View
224
Download
0
Category
Preview:
Citation preview
Behaviouralizing Finance
CARISMA
February 2010
Hersh Shefrin
Mario L. Belotti Professor of Finance
Santa Clara University
2Copyright, 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.
3Copyright, Hersh Shefrin 2010
Quantitative Finance
• Behaviouralizing ─Beliefs & preferences─Portfolio selection theory─Asset pricing theory─Corporate finance─Approach to financial market regulation
4Copyright, 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.
5Copyright, Hersh Shefrin 2010
Conference ParticipantsExamples
• 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).
6Copyright, Hersh Shefrin 2010
Beliefs
• Change of measure techniques.─Excessive optimism.─Overconfidence.─Ambiguity aversion.
7Copyright, 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?
8Copyright, Hersh Shefrin 2010
Excessive Optimism Sentiment Function
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
95.8
2%
96.1
5%
96.4
8%
96.8
1%
97.1
4%
97.4
8%
97.8
1%
98.1
5%
98.4
8%
98.8
2%
99.1
6%
99.5
0%
99.8
4%
100.
18%
100.
53%
100.
87%
101.
22%
101.
56%
101.
91%
102.
26%
102.
61%
102.
96%
103.
32%
103.
67%
104.
03%
104.
38%
104.
74%
105.
10%
105.
46%
105.
82%
106.
19%
Consumption Growth Rate g (Gross)
9Copyright, Hersh Shefrin 2010
Excessive PessimismSentiment Function
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
95.8
2%
96.1
5%
96.4
8%
96.8
1%
97.1
4%
97.4
8%
97.8
1%
98.1
5%
98.4
8%
98.8
2%
99.1
6%
99.5
0%
99.8
4%
100.
18%
100.
53%
100.
87%
101.
22%
101.
56%
101.
91%
102.
26%
102.
61%
102.
96%
103.
32%
103.
67%
104.
03%
104.
38%
104.
74%
105.
10%
105.
46%
105.
82%
106.
19%
Consumption Growth Rate g (Gross)
10Copyright, Hersh Shefrin 2010
OverconfidenceSentiment Function
-2.5
-2
-1.5
-1
-0.5
0
0.5
96
%
97
%
99
%
10
1%
10
3%
10
4%
10
6%
Consumption Growth Rate g (Gross)
11Copyright, 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.
12Copyright, Hersh Shefrin 2010
Prospect Theory Weighting Function
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Decumulative Probability
Prospect Theory Weighting FunctionBased on Hölder Average
Ingersoll Critique
13Copyright, Hersh Shefrin 2010
Functional Decomposition of Decumulative Weighting Function in SP/A Theory
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
D
h1(D)
h2(D)
h(D)
Inverse S in SP/A Rank Dependent Utility
14Copyright, Hersh Shefrin 2010
Prospect Theory
• Tversky-Kahneman (1992)─Value function
• piecewise power function
─Weighting function • ratio of power
function to Hölder average
─Editing / Framing
Prospect Theory Value Function
-10
-8
-6
-4
-2
0
2
4
6
-10
-9.2
5-8
.5-7
.75 -7
-6.2
5-5
.5-4
.75 -4
-3.2
5-2
.5-1
.75 -1
-0.2
5 0.5
1.25 2
2.75 3.
54.
25 55.
75 6.5
7.25 8
8.75 9.
5
Gain/loss
Prospect Theory Weighting Function
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.09 0.14 0.18 0.23 0.27 0.32 0.36 0.41 0.45 0.5 0.54 0.59 0.63 0.68 0.72 0.77 0.81 0.86 0.9 0.95 0.99
Probability
15Copyright, Hersh Shefrin 2010
SP-Function in SP/A Rank Dependent Utility
n
SP = (h(Di)-h(Di+1))u(xi) 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.
16Copyright, 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 }
17Copyright, 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.
18Copyright, Hersh Shefrin 2010
Testing CPT vs. SP/AExperimental 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.
19Copyright, 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.
20Copyright, Hersh Shefrin 2010
Baseline: Aggressive Investor With Unbiased Beliefs
cj/c0 vs. g
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
0.97
0.99
1.01
1.03
1.05
1.07
1.09
1.11
1.13
1.15
1.17
1.19
1.21
g
cj/
c0 cj/c0
g
21Copyright, Hersh Shefrin 2010
How Would You Characteize an Investor Whose Return Profile Has
This Shape?cj/c0 vs. g
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.79
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
0.97
0.99
1.01
1.03
1.05
1.07
1.09
1.11
1.13
1.15
1.17
1.19
1.21
g
cj/
c0 cj/c0
g
22Copyright, Hersh Shefrin 2010
Two Choices
• Aggressive underconfidence?
• Aggressive overconfidence?
23Copyright, Hersh Shefrin 2010
CPT With Probability Weights
24Copyright, Hersh Shefrin 2010
CPT With Rank Dependent Weights
25Copyright, Hersh Shefrin 2010
SP/A With Cautious Hope
26Copyright, Hersh Shefrin 2010
Associated Log-Change of Measure
27Copyright, 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.
28Copyright, 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
qZ = Z = E{MZ}
Et[Ri,t+1 Mt+1] = 1
29Copyright, Hersh Shefrin 2010
Graph of SDFWhat’s This?
• x-axis is a state variable like aggregate consumption growth.
• y-axis is M.
• SDF is linear.
30Copyright, 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.
31Copyright, 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?
32Copyright, Hersh Shefrin 2010
Aït-Sahalia – Lo’s SDF Estimate
33Copyright, Hersh Shefrin 2010
Rosenberg-Engle’s SDF Estimate
34Copyright, 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).
35Copyright, 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.
36Copyright, 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.
37Copyright, Hersh Shefrin 2010
Formally Defining Sentiment General Model
Measured by the random variable
= ln(PR(xt) / (xt)) + 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.
38Copyright, 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 PR=
• When all investors hold objective beliefs
= (PR/) (R/ R,) = 1
and
= ln() = 0
39Copyright, Hersh Shefrin 2010
Decomposition of SDF
m ln(M)
m = - R ln(g) + ln(R,)
Process <m, >─Note: In CAPM with market
efficiency, M is linear in g with a negative coefficient.
40Copyright, Hersh Shefrin 2010
ln SDF & Sentiment
-30.00%
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
95.8
2%
96.1
5%
96.4
8%
96.8
1%
97.1
4%
97.4
8%
97.8
1%
98.1
5%
98.4
8%
98.8
2%
99.1
6%
99.5
0%
99.8
4%
100.
18%
100.
53%
100.
87%
101.
22%
101.
56%
101.
91%
102.
26%
102.
61%
102.
96%
103.
32%
103.
67%
104.
03%
104.
38%
104.
74%
105.
10%
105.
46%
105.
82%
106.
19%
Gross Consumption Growth Rate g
ln(g)
Sentiment Function
ln(SDF)
Overconfident Bulls & Underconfident Bears
41Copyright, Hersh Shefrin 2010
Behavioral SDF vs Traditional SDF
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
96
%
97
%
97
%
98
%
99
%
10
0%
10
1%
10
2%
10
3%
10
3%
10
4%
10
5%
10
6%
Aggregate Consumption Growth Rate g (Gross)
Behavioral SDF
Traditional Neoclassical SDF
How Different is a Behavioural SDF From a Traditional Neoclassical SDF?
42Copyright, 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.
43Copyright, Hersh Shefrin 2010
44Copyright, Hersh Shefrin 2010
Taleb “Black Swan” SentimentOverconfidence
Sentiment Function
-2.5
-2
-1.5
-1
-0.5
0
0.5
96
%
97
%
99
%
10
1%
10
3%
10
4%
10
6%
Consumption Growth Rate g (Gross)
45Copyright, 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 PR.
• In BEM, equality broken between physical and risk neutral volatilities.
46Copyright, Hersh Shefrin 2010
SDF for 2002, 2003, Garch on Left, Gaussian on Right
47Copyright, 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.
ln SDF & Sentiment
-30.00%
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
95.8
2%
96.1
5%
96.4
8%
96.8
1%
97.1
4%
97.4
8%
97.8
1%
98.1
5%
98.4
8%
98.8
2%
99.1
6%
99.5
0%
99.8
4%
100.
18%
100.
53%
100.
87%
101.
22%
101.
56%
101.
91%
102.
26%
102.
61%
102.
96%
103.
32%
103.
67%
104.
03%
104.
38%
104.
74%
105.
10%
105.
46%
105.
82%
106.
19%
Gross Consumption Growth Rate g
ln(g)
Sentiment Function
ln(SDF)
• Fundamental disturbance relates to shock to dln(g).
• Sentiment disturbance relates to shift in sentiment.
• Marginal optimism drives E(dm) >0.
48Copyright, Hersh Shefrin 2010
Risk Premiums
Risk premium on security Z is the sum of a fundamental component and a sentiment component:
-cov[rZ g-]/E[g-] + (fundamental)
ie(1-hZ)/hZ + (sentiment)
ie-i (sentiment)
where
hZ = E[ g- rZ]/ E[g- rZ]
49Copyright, Hersh Shefrin 2010
Gross Return to Mean-variance Portfolio:Behavioral Mean-Variance Return vs Efficient Mean-Variance Return
75%
80%
85%
90%
95%
100%
105%
110%
96
%
97
%
99
%
10
1%
10
3%
10
4%
10
6%
Consumption Growth Rate g (Gross)
Me
an
-va
ria
nc
e R
etu
rn
Behavioral MV Portfolio Return
Neoclassical Efficient MV Portfolio Return
How Different are Returns to a Behavioural MV-Portfolio From Neoclassical Counterpart?
50Copyright, Hersh Shefrin 2010
MV Function Quadratic2-factor Model, Mkt and Mkt2
Gross Return to Mean-variance Portfolio:Behavioral Mean-Variance Return vs Efficient Mean-Variance Return
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
95
.82
%
96
.64
%
97
.48
%
98
.31
%
99
.16
%
10
0.0
1%
10
0.8
7%
10
1.7
4%
10
2.6
1%
10
3.4
9%
10
4.3
8%
10
5.2
8%
10
6.1
9%
Consumption Growth Rate g (Gross)
Me
an
-va
ria
nc
e R
etu
rn
Efficient MV Portfolio Return
Behavioral MV Portfolio Return
Return to a Combination of the Market Portfolio and Risk-free Security
51Copyright, 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 g2, whose coefficient corresponds to co-skewness.
52Copyright, Hersh Shefrin 2010
Summary of Key PointsBehaviouralizing 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.
Recommended