behavioral finance, session iv · plan for today behavioral biases barberis et al, 1998 harrison...

Plan for TodayBehavioral Biases

Barberis et al, 1998Harrison and Stein, 1999

Baker and Wurgler, 2006 JoFDuffy and Unver, 2006, ET

Behavioral Finance, Session IVWS 2013, Frankfurt Germany

Sascha Baghestanian

Sascha Baghestanian Behavioral Finance, Session IV




Today

So far we have discussed how rational investors behave under thepresence of irrational traders. Now we turn to the core of behavioralfinance: Modelling Behavioral Biases.

Quickly discuss some of the most important behavioral biases,adapted into behavioral finance (Kahneman, Tversky). We focuson Representativeness biases, Anchoring and Conservativism anddeal with Overconfidence later.

Turn to papers which adapt the biases into their modelingframework:

Barberis, Shleifer, Vishny (1998, JoF) - Over- and Underreactionof stock prices due to conservativism andrepresentativeness-heuristics (Theory).





Today

Harrison, Stein (1999, JoF) - Over and Underreaction due tolimited information dissipation and momentum (motivated viatrend-anchoring) (Theory).

Baker and Wurgler (2006, JoF): Empirical Investigation of theRelationship between Sentiment and Stock Prices.

Duffy and Unver (ET, 2006): Model with behavioral biasesrelated to experimental asset markets.





Tversky, Kahneman, Science, 2002

Simon (1955, 1979): Decision Makers should be viewed asboundedly Rational. Replaces Utility Maximizing by satisficing(searching through the available alternatives until anacceptability threshold is met).

Further developed by: Kahneman & Tversky: Detecting regularbehavioral biases, causing deviations from rational decisionmaking.






Starting Point:

Decisions are made under uncertainty and risk. Hence agentshave to form beliefs.

What determines such beliefs?

KT: People rely on heuristics, reducing complex task of assessingprobabilities. Leads to systematic errors.

Common Heuristics: Representativeness, Anchoring,Overconfidence, Optimism, Conservativism.






Representativeness Heuristics (RH):

Probabilistic statements usually of the form:

What is probability that A originates from B or A belongs toclass B?

Answers depend often on RH: What is the probability that A isrepresentative for B?

If A is representative for B - probability that A originates from Bis judged to be high and vice versa.






Experiments:

People were shown brief personality descriptions of 100professionals. Engineers and Lawyers.

Participants were told that 70 were engineers and 30 lawyers(treatment 1)

Participants were told that 30 were engineers and 70 lawyers(treatment 2)

Q: Without prior information what’s the probability that arandom individual is an engineer or lawyer?

Participants answer this question accurately in the absence ofprior information.






Step 2: Add information

Dick is a 30 yr old man. He is married with nochildren. A man of high ability and motivation. Hepromises to be successful. He is well liked.

Arguably, this statement contains 0 information. However,probabilities change.






Usually participants assert that Dick is engineer with 50%probability.

Invariance to sample size falls into the same category.

Misconception of chance: Fair coin tossed 6 times. 2 Outcomes:

H-T-H-T-T-H and H-H-H-T-T-T. People consider the firstsequence more likely than the second sequence, also if they onlyface the gamble only once.

RH: People see patterns, where there are no patterns. Relevantfor investment behavior and belief formation in general.






Anchoring:

Many time people make estimates by starting from an initialvalue and adjust it a little bit.

The initial value depends on the formulation of the problem.

Example: Subjects are asked about the fraction of Africancountries in the UN (0 - 100). A wheel was spinned in theirpresence, giving a number between 0 and 100. Answerscorrelated.






Example 2: YOU are the participant. Please take a sheet of paper.You have 10 seconds to answer the following question:What’s the solution to:

8× 7× 6× 5× 4× 3× 2× 1






Part II:What’s the solution to:

1× 2× 3× 4× 5× 6× 7× 8

Solution: 40.320Median answer ascending sequence: 512, Median answer descending2250.Other examples: Subjects writing their social security number thenguess a number in unrelated context.Anchoring: Beliefs are rooted in similar or previous observations.





Tversky, Riepe, 1998

Overconfidence - best described via example:

What is your best estimate of the value of the Dow Jonesone month from today? Next pick a high value, such that youare 99% sure (but not absolutely sure) that the Dow Jones amonth from today will be lower than that value. Now pick alow value, such that you are 99% sure (but no more) that theDow Jones a month from today will be higher than that value.

Usually confidence intervals are way too narrow - individuals are waytoo confident.






Overconfidence - best described via example:

What is your best estimate of the value of the Dow Jonesone month from today? Next pick a high value, such that youare 99% sure (but not absolutely sure) that the Dow Jones amonth from today will be lower than that value. Now pick alow value, such that you are 99% sure (but no more) that theDow Jones a month from today will be higher than that value.

Usually confidence intervals are way too narrow - individuals are waytoo confident. Overconfidence: Overestimating accuracy of beliefs.






Optimism - also best described via example:

How good a driver are you? Compared to the drivers youencounter on the road, are you above average, average, orbelow average? If an acquaintance purchased a stock thatlater did badly, do you think of this as a mistake, or as acase of bad luck?

Usually male subjects over predict their abilities. Optimism:Overestimating level of beliefs (recall DSSW). Note that optimismand overconfidence can be related to one another withstochastic-dominance properties of beliefs.





Edwards, 1968

Conservativism: Individuals are slow to change their beliefs in theface of new evidence. Edwards benchmarks a subjects reaction to newevidence against that of an idealized rational Bayesian in experimentsin which the true normative value of a piece of evidence is welldefined. Confirmed many times since then: Individuals do not updatetheir posteriors fast enough.





Barberis et al, 1998, JoF

A model of investor sentiment. 2 Empirical facts drive the analysis:

Stocks under react to news: Over short horizons returns arepositively autocorrelated (News are incorporated way too slowly).

A related way to make this point is to say that current go o dnews has power in predicting positive returns in the future

Stocks sometimes overreact to news: Securities that have had along record of go o d news tend to become overpriced and havelow average returns afterwards (they revert to the mean).DSSW-models can’t explain both. EMH can’t explain it either.

Authors incorporate representativeness heuristics andconservativism to explain the patterns.






Formal characterization of under(!!)-reaction to good news (G) vs badnews (B):

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

r are returns, zt is the state. The stock under-reacts to the good newsa mistake which is corrected in the following period giving a higherreturn at that time. For evidence see: Cutler et al. (1992), Bernard(1992), Jegadeesh and Titman (1993) ... etc.






Formal characterization of over(!!)-reaction to good news (G) vs badnews (B):

E(rt+1|zt = G, zt−1 = G, ..., zt−j = G)

< E(rt+1|zt = B, zt−1 = B, ..., zt−j = B)

The idea here is simply that after a series of announcements of goodnews the investor becomes overly optimistic that future newsannouncements will also be good and hence overreacts sending thestock price to unduly high levels. Subsequent news announcementsare likely to contradict his optimism, leading to lower returns.For evidence see: Poterba and Summers (1988), Campbell and Shiller(1988)...






Model:

Representative agent. Risk Neutral. One Risky asset, paysdividend Nt in period t. Discount factor is 1/(1 + δ). Asset Priceis therefore:

pt = Et(Nt+1/(1 + δ) +Nt+2/(1 + δ)2 + ...)

Dividends follow random walks (E(Nt+j = Nt)) - REE: Nt/δ.But RW-Structure is not known by the agents. They haveinaccurate beliefs.

Specifically Nt+1 = Nt + yt+1. yt+1 can take on two values: yand −y. Investor beliefs are characterized as follows






2 Markovian Models:

πL ∈ [0, 1/2], πH ∈ [1/2, 1]. The investor is convinced that he knowsthe parameters and he is also sure that he is right about theunderlying process controlling the switching from one regime toanother or equivalently from Model 1 to Model 2. It too is Markov sothat the state of the world to day depends only on the state of theworld in the previous period. Model 1: Conservativism, Model 2: RH.The transition matrix is






Assume that λ1 + λ2 < 1 and λ1 < λ2. Unconditional stateprobability: λiλ1 + λ2. Beliefs about states govern expected earningsand stock prices:






Let qt = Pr(st = 1|yt, yt−1, qt−1) (weight on model 1 - probabilitythat yt was generated by model 1). Bayes rule then implies:






If for instance shocks in t are the same as in t+ 1, we get

Barberis et al. show that then qt+1 < qt (more weight on model 2). Ifopposite sign: qt < qt+1.






Numerical example λ1 = 1/10, λ2 = 0.3, πL = 1/3, πH = 3/4. y0 = 0,q0 = 1/2.






Proposition 1:

pt =Ntδ

+ yt(p1 − p2qt)

where p1, p2 are functions of the underlying parameters. Homework:Go through the proof in the Appendix. It is only notationally difficult.Proposition 2: If

kp2 < p1 < kp2

p2 ≥ 0 Then price function exhibits under and overreaction withrespect to earnings. Intuition: p1 cannot be too large if prices shouldexhibit under reaction and vice versa for overreaction.






Next: Simulate returns if λ1 = 1/10, λ2 = 0.3,πL = 1/3, πH = 3/4. y0 = 0, q0 = 1/2.

Simulate 2000 samples with length n.

Form 2 portfolios: One with winners and one with losers (earningshocks).

Form rn+ − rn− - should be positive under under reaction forn = 1. Should turn negative if n grows (over-reaction).






Summary:

Barberis et al. present a simple framework to investigate thesources of stock market over- and underreaction.

Results are tightly connected to the behavioral assumptions onbelief-formation

Sticky and false beliefs generate over and under reactions.

Traders see patterns where there are no patterns.





Harrison and Stein, 1999, JoF

Similar goal as Barberis et al.

Explain over- and under reaction of stocks

Less weight on behavioral biases, more weight on heterogeneity.

News-watchers and Momentum Traders. Both not fully rational.

News Watchers obtain signals about the value of a risky asset butdiffuses only gradually (source for under-reaction).

With news watchers only - under-reaction but neverover-reaction.

Then add momentum traders- generates price overreaction tonews.






The model:

Dividend paid by the asset in period T: DT = D0 +∑Tj=0 εj . T is

assumed to be extremely large...

ε’s are iid. Variance: σ2.

Start with news-watchers only. They can be subdivided into zequally sized groups.

Each dividend shock can be decomposed into z independentsub-innovations ε = ε1 + ε2 + ..., each with variance σ2/z

Timing: At time t news about εt+z−1 start to spread. I.e. Group1 observes ε1t+z−1., Group 2 observes ε2t+z−1... Each subinnovation is seen by a fraction of 1/z traders in period t.

Next in period t+ 1 group 1 observes ε2t+z−1, group 2 observesε3t+z−1... rotate. Thus in period 2 each sub innovation has beenseen by 2/z - on average everybody is equally well informed.

z is a proxy for the speed of information diffusion.Sascha Baghestanian Behavioral Finance, Session IV





Agents maximize CARA utility, hence demands:

dt =Ei(DT )− pt

θ

Note θ is a function of risk aversion and variance (identical acrossagents). Note - not fully rational. Summing over agents and equatingto aggregate supply yields:

pt = Dt + ((z − 1)εt+1 + (z − 2)εt+2 + ....+ εt+z−1)/z − θQ

normalize θ = 1. Fully Revealing equilibrium (Prices under-react)

pt = Dt+z−1 − θQ






Adding j Momentum Traders. Have CARA utility and Demands haveto satisfy:

Ft = A+ φ∆pt

(first difference).

pt = Dt+((z−1)εt+1 +(z−2)εt+2 + ....+ εt+z−1)/z−θQ+ jA+ jφ∆pt

Momentum Traders have also CARA utilities. Maximize wealthpredicting prices in j periods ahead. Their demands:

A+ φ∆pt = γEM (pt+j − pt)/V arM (pt+j − pt)In most cases A and Q play no role: Let zero. Pin down φ inequilibrium (see homework):

φ =γCov(pt+j − pt,∆pt−1)

V ar(δpt−1)V arM (pt+j − pt)Sascha Baghestanian Behavioral Finance, Session IV





Equilibrium is a fixed point of:

pt = Dt + ((z − 1)εt+1 + (z − 2)εt+2 + ....+ εt+z−1)/z + jφ∆pt

φ =γCov(pt+j − pt,∆pt−1)

V ar(δpt−1)V arM (pt+j − pt)Shown in Appendix: In any covariance stationary equilibrium φ > 0 -momentum traders are trend chasers. It’s easy to see that φ cannotbe zero. If it’s zero then we are in the newswatcher case, with positivecovariance but this implies that φ > 0 Stationarity implies that |φ| < 1






Proposition In any covariance-stationary equilibrium, given a positiveone- unit shock et+z−1 that first begins to diffuse amongnewswatchers at time t:

There is always overreaction, in the sense that the cumulativeimpulse response of prices peaks at a value that is strictly greaterthan one.

If the momentum traders horizon j satisfies j ≥ z − 1, thecumulative impulse response peaks at t+ j and then begins todecline, eventually converging to one.

If the momentum traders horizon j satisfies j < z − 1, thecumulative impulse response peaks no earlier than t+ j and thenbegins to decline, eventually converging to one.






A Beautiful Model!

Over and Underreaction is linked to information diffusion andmomentum.

Delivers testable implications:

Both short-run continuation and long- run reversals should bemore pronounced in those small, low-analyst-coverage! stockswhere information diffuses more slowly;There may be more long- run overreaction to information that isinitially private than to public news announcementsThere should be a relationship between momentum traders?horizons and the pattern of return autocorrelations

Offer: Lab competition





Baker and Wurgler, 2006 JoF

Try to measure the impact of Sentiment on Stock Market Returns.Estimation of the form:

Et−1Rit = a+ a1Tt−1 + bxit + b2xitTt−1

Tt−1 - sentiment proxy. a1: Impact on market overall.xit - controlsAuthors focus on firm-codes 10-11 (Compustat) - between 1961 - 2001.






Sentiment:

CEFD - we discussed this. Inversely related to sentiment

NYSE share turnover (Log, detr). In a market with short-salesconstraints, irrational investors participate, and thus addliquidity, only when they are optimistic; hence, high liquidity is asymptom of overvaluation. (Baker, Stein 2004)

Average first-day returns on IPOs (Enthusiasm - think of FB)

The equity share (high equity share predicts low market returns)in new issues

The dividend premium (the log difference of the averagemarket-to-book ratios of payers and nonpayers)

... They construct an index from these measures... clean it fromaggregate shocks etc etc... End up with a measure calledSENTIMENT






Large sentiment drives up price and therefore lowers return.





Duffy and Unver, 2006, ET

Agent Based Model for experimental asset markets. Incorporatesbehavioral biases:

N agents interact in T periods and trade a single financial

Initially each agent i is endowed with xi0 units of cash and yi0units of the financial asset. At the end of every period the assetpays random dividends drawn with equal probability from acommonly known support (average: d)

Note REE

FVt = d(T − t+ 1) for t = 1, ..., T.

In each period a trader is a buyer with probabilityπt = max(0, 1/2− φ(t− 1)) (weak foresight; Note: φ < 0.5/T )

Each period t subdivided into S sub-periods.






Traders

If Buyer:bn,is,t = min

{(1− α)εt + αpt−1, x

is,t

}, (1)

α ∈ [0, 1], εt ∼ U [0, κFVt], κ ≥ 0

If seller:an,is,t = (1− α)εt + αpt−1, (2)

Use closed book double auction market to sort bids and asks.Trades:

xis,t = xis−1,t − pst1(bis,t>ast )

After the Sth (last) submission round in trading period t, therandom dividend Dt is realized and traders update their cashholdings according to:

xi1,t+1 = xiS,t +DtyiS,t.






Estimate parameters via:

SSD(α, κ, φ, S) =

T∑t=1

(pt(α, κ, φ, S)− pt

FV1

)2

+

T∑t=1

(qt(α, κ, φ, S)− qt

TSU

)2

,

(3)Here’s the code:


behavioral finance, session iv · plan for today behavioral biases barberis et al, 1998 harrison...

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