Behavioral Finance and Limited Arbitrage

Standard financial theory assumes a rational investor. Behavioral finance documents systematic deviations of real decisions from rationality and explains why irrationality persists—because arbitrage is limited. Kahneman and Tversky (Nobel Prize in Economics, 2002) laid the psychological foundation; Thaler (2017) applied it to finance.

Anomalies and the Efficient Market Hypothesis

EMH (Fama, 1970): Weak form: prices reflect all historical information. Semi-strong: all public data. Strong: all information, including insider.

Weak form test: Momentum (12-month) violates the weak EMH. Post-earnings announcement drift (PEAD): prices continue to move in the direction of the surprise 30–90 days after the quarterly report—violates the semi-strong EMH.

Excess volatility (Shiller, 1981): Var(P) ≫ Var(PV(D)) — stock prices are much more volatile than the present value of dividends. With rational expectations: σ_P ≤ σ_{PV(D)}. Data: violated by a factor of 5–10. “The most important econometric evidence in the history of finance” (Cochrane).

Prospect Theory (Kahneman-Tversky, 1979)

Value function: V(x) = xᵅ (x ≥ 0), −λ|x|^β (x < 0). Estimates: α = β ≈ 0.88, λ ≈ 2.25 — loss aversion coefficient.

Decoding: V(−1000) = −λ·1000^β ≈ −2.25·1000^{0.88} ≈ −2.25·398 ≈ −895. V(+1000) ≈ +398. A loss of 1000 “feels” 2.25 times stronger than a gain of 1000. Diminishing returns for both gains (α<1) and losses (β<1).

Probability weighting: π(p) ≠ p. Small probabilities are overestimated: π(0.01) ≈ 0.05. Large probabilities are underestimated: π(0.99) ≈ 0.94. Explains: simultaneous buying of lotteries (risk-seeking) and insurance (tail avoidance).

Disposition effect (Odean, 1998): Investors sell “winners” (profitable positions) too early and hold “losers” too long. Data on hundreds of thousands of brokers’ client accounts. Probability of selling a “winner” is 1.7 times higher than a “loser”—violates rationality. Explanation via the value function: above the reference point (purchase price)—risk-averse (sell profit), below—risk-seeking (hold loss).

Limited Arbitrage (Shleifer & Vishny, 1997)

Basic logic: Irrational prices → rational actors open arbitrage positions → prices are corrected. Why doesn’t this happen in reality?

Agency problem: Professional arbitrageurs (hedge funds) manage other people’s money. If a short is loss-making in the short term (price went up further) → clients withdraw capital → forced closure of loss-making position. “The market can stay irrational longer than you can stay solvent” (Keynes).

Fundamental risk: There is no “true” asset price to use as a benchmark—only an uncertain future. Short positions = unlimited potential loss.

Noise trader risk (De Long et al., 1990): Irrationality can intensify until the rational arbitrageur is forced out. LTCM (1998): correct positions, wrong timing—forced liquidation with $4.6 billion loss. Quantitative example: if a short is opened at the “wrong” price P₀, and before correction the price goes to P₀ + 2σ—the loss by that moment is already critical.

Behavioral Explanation of Anomalies

Momentum: Market participants insufficiently respond to good news (under-reaction, anchoring) → price slowly approaches “fair” level. Long-term rebalancing → correction in 3–5 years.

Value premium: Investors extrapolate past results (representativeness heuristic): “growth” stocks seem like “winners” → overvalued. “Value” stocks with poor history—undervalued → higher future returns.

Overconfidence: Investors trade too actively (Barber & Odean, 2000): active traders (40% of portfolio per year) earn 6.5% less than passive investors due to transaction costs + overconfidence.

Numerical Example

A stock is trading at 120, “fundamental” price (DCF): 100 rubles. Signal of expected correction in 18 months. Short: cost 5%/year = 7.5% for 1.5 years. Strategy: sell short at 120, close at 100 after 18 months. Expected return: (120−100)/120 − 7.5% = 16.7% − 7.5% = 9.2%. But risk: price may rise to 150 by 12 months → loss already (150−120)/120 = 25% → margin call → forced closure. Rational actor does not enter the position.

Assignment: (1) Implement the De Long et al. model: a market with rational actors (S) and noise traders (N). Rational actors trade against the “irrational component,” but are exposed to the risk of even greater noise. Simulate: at what N/S ratio do rational actors “survive” (do not lose capital before correction)? (2) Data: download 10-year S&P500 stock prices. Assess the disposition effect: for 100 random “trades”, in what % of cases are “winners” sold faster than “losers”? (3) Test the momentum strategy (12-1 months): buy the top-10% past winners, sell short the bottom-10%. What is the SR?