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Behaviouralizing Finance CARISMA February 2010 Hersh Shefrin Mario L. Belotti Professor of Finance Santa Clara University

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2 Copyright, Hersh Shefrin 2010 Outline Paradigm shift. Strengths and weaknesses of behavioural approach. Combining rigour of neoclassical finance and the realistic psychologically- based assumptions of behavioural finance.

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3 Copyright, Hersh Shefrin 2010 Quantitative Finance Behaviouralizing ─Beliefs & preferences ─Portfolio selection theory ─Asset pricing theory ─Corporate finance ─Approach to financial market regulation

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4 Copyright, Hersh Shefrin 2010 Weaknesses in Behavioural Approach Preferences. ─Prospect theory, SP/A, regret. ─Disposition effect. Cross section. Long-run dynamics. Contingent claims (SDF: 0 or 2?) Sentiment. Representative investor.

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5 Copyright, Hersh Shefrin 2010 Conference Participants Examples Continuous time model of portfolio selection with behavioural preferences. ─He and Zhou (2009), Zhou, De Georgi Prospect theory and equilibrium ─De Giorgi, Hens, and Rieger (2009). Prospect theory and disposition effect ─Hens and Vlcek (2005), Barberis and Xiong (2009), Kaustia (2009). Long term survival. ─Blume and Easley in Hens and Schenk-Hoppé (2008). Term structure of interest rates. ─Xiong and Yan (2009).

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6 Copyright, Hersh Shefrin 2010 Beliefs Change of measure techniques. ─Excessive optimism. ─Overconfidence. ─Ambiguity aversion.

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7 Copyright, Hersh Shefrin 2010 Example: Change of Measure is Log-linear Typical for a variance preserving, right shift in mean for a normally distributed variable. Shape of log-change of measure function?

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8 Copyright, Hersh Shefrin 2010 Excessive Optimism

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9 Copyright, Hersh Shefrin 2010 Excessive Pessimism

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10 Copyright, Hersh Shefrin 2010 Overconfidence

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11 Copyright, Hersh Shefrin 2010 Preferences Psychological concepts ─Psychophysics in prospect theory. ─Emotions in SP/A theory. Inverse S-shaped weighting function, rank dependent utility. ─Regret. ─Self-control.

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12 Copyright, Hersh Shefrin 2010 Prospect Theory Weighting Function Based on Hölder Average Ingersoll Critique

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13 Copyright, Hersh Shefrin 2010 Inverse S in SP/A Rank Dependent Utility

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14 Copyright, Hersh Shefrin 2010 Prospect Theory Tversky-Kahneman (1992) ─Value function piecewise power function ─Weighting function ratio of power function to Hölder average ─Editing / Framing

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15 Copyright, Hersh Shefrin 2010 SP-Function in SP/A Rank Dependent Utility n SP = (h(D i )-h(D i+1 ))u(x i ) i=1 Utility function u is defined over gains and losses. Lopes and Lopes-Oden model u as linear. ─suggest mild concavity is more realistic Rank dependent utility: h is a weighting function on decumulative probabilities.

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16 Copyright, Hersh Shefrin 2010 The A in SP/A The A in SP/A denotes aspiration. Aspiration pertains to a target value to which the decision maker aspires. The aspiration point might reflect status quo, i.e., no gain or loss. In SP/A theory, aspiration-risk is measured in terms of the probability A=Prob{x }

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17 Copyright, Hersh Shefrin 2010 Objective Function In SP/A theory, the decision maker maximizes an objective function L(SP,A). L is strictly monotone increasing in both arguments. Therefore, there are situations in which a decision maker is willing to trade off some SP in exchange for a higher value of A.

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18 Copyright, Hersh Shefrin 2010 Testing CPT vs. SP/A Experimental Evidence Lopes-Oden report that adding $50 induces a switch from the sure prospect to the risky prospect. Consistent with SP/A theory if A is germane, but not with CPT. Payne (2006) offers similar evidence that A is critically important, although his focus is OPT vs. CPT.

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19 Copyright, Hersh Shefrin 2010 Behaviouralizing Portfolios Full optimization using behavioural beliefs and/or preferences. What is shape of return profile relative to the state variable? In slides immediately following, dotted graph corresponds to investor with average risk aversion.

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20 Copyright, Hersh Shefrin 2010 Baseline: Aggressive Investor With Unbiased Beliefs

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21 Copyright, Hersh Shefrin 2010 How Would You Characteize an Investor Whose Return Profile Has This Shape?

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22 Copyright, Hersh Shefrin 2010 Two Choices Aggressive underconfidence? Aggressive overconfidence?

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23 Copyright, Hersh Shefrin 2010 CPT With Probability Weights

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24 Copyright, Hersh Shefrin 2010 CPT With Rank Dependent Weights

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25 Copyright, Hersh Shefrin 2010 SP/A With Cautious Hope

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26 Copyright, Hersh Shefrin 2010 Associated Log-Change of Measure

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27 Copyright, Hersh Shefrin 2010 Caution! Quasi-Optimization Prospect theory was not developed as a full optimization model. It’s a heuristic-based model of choice, where editing and framing are central. It’s a suboptimization model, where choice heuristics commonly lead to suboptimal if not dominated acts.

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28 Copyright, Hersh Shefrin 2010 Behaviouralizing Asset Pricing Theory Stochastic discount factor (SDF) is a state price per unit probability. SDF M = / . Price of any one-period security Z is q Z = Z = E {MZ} E t [R i,t+1 M t+1 ] = 1

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29 Copyright, Hersh Shefrin 2010 Graph of SDF What’s This? x-axis is a state variable like aggregate consumption growth. y-axis is M. SDF is linear.

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30 Copyright, Hersh Shefrin 2010 How About This? Logarithmic Case? x-axis is a state variable like log- aggregate consumption growth. y-axis is log-M. Relationship is linear.

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31 Copyright, Hersh Shefrin 2010 Empirical SDF Aït-Sahalia and Lo (2000) study economic VaR for risk management, and estimate the SDF. Rosenberg and Engle (2002) also estimate the SDF. Both use index option data in conjunction with empirical return distribution information. What does the empirical SDF look like?

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32 Copyright, Hersh Shefrin 2010 Aït-Sahalia – Lo’s SDF Estimate

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33 Copyright, Hersh Shefrin 2010 Rosenberg-Engle’s SDF Estimate

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34 Copyright, Hersh Shefrin 2010 Behavioral Aggregation Begin with neoclassical EU model with CRRA preferences and complete markets. In respect to judgments, markets aggregate pdfs, not moments. ─Generalized Hölder average theorem. In respect to preferences, markets aggregate coefficients of risk tolerance (inverse of CRRA).

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35 Copyright, Hersh Shefrin 2010 Representative Investor Models Many asset pricing theorists, from both neoclassical and behavioral camps, assume a representative investor in their models. Aggregation theorem suggests that the representative investor assumption is typically invalid.

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36 Copyright, Hersh Shefrin 2010 Typical Representative Investor: Investor Population Heterogeneous Violate Bayes rule, even when all investors are Bayesians. Is averse to ambiguity even when no investor is averse to ambiguity. Exhibits stochastic risk aversion even when all investors exhibit CRRA. Exhibits non-exponential discounting even when all investors exhibit exponential discounting.

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37 Copyright, Hersh Shefrin 2010 Formally Defining Sentiment General Model Measured by the random variable = ln(P R (x t ) / (x t )) + ln( R / R, ) R, is the R that results when all traders hold objective beliefs Sentiment is not a scalar, but a stochastic process, involving a log-change of measure.

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38 Copyright, Hersh Shefrin 2010 Neoclassical Case, Market Efficiency = 0 The market is efficient when the representative trader, aggregating the beliefs of all traders, holds objective beliefs. ─i.e., efficiency iff P R = When all investors hold objective beliefs = (P R / ) ( R / R, ) = 1 and = ln( ) = 0

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39 Copyright, Hersh Shefrin 2010 Decomposition of SDF m ln(M) m = - R ln(g) + ln( R, ) Process ─Note: In CAPM with market efficiency, M is linear in g with a negative coefficient.

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40 Copyright, Hersh Shefrin 2010 Overconfident Bulls & Underconfident Bears

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41 Copyright, Hersh Shefrin 2010 How Different is a Behavioural SDF From a Traditional Neoclassical SDF?

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42 Copyright, Hersh Shefrin 2010 It’s Not Risk Aversion in the Aggregate Upward sloping portion of SDF is not a reflection of risk-seeking preferences at the aggregate level. Time varying sentiment time varying SDF. After 2000, shift to “black swan” sentiment and by implication SDF.

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43 Copyright, Hersh Shefrin 2010

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44 Copyright, Hersh Shefrin 2010 Taleb “Black Swan” Sentiment Overconfidence

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45 Copyright, Hersh Shefrin 2010 Barone Adesi- Engle-Mancini (2008) Empirical SDF based on index options data for 1/2002 – 12/2004. Asymmetric volatility and negative skewness of filtered historical innovations. In neoclassical approach, RN density is a change of measure wrt , thereby “preserving” objective volatility. In behavioral approach RN density is change of measure wrt P R. In BEM, equality broken between physical and risk neutral volatilities.

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46 Copyright, Hersh Shefrin 2010 SDF for 2002, 2003, Garch on Left, Gaussian on Right

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47 Copyright, Hersh Shefrin 2010 Continuous Time Modeling E(M) is the discount rate exp(-r) associated with a risk-free security. m=ln(M) Take point on realized sample path, where M is value of SDF at current value of g. dM has drift –r with fundamental disturbance and sentiment disturbance. r>0 expect to move down the SDF graph. Fundamental disturbance relates to shock to dln(g). Sentiment disturbance relates to shift in sentiment. Marginal optimism drives E(dm) >0.

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48 Copyright, Hersh Shefrin 2010 Risk Premiums Risk premium on security Z is the sum of a fundamental component and a sentiment component: -cov[r Z g - ]/E[g - ] + (fundamental) i e (1-h Z )/h Z + (sentiment) i e -i (sentiment) where h Z = E[ g - r Z ]/ E[g - r Z ]

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49 Copyright, Hersh Shefrin 2010 How Different are Returns to a Behavioural MV-Portfolio From Neoclassical Counterpart?

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50 Copyright, Hersh Shefrin 2010 MV Function Quadratic 2-factor Model, Mkt and Mkt 2

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51 Copyright, Hersh Shefrin 2010 When a Coskewness Model Works Exactly The MV return function is quadratic in g, risk is priced according to a 2-factor model. The factors are g (the market portfolio return) and g 2, whose coefficient corresponds to co-skewness.

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52 Copyright, Hersh Shefrin 2010 Summary of Key Points Behaviouralizing Finance Paradigm shift. Strengths and weaknesses of behavioural approach. Agenda for quantitative finance? Combine rigour of neoclassical finance and the realistic psychologically-based assumptions of behavioural finance.

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