Time Varying Risk Aversion
Luigi Guiso
(Einaudi Institute for Economics & Finance- EIEF)
Paola Sapienza
(Northwestern University)
Luigi Zingales
(University of Chicago)
Banca d’Italia, December 3 2015
Large Fluctuations In The Discount Rate and
Asset Prices
Campbell, Giglio, and Polk, 2011 show that at the end of 2008
there was a sharp change in the aggregate discount rate.
Where do they come from?
 Fluctuations
in the individual risk aversion
 Shifts
in the distribution of wealth that
change the aggregate risk aversion
 Changes
in “sentiment”
What Explains Them?

If changes in individual risk aversion, what
explains them?

Changes in wealth ?



Changes in preferences (curvature)?



Due to habit persistence ?
Due to loss version?
Why?
At the center of the debate on rationality of
markets
At the center of the debate on fair value
accounting
This Paper
 All
the evidence points to a change in the
aggregate risk aversion around the crisis.
 In this paper we study whether around
the crisis
1.
2.
3.
Individual risk aversion changes
These changes are large enough to explain
changes in the aggregate risk aversion
What can explain these changes
How to Measure Risk Aversion?
Indirectly:
1.
From asset prices’ movements: self referential
2.
From holdings of risky assets: a) need assume homogenous
beliefs; b) adjustment costs bias results
Directly:
1. Experiments:

Selected participants; Limited size gambles
2. Survey based:

Hypothetical questions but

external validation

lots of control
Sample



Sample of 1,686 random clients of a major Italian bank
(Unicredit) first sampled in 2007.
With respect to Italian population:
 Richer, More North than South, a bit older than
average
Re-interviewed in June 2009 with a much more limited
set of questions: 1/3 response rate, no evidence of
selection
Selection
Age
Male
Married
North
Center
Education
Trust
Trust advisors
Risk attitude: qualitative
Risk attitude: quantitative indicator
Willingness to accept lottery in euro
Stock financial asset Jan 2007 in euro
Stock financial asset Jun 2009 in euro
Stockownership Jan 2007
Stockownership June 2009
Share in stocks Jan 2007
Share in stocks Jun 2009
Holder of risky assets Jan 2007
Holder of risky assets Jun 2009
Non participants
(N. 1,020)
55.02
0.7
0.69
0.53
0.24
12.44
0.25
2.25
2.88
5.85
3,278.13
150,976.6
139,723.4
0.438
0.413
0.1
0.084
0.793
0.743
Participants
(N. 666)
54.5
0.7
0.67
0.49
0.25
13.18
0.27
2.17
2.85
5.85
3,266
158,950.2
142,287.2
0.44
0.42
0.106
0.078
0.81
0.732
p-value of test of
equality
0.395
0.767
0.40
0.12
0.606
0
0.229
0.05
0.305
0.888
0.935
0.219
0.727
0.933
0.798
0.54
0.511
0.411
0.627
Data content

For all the sample (even non respondents)
we have administrative records on




26 financial assets categories at this bank before
and after the crisis (stocks and flows)
We know the proportion of financial wealth held at
the bank
We have the value of the house
Can estimate stock of wealth and its change
Risk Aversion Questions: 1
 Qualitative
(SCF): “when I invest I try to
achieve”
1. Very
high returns, even at the risk of a high
probability of losing part of my principal
2. A good return, but with an OK degree of safety of
my principal;
3. A OK return, with good degree of safety of my
principal
4. Low returns, but no chance of losing my principal
.6
Qualitative Measure
proportion
.4
.5511
.2
.2718
.1592
0
.018
0
1
2
risk aversion
3
4
Risk Aversion Questions: 2
 Quantitative: “Imagine being in a room. To get
out you have two doors. Behind one of the two doors
there is a 10,000 euro prize, behind the other nothing.
Alternatively, you can get out from the service door
and win a known amount.” [Deal or no deal]
=> If you were offered 100s euro, would you choose the
service door?
 500, 1500, 3000, 4000, 5000, 5500, 7000,9000, > 9000

Allows to obtain an estimate of the investor (absolute)
certainty equivalent [Holt & Laury, AER ]
100
.15
3000
5000
.1
>9000 9000
1500
500
7000
4000
.05
5500
0
fraction
Quantitative Measure
0
2
4
6
8
risk aversion indicator : lottery 2007
10
Self Assessment
 After
the financial crisis, in your investment
choices you are:
0: More or less like before
1: More cautious
2: Much more cautious
Outline
1.
2.
3.
4.
5.
6.
7.
Are these measures just noise?
Did they change?
Did they change enough?
Why did they change?
An hypothesis
An experiment
Conclusions
1
Are These Measures Just
Noise?
Check Consistency
1.
2.
3.
4.
Consistency across measures
Consistency over time
Correlated with self-assessment
Correlated with actual choices
1. Level predict stockholding in 2007
2. Change predicts change in risky
assets holding and in risky asset
share
Consistency across measures
Correlations between
p-value
qualitative
and
quantitative
indicator:
2007
qualitative
and
quantitative
indicator:
2009
change in
qualitative and
change in
quantitative
indicator:
2007-2009
change in
qualitative
indicator and
change in
cautiousness
change in
quantitative
indicator and
change in
cautiousness
0.1163
0.1596
0.1184
0.119
0.074
0.00
0.00
0.002
0.002
0.056
Predicts stockholding in 2007
Whole sample
(1)
Risk Aversion
Qualitative: 2007
-0.001
(0.005)
0.154***
0.025***
-0.023***
0.020***
0.047***
0.152***
1,464
-0.012***
(0.004)
0.162***
0.026***
-0.023***
0.019***
0.049***
0.137***
1,311
-0.122***
(0.032)
Risk Aversion
Quantitative: 2007
Male
Age
Age2/100
Education
Trust Advisor 2007
Log Net Wealth: 2007
Observations
(2)
Drop inconsistent
answers
(3)
0.129***
0.022**
-0.020**
0.018***
0.039***
0.145***
1,494
Predicts risky share in 2007
Whole sample
RA qualitative 2007
-0.139***
(0.020)
RA quantitative: 2007
Male
Age
Age2
Education
Trust advisor 2007
Log net wealth 2007
Log(1-habit): 2007
Obs.
Drop inconsistent
answers
0.073***
0.012
-0.000
0.008**
0.020**
(0.009)
0.213***
(0.024)
-2.280***
(0.550)
1463
-0.003
(0.005)
0.115***
0.022**
-0.000**
0.015***
0.032***
(0.008)
0.121***
(0.029)
1494
-0.012***
(0.004)
0.099***
0.016*
-0.000
0.010***
0.030***
(0.010)
0.220***
(0.037)
-2.450***
(0.290)
1281
Change in RA predicts change in
ownership and risky share
Change in RA:
qualitative measure
Change in ownership
-0.175*
Change in share
-0.010
(0.106)
(0.013)
Change in RA:
quantitative measure
Male
Age
Age2
Education
Δ trust in advisor
Δ Log net wealth 20092007
Obs.
-0.050**
-0.006**
0.379**
0.074
-0.001
0.008
-0.068
0.902
(0.021)
0.322*
0.069
-0.001
0.013
-0.085
1.101
-0.018
-0.000
-0.000
-0.002
-0.006
-0.168***
(0.003)
-0.032
-0.001
0.000
-0.001
-0.014
-0.155***
568
499
571
568
TVRA
2
Did These Measures
Change?
Did Risk Aversion Change? : Qualitative Indicator
Moderate RET &
RIS
.6
.4369
.3
No
risk
.2
.2718
No
risk
.2
proportion
Medium RET
& RIS
.4
.4
.5511
.4264
.1231
.1592
.1
High RET
& High RIS
i
.0135
0
0
.018
0
1
2
risk aversion
2007
3
4
0
1
2
risk aversion
2009
3
4
4,000
Did Risk Aversion Change: Quantitative Measure
2009
3,000
2,000
1500
2007
2009
0
0
1,000
2007
4000
1,000
2,000
2816.07
Risk aversion indicator
3,000
4,000
4257.06
mean of ra06
mean of ra09
Mean
p 50 of ra06
Median
Certainty Equivalent
p 50 of ra09
3
Did They Change
Enough?
Magnitude

These changes imply an increase



in the average risk premium from 800 to around
2,200 euros and
in median risk premium from 1000 to 3500 euros.
These estimates imply that



average risk aversion increased by a factor of 2.7
the median risk aversion by a factor of 3.5!
Since net worth decreased on average by 6%
between end of 2007 and June 2009 most of the
change is a change in relative risk aversion
Does change in individual risk aversion
drives aggregate risk aversion?
Total sample
Wealth Wealth
weights: weights:
current 2007
ARA 2007 1.30
1.30
ARA 2009 2.25
2.27
ARA_09/ARA_07 1.70
1.95
Stockholders
Wealth
weights:
current
1.22
2.40
1.97
Wealth
weights:
2007
1.22
2.42
1.98
4
What Does Explain These
Changes?
Natural candidates
1.
Changes in wealth because of preferences
1-g
with habits
(Wit - X )
g itWit
u(Wit ) =
it
1- g it
=> A(W )W =
(Wit - X i )
2. Experienced losses in Loss-Gains utility
models (Barberis, Huang, Santos, 2001)
– after the initial hit, investors are “fragile”, “shaken up”
– can’t take any more bad news => become more risk
averse
=> Negative correlation between financial losses
(change in wealth) and change in risk
aversion
Evidence: non parametric
 Estimate
non parametric relation
between change in risk aversion and
financial losses during the crisis
 Financial loss:

Proportional loss in financial portfolio between
September 2008 (pre-Lehman) and February
2009 (bottom of stock market)
Change in qualitative indicator
Half of the
sample
• RA increases for all groups, even those experiencing no losses ;
• no negative correlation
Change in CE of quantitative indicator
(Change in CE)/expected value of lottery
Half of the
sample
Correlation should be strongly positive. CE increases for all even at
no losses; no positive correlation
Change in qualitative indicator and
change in total wealth
Change in CE and change in total wealth
(Change in CE)/expected value of lottery
Summing
 No
correlation between financial losses
and qualitative indicator
 Some positive correlation with CE using
quantitative indicator for large losses

Consistent with loss aversion models
What about those who suffer no losses?
(295 individual, half of the sample)
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
4500
4350
2740
2007
Median certainty equivalent: no
losses incurred (n=295)
2009
Certainty equivalent:mean
Certainty equivalent:mean
Mean certainty equivalent: no
losses incurred (n=295)
4000
4000
3500
3000
2500
2000
1500
1500
1000
500
0
2007
2009
• CE decreases as in total sample also for those
who experience no loss or even gain
• Same if we look at qualitative indicator (change of
similar magnitude as in total sample)
Other channels/objections
1.
Background risk:
Risk of unemployment and earnings variability
=> Public employees and retirees are completely
shielded

2.
Reduction in future earnings
=> Should have a larger effect on the RA of the
younger than that of the older (if shocks to
income persistent)
Background risk & non losses
0
Change in CE/Lottery expected
value
Government employee
-0.05
Change in CE/Lottery expected
value
Not gov employee
0
-0.05
-0.1
Retired
Not retired
-0.1
-0.15
-0.15
-0.2
-0.2
-0.25
-0.3
-0.25
-0.3
-0.35
-0.4
-0.45
-0.35
CE equivalent does not drop less for those facing less
background risk (same if use qualitative measure)
Drop in future earnings & no losses
Change in qualitative indicator
(sample: no financial losses)
Change in CE/Lottery expected
value (sample:no financial
losses)
0
Age <=40
Age >=65
-0.1
-0.2
Age
-0.3
-0.4
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Age <=40
Age >=65
-0.5
CE equivalent does not drop more for the young who
have a longer horizon , qualitative indicator of RA does
not increase more
Expectations and Risk Aversion?

Do people mix expectation and risk aversion?
We elicited the subjective distribution of stock
returns in 2007 and 2009
 Obtain a measure of the change in expected stock
market return and of change in uncertainty about
stock market returns
 Both have no effect on RA
 Some evidence that a measure of change
knightian uncertainty and trust has affected
change in RA

RA: stock market expectations and trust
Δ Qualitative measure of RA
Risk aversion qualitative 2007
Age
Male
Education
Diff. Log W 2009-2007
Δ Total Habit 2009-2007
Δ Stock Market Expectation
Δ Range Stock Market
Δ Trust Stock Market
-0.630***
(0.051)
0.003
-0.169**
-0.017**
-0.177
(0.263)
-1.143
(3.444)
0.025
(0.051)
-0.054
(0.098)
-0.082**
(0.035)
Δ Quantitative
measure of RA
-0.875***
(0.044)
0.033***
0.632*
0.001
-0.152
(0.932)
0.856
(13.057)
-0.140
(0.209)
-0.326
(0.391)
-0.431***
(0.123)
Conclusions so Far
 Survey
measures of risk aversion
increase substantially after the crisis
 Even individuals holding only safe assets
see their risk aversion go up.
 Changes not driven by losses, changes in
wealth, or background risk.
 In fact, none of the existing models can
explain them -> deficient models ?
5
An Hypothesis
The Neuro Biology of Fear
 Increasing
number of studies have identified
the neurological bases of risk aversion.
De Martino et al. (2010): amygdala-damaged
patients take risky gambles much more often
 Kuhnen and Knutson (2005): activation anterior
insular followed by an increase in risk aversion.
 KK (2011): erotic pictures induce people to take risk,
while negative emotions have the opposite effects.

An Hypothesis
 Risky
decisions are made by the frontal lobe
(the computational part of the brain)
 The frontal lobe takes for granted the “values”
(parameters of the utility function).
 A scary experience activates the amygdala,
which sends signal to the frontal lobe to be
more risk averse in its calculations.
 How to prove it?
5
An Experiment
The Experiment

We conducted a laboratory experiment with students
at Northwestern.

In the lab everything (background risk, expectations,
etc.) is controlled for.

Treat half of participants with an excerpt from the
2005 movie, “The Hostel” (2007 best horror movie)
 Face all with the same risky choice questions as in
sample of investors
 Does an horror movie experience change the risk
aversion? By as much as in the data?
HOSTEL
Results
(1)
VARIABLES
Treated
Certainty equivalent of lottery
-671.7**
(300.2)
Sex
Income in $M
Constant
Observations
R-squared
(2)
-637.5**
(300.1)
(5)
(6)
Prob. Choose Low Risk Inv.
0.135*
(0.0689)
0.14*
(2.02)
347
-0.162*
(313.3)
(2.31)
-980.8
0.195
(1,032)
(0.65)
2474***
2415.5***
0.391***
0.428**
(214.9)
(293.5)
(0.046)
(6.76)
207
203
210
206
0.023
0.03
0.02
0.04
Heterogeneity





Not everybody is scared the same.
Some people like horror movies.
Does the impact differ depending on how
scared you were?
In half of the sample we asked people how
much they liked horror movies on a scale
from 0 to 100.
Roughly a third do not like it at all
Splitting on Preferences for Horror Movies
Effect of fear on risk aversion
3500
Certainty equivalent
3000
non treated; 2632
14%
28%
2500
2000
1500
non treated; 3070
non treated; 3051
treated; 2648
treated; 2200
55%
treated; 1200***
1000
500
0
Dislike
1
Indifferent
Like
• Not everybody is scared the same, some people like horror movies
•Split according to how much they like horror movies
A Circular Argument?
 Was
an increase in risk aversion that
caused the crash or vice versa?
 Initial drop in expected cash flow -> fear ->
-> increase in risk premium-> further drop
 Our argument suggests that stock prices
may overshoot movements in
fundamentals (cash flow).
Conclusion
 We
showed that individual risk aversion
increased a lot during the financial crisis:
average risk aversion increased by a factor 2.5
 median by a factor of 3.5

 These
changes cannot be explained by
standard models
 They are consistent with a sudden increase
in fear
Persistency?
 Malmendier
and Nagel (2011) find a cohort
effect of depression-babies in the risk
aversion measure of the SCF.
 Unfortunately, our sample is unable to
answer this question (even if we were to
go back) because of the subsequent
events in the eurozone that made the 2008
shock not an isolated incident.
Short and clearer version?
Risk off
“Why some people are more cautious with their finances
than others”,
The Economist, Jan 25 2014
Expectations
 If
you invest 10,000 euro in a mutual fund
that replicates the Italian stock market, in a
year what is the
1. The minimum value of your investment
2. The maximum value of your investment
3. The probability that value greater than or
equal to (Min+Max)/2
(uniform or triangular)
Evidence: controlled regressions
Dlog Ait = b Ait-1 + a 0DlogWit + a 2DlogZit + a 3Ds + eit
2
it
Negative effect
Control for initial risk aversion
2
 where  it = variance of log earnings, proxying
background risk
 Method: ordered probit and interval regression
 Change in total wealth: change in home equity +
change in fin wealth invested through Unicredit /
proportion of fin wealth invested through Unicredit

Controlled regression
Noisy data or deficient models?
 If
RA measures just reflect noisy data they
should have little little predictive power on
investors portfolio decisions
 If have content, measured changes in risk
aversion should be reflected in portfolio
rebalancing
Implementation
Let R = a * - a = active rebalancing after a drop in the price of stock p <1
a = share in stocks after drop in stock price but prior to adjustment
a * = new optimal share in stocks
a M = Merton share
M
g
p
a
R =aM - M
= k 1Z1 + k 2 Z21 Þ sell stocks if g increases and buy if p drops
M
g F pa +1- a
g F : post shock RA. Construct emprical counterparts of Z1 and Z2 and run
R = k 1Z1 + k 2 Z2
Can be estimated because we observe actual monthly transactions from administrative data
Rebalancing and risk aversion
Oct 08
(1)
Fear Model Factors
Risk aversion ratio (Z1)
Post shock share: Sep 08 (Z2)
Post shock share: Oct 08 (Z2)
Post shock share: Nov 08 (Z2)
Post shock share: Dec 08 (Z2)
Post shock share: Jan 08 (Z2)
Post shock share: Feb 08 (Z2)
0.049**
(0.024)
-0.054*
(0.031)
Oct 08
/Jan 09
(2)
Oct 08
/Feb 09
(3)
Oct 08
/Mar 09
(4)
Oct 08
/Apr 09
(5)
Oct 08
/May 09
(6)
0.040
(0.026)
0.036
(0.028)
0.079**
(0.038)
0.077**
(0.037)
0.082*
(0.042)
-0.026
(0.037)
-0.048
(0.042)
-0.112**
(0.050)
-0.137***
(0.052)
-0.143**
(0.058)
6
Testing the Fear
Hypothesis
Discerning fear and habits
 Experiment
not directly connected to field
data
 Can we discern fear from habit in the
data?
 Models with habits and models with fear
have different implications for active
rebalancing after a shock to stock prices
Implementation
Let R = a * - a = active rebalancing after a drop in the price of stock p < 1
W / W ' = (S + F ) / ( pS + F ) = ratio of initial and post-shock wealth
a = share in stocks after drop in stock price but prior to adjustment
a * = new optimal share in stocks
a M = Merton share, h initial habit
Habit Model
a M (1- a M )(1- h)(1- p)
R=
= Z 2 ³ 0 Þ buy stocks
M
M
pa (1- h) + 1- a (1- h)
Fear Model
R =aM(
g
p
) = Z1 Þ sell stocks if drop in g (curvature) large
g F pa M + 1- a M
Constructs emprical counterparts of Z1 and Z 2 and run horse race
R = k 1Z1 + k 2 Z 2
Can be estimated because we observe actual monthly transactions from administrative data
Fear and Rebalancing
Oct 08
(1)
Fear Model Factors
Risk aversion ratio (Z1)
Post shock share: Sep 08 (Z2)
Post shock share: Oct 08 (Z2)
Post shock share: Nov 08 (Z2)
Post shock share: Dec 08 (Z2)
Post shock share: Jan 08 (Z2)
Post shock share: Feb 08 (Z2)
0.049**
(0.024)
-0.054*
(0.031)
Oct 08
/Jan 09
(2)
Oct 08
/Feb 09
(3)
Oct 08
/Mar 09
(4)
Oct 08
/Apr 09
(5)
Oct 08
/May 09
(6)
0.040
(0.026)
0.036
(0.028)
0.079**
(0.038)
0.077**
(0.037)
0.082*
(0.042)
-0.026
(0.037)
-0.048
(0.042)
-0.112**
(0.050)
-0.137***
(0.052)
-0.143**
(0.058)
Implications
 The
portfolio rebalancing we observe after
the crisis is inconsistent with a model of
habit persistence and consistent with a
change in risk aversion driven by fear.

The fear-based model is also the only one
able to account for the experimental
evidence.
 Question
designed to resemble a popular
game (“Deal or no Deal”), analyzed by
Bombardini and Trebbi (2010).
 They find that in this game people exhibit
a Von Neumann and Morgenstern utility
function with a constant relative risk
aversion close to 1.