WHY does loss aversion → disposition effect?

Look at the shape. In the loss region the curve is convex (risk-seeking): after a loss you're on the steep-then-flattening part where the marginal pain of losing more is small, so you'd rather gamble ("hold and hope it recovers") than lock in the pain. In the gain region the curve is concave (risk-averse): you rush to secure the sure gain rather than risk it. Result:

Winner (in gains, concave, risk-averse): sell now → realize gain too early.
Loser (in losses, convex, risk-seeking): hold on → defer the loss.

Common mistakes (Steel-manned)

Forecast-then-Verify

Feynman

Recall Explain to a 12-year-old

Imagine you find ₹100 on the road — you're happy. Now imagine you lose ₹100 from your pocket — you're more than twice as sad as you were happy. That's it! Now with stocks: if a stock made you money you quickly sell it so nobody can take that happy feeling away. If a stock lost you money, you refuse to sell because selling would make the sadness real, so you keep hoping it comes back. So people sell the good ones and keep the bad ones — usually the opposite of smart. The trick to beat it: pretend you have no stocks and only cash. Ask "would I buy THIS one today?" If not, sell it.

Flashcards

What is loss aversion?

The disutility of a loss exceeds the utility of an equal-sized gain; losses "loom larger" (λ≈2.25×).

What is the disposition effect?

Tendency to sell winners too early and hold losers too long.

What value function branch applies to gains, and its risk attitude?

Concave branch

v(x)=x^{\alpha}

0<\alpha<1

→ risk-averse.

What value function branch applies to losses, and its risk attitude?

Convex branch

v(x)=-\lambda(-x)^{\beta}

→ risk-seeking.

Why do people hold losers?

In the convex loss region they become risk-seeking, gambling on recovery rather than locking in the painful loss at the kink.

What is the typical loss-aversion coefficient λ?

About 2.25.

Reference point in prospect theory is usually

The purchase price (a sunk cost), or a recent high/expectation.

Is a ₹200 loss twice as painful as a ₹100 loss?

No — less than twice, because β<1 gives diminishing sensitivity:

200^{0.88}<2\cdot100^{0.88}

One practical fix for the disposition effect

Ask "would I buy this stock today at its current price?"; ignore purchase price.

Who formalized prospect theory / the disposition effect?

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

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, idea bahut simple hai: humein loss ka dard, same size ke gain ki khushi se roughly 2.25 guna zyada feel hota hai. Isko bolte hain loss aversion. Kahneman aur Tversky ne isko measure kiya — ₹100 kamane pe jitni khushi, ₹100 gawane pe usse double takleef. Aur yeh dard/khushi hum purchase price ke relative naapte hain, absolute wealth se nahi. Yahi "reference point" hamare dimaag ka anchor ban jaata hai.

Ab iska stock market pe asar: gain wale zone mein curve concave hota hai, matlab hum risk-averse ban jaate — sure profit ko turant lock kar lete hain (winner bech dete jaldi). Loss wale zone mein curve convex hota hai, matlab hum risk-seeking ban jaate — "recover ho jayega yaar" bolke loser ko pakde rehte, kyunki bechne se loss real ho jaata aur wo kink pe wala teekha dard sehna padta. Isi ko bolte hain disposition effect: winners jaldi bechna, losers zyada der pakadna — jo aksar galat hota hai.

Practical mistake yeh hai ki log sochte hain "profit book karna hamesha smart hai" — par same logic loss pe bhi lagana chahiye, aur hum lagate nahi. Yahi inconsistency bias hai. Ek reference point (jaise ₹100 buy price) sirf ek sunk cost hai, future return se koi lena-dena nahi.

Fix simple hai: apne aap se poocho — "agar mere paas sirf cash hota, kya main yeh stock aaj is price pe kharidta?" Agar answer NO, to bech do, chahe profit ho ya loss. Bias ko haraane ka yehi shortcut hai: decision ko purchase price se de-link karo aur forward-looking expected return pe focus karo.

Test yourself — Factor & Behavioral Finance

Connections