EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 203
MYOPIC LOSS AVERSION,
DISAPPOINTMENT AVERSION,
AND THE EQUITY PREMIUM
PUZZLE
BY DAVID FIELDING
AND LIVIO STRACCA
January 2003
EUROPEAN
CENTRAL
BANK
WO R K I N G PA P E R S E R I E S
WORKING PAPER NO. 203
MYOPIC LOSS AVERSION,
DISAPPOINTMENT AVERSION,
AND THE EQUITY PREMIUM
PUZZLE1
BY DAVID FIELDING2
AND LIVIO STRACCA3
January 2003
1 We thank Ali al-Nowaihi, participants at a seminar at the University of Leicester and an anonymous referee for useful comments.The
views expressed in this paper are only those of the author and are not necessarily shared by the European Central Bank.The
opinions expressed herein are those of the authors and do not necessarily represent those of the European Central Bank.
This paper can be downloaded without charge from http://www.ecb. int or from the Social Science Research Network electronic library
at: http://papers.ssrn.com/abstract_id=xxxxxx
2 University of Leicester, Department of Economics
3 European Central Bank (ECB), corresponding author, email: [email protected]
© European Central Bank, 2003
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ISSN 1725-2806 (online)
Contents
Abstract
4
Non-technical summary
5
1
Introduction
7
2
The “behavioural finance” explanations of the equity premium
puzzle
2.1 The Benartzi and Thaler (1995) approach
2.2 The Ang-Bekaert-Liu (2000) approach
3
Loss aversion, disappointment aversion, and the investor time
horizon
3.1 A simple specification of preferences for loss and
disappointment aversion
3.2 A model of expected returns under loss aversion and
disappointment aversion
10
10
11
12
12
15
4
The empirical analysis
4.1 The data
4.2 Results
17
17
18
5
Discussion
21
6
Conclusions
23
References
24
Charts and tables
26
European Central Bank working paper series
32
ECB • Working Paper No 203 • January 2003
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ECB • Working Paper No 203 • January 2003
Non-technical summary
The equity premium puzzle introduced by Mehra and Prescott (1985) is still far
from having received a fully-fledged and convincing explanation in the literature.
Despite the sheer research effort, the profession has still to reach a consensus on
the explanation of the large equity premium observed historically in the United
States and in other industrialized countries.
This paper takes a close look at the ’’behavioural finance’’ explanations of the
equity premium puzzle proposed thus far in the literature, namely myopic loss
aversion (Benartzi and Thaler, 1995) and disappointment aversion (Ang, Bekaert
and Liu, 2000). Both theories posit that agents’ preferences, unlike in the expected
utility approach, are defined not in absolute terms but against a reference point.
Moreover, the maintained assumption under both approaches is that agents narrowframe the problem of how to allocate wealth between safe and risky assets and
consider this problem in an independent manner, focusing on the prospects for
returns without considering other sources of variability in consumption.
In particular:
•
Myopic loss aversion posits that economic agents are averse to losses at an
irrationally short horizon, due to institutional reasons or because they are
affected by a behavioural bias (in particular, because they are too anxious to
evaluate the performance of their portfolio on a short-term basis). Benartzi and
Thaler showed that the observed equity premium is consistent with a moderate
degree of loss aversion at an investment horizon of approximately one year.
Under loss aversion, agents have a fixed reference point against which they
evaluate gains and losses.
•
Disappointment aversion shares some features with loss aversion but is based
on the idea that reference points are determined endogenously. In particular,
the certainty equivalence of a lottery may become a reference point for agents,
and outcomes in excess (short of) the certainty equivalence are a source of
elation (disappointment) for the agent. Reflecting the idea that pain is more
urgent than pleasure, the disappointment related to outcomes below
expectations is assumed (and normally found) to be stronger than the elation
related to outcomes exceeding expectations.
ECB • Working Paper No 203 • January 2003
5
This paper focuses especially on the role of the time horizon in determining the size
of the equity premium. This seems a crucial dimension of the problem because it is
quite easy to explain a high equity premium with a short time horizon, at which
stocks are very volatile, while it may be more difficult at longer time horizons. The
empirical analysis in the paper, based on data for excess returns on stocks in the
United States from 1871 onwards, shows that an explanation based on loss
aversion is crucially dependent on a very short time horizon, and already a horizon
of three years or so seems too long for loss aversion to be a satisfactory explanation
of the historical equity premium. By contrast, disappointment aversion appears to
be a satisfactory explanation of the historical equity premium even at horizons as
long as ten years. This reflects the empirical finding that, while it is almost
impossible to lose on stocks compared with safe assets if the time horizon is
relatively long, stocks may disappoint very strongly even in the long run.
Overall, the results in this paper suggest that the invariance to the time horizon of
disappointment aversion makes it an interesting explanation of the equity premium,
possibly more robust than loss aversion because it can accommodate different time
horizons. Moreover, we offer some speculations which point to the idea that
disappointment aversion can be considered as a quite realistic representation of
preferences especially in the context of delegated portfolio management with a
principal-agent relationship affecting the nature of the portfolio selection problem.
6
ECB • Working Paper No 203 • January 2003
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ECB • Working Paper No 203 • January 2003
25
Chart 1 – Value of one dollar invested in equity and Treasury bills in 1871
120000
300
100000
250
80000
200
60000
150
40000
100
20000
50
0
0
30
40
50
60
Equity (l.h.s.)
70
80
90
00
T reas ury bi ll (r.h.s.)
Chart 2 – Value share of equity and Treasury bill investment, in USD
500
400
300
200
100
0
1880
26
1900
1920
1940
1960
1980
2000
ECB • Working Paper No 203 • January 2003
Chart 3 – Excess returns on equity, 1871-2001
1-year horizon
60
40
20
0
-20
-40
-60
1880
1900
1920
1940
1960
1980
2000
1900
1920
1940
1960
1980
2000
10-year horizon
500
400
300
200
100
0
- 100
1880
ECB • Working Paper No 203 • January 2003
27
Table I – Excess returns on equity at a 1-year and 10-year horizon
Sample period: 1881-2001
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
ER1
ER10
6.590311
7.015681
52.65015
-46.19185
19.46995
-0.129030
2.815639
115.5088
78.71211
494.6028
-59.84369
132.0429
0.896184
2.872475
0.507110
0.776037
16.27876
0.000292
Pos./Neg.
2.27
24.67
Observations
121
121
ER1
ER10
8.519619
9.777976
52.65015
-46.19185
20.68226
-0.195230
2.768986
162.4898
140.4511
494.6028
-59.84369
142.1342
0.336087
2.120308
0.651786
0.721883
3.881302
0.143610
Sample period: 1926-2001
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
Probability
28
Pos./Neg.
2.74
37.2
Observations
76
76
ECB • Working Paper No 203 • January 2003
Chart 4 – Loss aversion and the time horizon
Sample period: 1881–2001
Estimated loss aversion
30
Loss aversion
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
8
9
10
Tim e horizon (ye ars)
Sample period: 1926–2001
Estimated loss aversion
40
Loss aversion
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
Time horizon (years)
ECB • Working Paper No 203 • January 2003
29
Chart 5 – Disappointment aversion and the time horizon
Sample period: 1881-2001
Disappointment aversion
E s tim ated dis appointm ent avers ion
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10
8
9
10
T im e h o riz o n (ye a rs)
Sample period: 1926-2001
Disappointment aversion
E s tim ated dis appointm ent avers ion
3
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
7
Tim e horiz on (ye a rs)
30
ECB • Working Paper No 203 • January 2003
Table II – Excess returns on equity, 1872-2001
Dependent Variable: ER1
Method: Least Squares
Sample(adjusted): 1872 2001
Included observations: 130 after adjusting endpoints
Coefficient
6.381532
Variable
C
0.000000
0.000000
19.42507
48676.02
-569.6135
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Std. Error t-Statistic
1.703692 3.745708
Prob.
0.0003
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
6.381532
19.42507
8.778669
8.800727
1.944997
60
40
20
0
- 20
- 40
- 60
1880
1900
1920
1940
1960
Recursive Residuals
1980
2000
± 2 S.E.
20
10
0
- 10
- 20
1880
1900
1920
1940
1960
Recursive C(1) Estimates
ECB • Working Paper No 203 • January 2003
1980
2000
± 2 S.E.
31
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