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L1: Behavioral Finance. Discussions on Barberis and Thaler (2003) – A Survey of Behavioral Finance Discussions on Other Papers. Market Efficiency and Limit to Arbitrage.

L1: Behavioral Finance

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- Discussions on Barberis and Thaler (2003) – A Survey of Behavioral Finance
- Discussions on Other Papers

- In a world where agents are rational and there are no frictions, a security’s price equals its “fundamental value”. Friedman (1953): rational traders will quickly undo any dislocations caused by irrational traders
- Limit to arbitrage:
- Fundamental Risk
- Risk that a surprise is related to a specific company

- Noise Trader risk
- They trade irrationally

- Implementation costs

- Fundamental Risk

- Twin shares
- E.g., Royal Dutch and Shell Transport

- 3Com and Plam Inc.
- A case where there is no fundamental risk and no noise trader risk
- The key is the barrier to short selling arbitrade was limited and mispricing persists

- Overconfidence
- Optimism
- People are overconfident of their judgements
- biased parameters

- Representativeness
- People tend to draw a conclusion after observing few data points

- Conservatism
- Opposite to representativeness

- Belief perseverance
- Once people have an opinion, they stick to it too long
- Reluctant to search for evidence against their belief
- Treat such evience with excessive skepticism

- Once people have an opinion, they stick to it too long
- Anchoring
- Anchoring too much on the initial number

- Availability Biases

- Prospect Theory
- About investor preferences
- Risk aversion to gains (loss aversion); risk loving to losses

- Ambiguity Aversion
- People do not like situations where they are uncertain about the probability distribution of a gamble.
- Prefer certainty

- Equity premium
- using annual data from 1871-1993, Campbell and Cochrane (1999) report that the average log return on the S&P 500 index is 3.9% higher than the average log return on short-term commercial paper.

- Volatility
- Stock returns and price-dividend ratios are highly volable. Annual standard deviation of excess log returns on the S&P is 18%, while that of log price-dividend ratio is 0.27

- Predictability
- Stock returns are forecastable. Using monthly, real, equal-weighted NYSE returns from 1941-1986, FF (1988) show that dividend-price ratio is able to explain 27% of the variation of cumulative stock return over the subsequent four years.

- Size premium
- Long-term reversals
- The predictive power of scaled-price ratios
- Momentum
- Earnings announcement effect
- Dividend initiations and omissions
- Stock repurchases
- IPOs and SEOs

- Representativeness
- Overconfident
- others

- Insufficient diversifications (home bias)
- Ambiguity aversion

- Naïve diversification
- Excessive trading
- Disposition effect
- Buying decision is attention driven

Main Idea: present a unified framework for underreaction, momentum trading and overreaction in asset market. It assumes there are two types of investors: (1) newswatchers who observe some private invormation, but don’t extract information from prices, and (2) momentum traders. If information diffuses gradually across the population, prices underract in the short run, thus momentum traders can profit from trend chasing. Simple implementation of momentum trading leads to over-reaction at long horizons.

- Stocks with most information asymmetry enjoy the biggest momentum effect
- Small stocks
- Stocks having few analysts to follow

- Stocks most momentum-prone are most reversal-prone.

Mental accounting, loss aversion and individual stock returns

by Barberis, N., and M. Huang(2001, JoF) -- Fu

Improving the way we model investor preferences:

Loss aversion – People are more sensitive to losses than to gain

Dynamic loss aversion: the degree of loss aversion depends on Ri,t-1

Mental accounting: over which people think about and evaluate?

Narrow framing – People pay attention to narrowly defined gains and losses (firm-level stock returns) when making decision

1.Individual stock accounting: U(Ct, Ri,t-1), high mean, more volatile, large value premium (P/D effect); aggregate stock returns are predictable in the TS.

2.Portfolio accounting:U(Ct, Pt-1), mean value falls, less volatile, value premium in CS disappears, more correlated with each other. Less successful

WHY？ Change discount rate – Δri,t = f(Ri,t-1)

- Purpose: study asset prices in an economy where some investors categorize risky assets into different styles and move funds among these styles depending on their relative performance.

Findings:

1. assets in the same style comove too much

2. assets in different styles comove too little

3. reclassifying an asset into a new style raises its correlation with that style

4. style returns exhibit a rich pattern of own- and cross-autocorrelations

5. style-level momentum and value strategies are even more profitable than those of asset-level

“Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency” by Jegadeesh and Titman (1993) -- Jeff

Buying past winners and shorting past losers generates

significant positive stock returns over 3 to 12 months holding

periods. For example, 6-month/6-month strategy can realize a

compounded excess return of 12.01% per year.

Profitability is not persistent: Part of abnormal returns

generated in the first year after portfolio formation dissipates

in the following two years.

- J-month/K-month strategy: select stocks on the basis of returns over the past J months and holds them for K months.
- At the beginning of each month t, the stocks are ranked in ascending order based on their returns in the past J months.
- Based on these rankings, ten decile portfolios are formed that equally weight the stocks contained in each decile.
- Top is losers and bottom is winners.
- In each month t, buy winners and sell losers and hold this position for K months.

- 3 sources of excess returns: cross-sectional dispersion in expected returns; market factor; and firm-specific (idiosyncratic) components;
- Profitability is not related to systematic risk; not related to delayed stock price reactions to common factors.
- But consistent with delayed price reactions to firm-specific information.
- Other tests:
- Size and beta based subsamples
- Subperiod: January effect
- Event time
- Back-testing

“Investor Psychology and Security Market Under-and Overreaction” by Daniel, Hirshleifer, and Subrahmanyam (1998) -- Jeff

Propose a theory of stock market under- and overreaction

based on two psychological biases:

Overconfidence – Overestimate the precision of privation

information, but not public information;

Biased self-attribution – Attribute events that confirm the

validity of actions to high ability; and events that disconfirm the actions to noise.

- 2 investors and 4 days
- I (informed): those who receive the signal
- U (uninformed): those who do not receive the signal
- Day 0: endowment;
- Day 1: I receives the signal and trades with U;
- Day 2: Noisy public signal comes; trade further;
- Day 3: conclusive public info arrives.

- The risky security has a terminal value of ; the private information signal received by I at day 1 is:
- s1 = + εU correctly assesses the ε but I underestimate it to be c2 < ε2 (key overreaction assumption)

- No longer require, initial overconfidence, c2 < ε2
- Assume public signal is discrete, with s2 = 1 or -1 at day 2.
- If sign (θ + ε) = sign (s2), confidence increases, so investor’s assessment of noise variance decreases to c2 – k,0 < k < c2
- If sign (θ + ε) ≠ sign (s2), confidence remains constant c2
- Model 1 or Overconfidence implies negative long-lag autocorrelations, excess volatility, and, when managerial actions are correlated with stock mispricing, public-event-based return predictability.
- Model 2 or attribution implies short-lag autocorrelations (momentum), short-run earnings drift.

Evidence on the Characteristics of Cross Sectional Variation in Stock Returns (Daniel and Titman – JF 1997) -- Liem

Firm sizes and B/M ratios are both highly correlated with average returns of common stocks. D&T find that return premia on small cap and high B/M does not arise because of the co-movements of these stocks with pervasive factors. It is the characteristics rather than the covariance structure of returns that appear to explain the cross-sectional variation in stock returns.

Model 1 – The Null Hypothesis

Returns are generated by the following factor structure

Evidence on the Characteristics of Cross Sectional Variation in Stock Returns (Daniel and Titman – JF 1997)

Model 2 – A Model with Time Varying Factor Risk Premia

Factor loadings do not change as firms become distressed. A factor’s risk premium increases following a string of negative factor realizations.

There is no separate distress factor fD. The remaining ß’s in this model are constant over time.

Evidence on the Characteristics of Cross Sectional Variation in Stock Returns (Daniel and Titman – JF 1997)

Model 3 – A Characteristic-based Pricing Model

Firms exist that load on the distressed factors but which are not themselves distressed, and therefore have a low ‘theta’ and commensurately low return.

There is no separate distress factor fD. The remaining ß’s in this model are constant over time.

What is the Intrinsic Value of the Dow? (Lee, Myers and Swaminathan – JF 2000) -- Liem

They model the time-series relation between price and intrinsic value as a co-integrated system so that price and value are long-term convergent. They compare the performance of alternative estimates of intrinsic value for the Dow 30 stocks.

Traditional market multiples such as B/P, E/P, and D/P ratios had little predictive power.

However, a V/P ratio, where “V” is based on a residual income valuation model, has statistically reliable predictive power. Further analysis shows time-varying interest rates and analyst forecasts are important to the success of V. Alternative forecast horizons and risk premia are less important.

What is the Intrinsic Value of the Dow? (Lee, Myers and Swaminathan – JF 2000)

The Residual-Income Valuation Model

Returns are generated by the following factor structure

Model Implementation Issues

Forecast horizons and terminal values

Cost of equity capital

Explicit earnings forecasts

Matching book value to I/B/E/S forecasts

Dividend payout ratios

What is the Intrinsic Value of the Dow? (Lee, Myers and Swaminathan – JF 2000)

- Business Cycle Variables
- Default spread
- Term spread
- Returns prediction
- Forecast regression methodology (eq 12)
- Forecasting regression results
- Univariate regressions (eq 13)
- Multivariate regressions involving DJDP, DJEP, DJBM, and VP

Intrinsic Value Measures

DJDP

DJEP

DJBM

VP

Tracking the Dow Index

Without time trend (eq 10)

With time trend (eq 11)

- The paper tests that whether “overreaction” affect stock prices.
- “overreaction” is an implicit comparison to “appropriate reaction”, which tells us Bayes’ rule prescribes the correct reaction to new information.
- Individuals tend to overweight recent information and underweight prior information.
- Early researchs: J. M. Keynes, Williams, Arrow, Shiller, Kleidon’s, Reinganum, Basu, Graham, Russell and Thaler.

- Two hypothesis: 1. extreme movements in stock will be followed by subsequent price movement in the opposite direction,; 2. the more extreme the initial price movement , the greater will be the subsequent adjustment. ------ To test whether the overreaction hypothesis is predictive. and .
is market-adjusted excess return , and if it is a efficient market, then

Use , , to test and find “overreaction”.

loser and winner are both overreacting, and loser overreact more (asymmetric );

most of the excess return realized in January (January effect);

the overreaction mostly occurs during the second and third year of the test period.

“A model of investor sentiment”

N. Barberis, A. Shleifer, R. Vishny. JFE (1998) -- Daryl

- Earnings streams follow a random walk process
- Investors form expectations based on one of two non-random walk models: “mean-reverting” or a “trend”.
- Investors exhibit “representativeness”, the tendency to view events as typical and ignore statistical probabilities.
- Investors make forecasts based on (i) the strength of evidence & (ii) the statistical weight of evidence
- Model predicts that stocks:
- Underreact to low strength evidence & high weight
- Corporate announcements

- Overreact to high strength and low statistical weight of evidence.
- Consistent patterns of good or bad news

- Underreact to low strength evidence & high weight

Underreaction: E(rt+1|zt=G) > E(rt+1|zt=B)

- over-confidence about prior information
Overreaction: E(rt+1|zt=G,…, zt-j=G) < E(rt+1|zt=B,…,zt-j=B)

- seeing “order among chaos”
Model:

Model 1= Mean Reverting or Model 2= Trend (Markov)

- To value a security, an investor needs to forecast earnings.
- Investor task is then to understand which of the two regimes is currently governing earnings.
- At time t, after observing shock yt, investor estimates the probability qt that yt was generate by Model 1. Formally,
- qt = Pr (st=1|yt, yt-1, qt-1) or
- qt+1 =
- If earnings are generated by regime-switching process, then prices may be decomposed to a random-walk component and and a deviation component from fundamental value. (Prop 1)

Regime switching between models based on probability parameters,λi , which are assumed low.