BeFi Web Seminar for January 30, 2008
Customer-Focused Investment Advice:
Constructing Preferences for Outcomes
© BeFi Forum 2007
by Dan Goldstein
London Business School
Customer-Focused Investment Advice:
Constructing preferences for outcomes
Dan Goldstein
BeFi Webinar 30 Jan 2008
1
Collaborators
William F. Sharpe
Eric J. Johnson
2
Central question
How do retirement investors
think about risk and return?
3
To investigate, I present a research technique
to measure, model, & analyze risk-return
tradeoffs.
I consider the two models of risk preference:
Constant Relative Risk Aversion, and a lossaverse (reference dependent) variants.
4
Central question 2
Part I:
Background
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Domain: Investing for retirement
• $3.7 trillion in IRAs
• $2.9 trillion in 401(k)s
• Magnitude of decision
6
The market solution:
Risk tolerance questionnaires
How stable are your current and future income
sources?
A.Very unstable
B.Unstable
C.Stable
D.Very Stable
E. I Have Tenure
7
The $6,600,000,000,000 question
$$$$
? %
Stocks
Uncertainty
? %
? Covariances ?
?
? Interest Rates ?
Bonds
? Inflation Rates ?
? %
$
Money Market
Probability Distribution
Of Wealth
8
Rapid choices
• Assume
• choice between 1 and 10 funds
• Allocations in units of 5% of contribution
• 16 levels of contribution $1,000 to $16,000
= 160 million ways to complete the form
9
The $6,600,000,000,000 question
$$$$
? %
Stocks
Uncertainty
? %
? Covariances ?
?
? Interest Rates ?
Bonds
? Inflation Rates ?
? %
$
Money Market
Probability Distribution
Of Wealth
10
Central question 2
Part II:
Questions
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Central question
Investment advice and economic models often
prescribe strategies resulting in lognormal
distributions of wealth.
In the following experiments, people with
Constant Relative Risk Averse (CRRA) utility
should prefer lognormal distributions of wealth.
People with loss-averse (reference dependent)
preferences should prefer distributions that
deviate predictably from lognormality.
How many people want lognormal distributions?
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How to find out
$
?
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Aims of research
Question
Answer
1. How can we measure preferences for risk and return?
?
2. What are people’s preferences and how can we
represent them?
?
3. How well do Constant Relative Risk Aversion and lossaversion describe the data?
?
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Question 1 and answer 1: How can we measure
distribution risk preferences?
Income levels (% of pre-retirement income)
Cost
100 moveable people, one
of which represents the user
(experienced frequency
representation of probability)
Typical level of
retirement income
(Perceived loss point)
Minimum level
15
16
Riskless alternative
17
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State prices
The investor has a budget B and wishes to obtain a
probability distribution that will maximize his or her
expected utility without exceeding the budget.
Each one of the 100 people represents a different state
of the world, ranging from the best markets to the worst
markets. The cost of obtaining $1 in the ith state of the
world is the state price si (Arrow, Debreu, Dybvig)
The participant must choose wealth levels wi such that
w s
i i
i
19
=B
Assignment of state prices to markers
Cost
This marker has the lowest state price
(smallest influence on the meter)
This marker has the highest state price
(biggest influence on the meter)
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Inferring attributes of utility functions
from distributions
Given outcome wealth levels
and state prices si and budget
wi
B
We assume that a person building a p • u (w)
distribution is maximizing
N
subject to the cost constraint
w s
i i
=B
i =1
Maximizing the Lagrangian p • u ( w) k ( w'•s B)
results in the family of equations
u ' ( wi ) = Ksi
In other words, the slope of the utility curve at a
wealth level is proportional to the weight of the marker
assigned to that wealth level
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Estimating loss aversion
Marginal utility is the slope of the utility function. The ratio
of slopes at the loss point gives loss aversion parameter u'(w) for losses
=
u'(w) for gains
Perceived loss
Perceived gain
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Q2: What are people’s preferences?
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Q2: What are people’s preferences?
Do preferences
conform with
maximization of a
CRRA utility function?
Or do preferences exhibit
loss aversion?
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Design
141 Participants
• Age 30 – 60 μ=42 =7
• Income μ=$56,700 =$32,600
• Net worth μ=$112K, saved toward retirement μ=$30,000
• 74% married, 16% single, 10% divorced/widowed
Method
• Training: Participants made distribution and saw outcome
• Created two probability distributions of desired wealth in retirement
• Answered 50 question survey
• Actual industry risk tolerance quiz
• Psychological risk-taking scale
• Demographics
• Follow up one year later
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Q3: How well do CRRA and Loss Averse utility
functions capture preferences?
CRRA
x (1 )
u ( x) =
1
has been estimated to range from 1 to 10
Prospect Theory
x for x > 0
v( x) = (
)
for x < 0
x
Perceived loss
has been estimated to be 2.25
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Perceived gain
Central question 2
Part III:
Results
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Results of Q2:
What are people’s preferences?
40
35
30
25
20
15
10
5
Percentage of pre-retirement income
28
5
19
5
18
5
17
5
16
5
15
5
14
5
13
5
12
5
11
5
10
95
85
75
65
55
45
35
0
25
Average number of markers
45
Results of Q3:
Two different types of people
HighR2
60
50
40
30
20
10
95
10
5
11
5
12
5
13
5
14
5
15
5
16
5
17
5
18
5
19
5
85
75
65
55
45
35
0
25
Average number of markers
Low R2
Percentage of pre-retirement income
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30
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Eight Validations Within And Between Years
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Eight Validations Within And Between Years
Risk of chosen
portfolio
DB CRRA Coefficient
20-60% of explained variance
Psych Risk Scale
Industry Risk Scale
Age
Income
Gender
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Demographics
Correlation w/ Risk Aversion
Age
Income
Gender
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Test re-test reliability
Pearson
Within Y1
.70
Within Y2
.80
Between Years
.58
>$25K Saved
.78
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Conclusions
Question
Answer
How can we measure
Distribution Builder, a validated market research
risk return preferences
technique to measure, model, and analyze riskfor complex distributions? return preferences
How can we describe
preferences?
Roughly lognormal with some participants
massing probability at a reference point.
Can we model these
preferences?
CRRA fits half the participants well, while a loss
averse value function describes the other half.
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The end
(This talk is over.)
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PRESENTED BY
Shlomo Benartzi
Co-Founder, BeFi
Associate Professor Co-chair of the
Behavioral Decision Making Group
The Anderson School at UCLA
Warren Cormier
© BeFi Forum 2007
Co-Founder, BeFi
President, Boston Research Group