Economics Letters 114 (2012) 69–71
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Economics Letters
journal homepage: www.elsevier.com/locate/ecolet
A new measurement method of investor overconfidence
Ronald Huisman, Nico L. van der Sar, Remco C.J. Zwinkels ∗
Erasmus School of Economics, Erasmus University Rotterdam, The Netherlands
article
info
Article history:
Received 2 November 2010
Received in revised form
2 September 2011
Accepted 22 September 2011
Available online 2 October 2011
abstract
We present an alternative measurement method of investor overconfidence, using unique survey data on
stock market predictions of investors. We apply the Parkinson estimate based on extreme bounds around
the stock forecast to deduce investor confidence. The results support overconfidence.
© 2011 Elsevier B.V. All rights reserved.
JEL classification:
D1
G1
G2
Keywords:
Investor overconfidence
Survey data
Parkinson volatility
1. Introduction
Overconfidence is a key concept to understand why investment
strategies are so actively pursued and trading is excessive,
according to DeBondt and Thaler (1995) in their review on
behavioral finance (see also Barber and Odean, 2001). An
explanation for short-term momentum, long-term reversals and
the predictive power of fundamental to price ratios, among other
anomalies, is offered by the theory of Daniel et al. (1998). An
important aspect of their theory is overconfidence about the
precision of private information. Market outcomes appear to be
consistent with the implications induced by overconfidence and,
thus, supposedly reveal this judgment bias. It is an open question
what investor type is at the root of all this. According to Daniel
et al. (1998), even small individual investors may be overconfident,
though they presumably have less information.
The purpose of this paper is to examine the overconfidence
of retail investors, but not as revealed by realized returns in the
market or in an experimental setting. Instead, we directly test
whether a group of individual investors with accounts at one of
the biggest Dutch banks is overconfident in their stock market
predictions. Confidence measures are drawn from a repeated
∗ Correspondence to: Erasmus School of Economics, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands. Tel.: +31 10 408 1428;
fax: +31 10 408 9165.
E-mail address: [email protected] (R.C.J. Zwinkels).
0165-1765/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.econlet.2011.09.022
survey run on a biweekly basis from December 2009 through
October 2010. A novelty of our approach is the use of the
Parkinson (1980) volatility estimate. This measure is based on
predictions of the highest and lowest bounds around the twoweek Amsterdam Exchange (AEX) stock index forecast. Other
studies apply upper and lower bounds for 80% or 90% confidence
intervals (e.g. DeBondt, 1998, Graham and Harvey, 2005 and Glaser
and Weber, 2007). We argue that the maximum and minimum
bounds have the advantage of an easy appeal to respondents. In
order to measure the degree of overconfidence, the AEX volatility
index (VAEX) is used as an expected volatility benchmark. Our
results confirm that surveyed small individual investors exhibit a
significant overconfidence bias.
This paper is organized as follows. Section 2 describes the
survey data. Section 3 details the methodology applied. Section 4
presents our empirical results. Section 5 offers some concluding
remarks.
2. Data
The data we use is obtained from a repeated biweekly survey
we have unique access to. The sample of respondents consists
of private investors being a client of the Dutch ABN Amro bank,
one of the biggest Dutch banks. These private investors are active
investors who trade at least multiple times per week. ABN Amro
bank runs a specific operation for these investors; they therefore
know that they are part of a specific group within the ABN Amro
clientele. The group is referred to as ABN Amro Trading clients. We
have no additional insight into other client specific information.
70
R. Huisman et al. / Economics Letters 114 (2012) 69–71
Biweekly on Friday after the close of the exchange the
investors are invited by email to participate in a survey, an online
questionnaire. Each survey consists of two sets of questions. One
set of questions is designed by us and is the same over all surveys.
Our set of questions starts with the observation (translated from
Dutch): ‘‘Today, the AEX Index closed at XXX’’, with XXX replaced
by the exact closing price of the AEX Index. Then, the investors are
asked to answer the following questions (translated from Dutch
and in the exact order of questioning):
1. ‘‘On what level will the AEX Index end on dd-mm-yyyy?’’
2. ‘‘On what level will the AEX Index end maximally on dd-mmyyyy?’’
3. ‘‘On what level will the AEX Index end minimally on dd-mmyyyy?’’
With dd-mm-yyyy being a specific date of the Friday two weeks
after the survey.1
We use the outcomes of this set of questions as our
data. Because we specifically ask for both the expected level
and confidence bounds, this survey allows us to separate
overoptimism (i.e., an overly optimistic expectation for the level)
from overconfidence (i.e., a too narrow confidence bound).
The second set of questions is designed by ABN Amro bank and
varies each survey. These would be open questions such as ‘‘What
do you think that 2010 will offer you?’’ or ‘‘What is currently your
favorite stock?’’. After the forecasts were received, ultimately on
Sunday, a report is sent back to the ABN Amro Trading clients with
a summary of the outcomes and a sentiment index derived from
the results.
Table 1 contains a summary of the surveys. The first survey
(t = 1) was sent out on December 18, 2009 and the last was sent
out on October 8, 2010 (t = 21) resulting in 21 surveys.2 The table
shows for each survey the date on which the survey invitation was
sent (in the column heading survey date), the indicated forecast
date (forecast date), the close price of the AEX Index as mentioned
in the survey invitation (St ), the average forecast of the price
at the forecast date over the respondents (average Et (St +1 ) and
the number of respondents (n). The total number of responses
(obtained from all the surveys) is 2405.
Although it is not the focus of our paper, it can be seen from
the table that the average forecasts Et (St +1 ) are rather high:
the resulting average two-week log-return of 0.71% is equivalent
to 18.34% annually. Thus, expectations seem to be somewhat
optimistic. This does not mean, however, that our investors
are also overconfident. In the next section we will show that
overconfidence is directly related to the second moment of the
expected returns distribution and not to the first moment.
3. Methodology
This section describes the method we use to measure overconfidence. To do so, we compare the investors’ expected volatility for
the AEX Index with an implied volatility estimate. As we ask the investors specifically to forecast the maximum and minimum closing
price after two weeks, we can measure price uncertainty after two
weeks using the Parkinson (1980) measure. To do so, we introduce
some notation here. Let t be the survey number, as used in Table 1,
covering the forecast for period t + 1. Let nt be the number of respondents for survey t. Let Ei,t (St +1 ) be the forecast of investor i
in survey t about the of the closing price of the AEX Index on date
1 Or a Thursday if the specific Friday is a holiday.
2 The survey sent out on July 30, 2010 about the forecast for August 13, 2010 is
missing due to a technical error because of which the survey results were not saved.
t + 1. Let Hi,t and Li,t be trader i’s estimate for respectively the maximum (high) and minimum (low) value that the AEX Index might
obtain after two weeks in survey t.
Given Hi,t and Li,t we can apply the method proposed by
Parkinson (1980) to estimate trader i’s expected uncertainty or
volatility in survey t , σi,t , regarding the price of the AEX Index
over two weeks. Assuming a random walk, the Parkinson (1980)
volatility estimator is an estimate for volatility based on highs and
lows and reads:
σi,t =
√

26
ln(Hi,t /Li,t )2
4 ln(2)
,
(1)
√
where the 26 is used to annualize the volatility estimate.3 Since
we ask for expectations over two-week periods, this estimator
represents a forward-looking measure for volatility. It is therefore
not hampered by effects of discontinuous trading and market
frictions4 and provides an unbiased and highly efficient estimator
of the true volatility as shown in Parkinson (1980).
As said, we shall compare these estimates with a benchmark
volatility and for that we use the AEX volatility index (VAEX).
In capturing the implied volatility in prices of out-of-the-money
call and put options in the AEX index, the VAEX proxies for the
implied volatility in the market. The VAEX is published online and
is real-time available for free for everyone.5 Therefore it is not
just a theoretical construct but can be applied as a benchmark
in practice. As is the case for our (Parkinson, 1980) measure
applied to the survey data, implied volatility can be viewed as the
market’s expectation of future volatility and therefore serves as a
natural comparison. Several studies have looked into the predictive
accuracy and found implied volatility measures to be unbiased and
informationally efficient, see e.g. Yu et al. (2010).
4. Results
Table 2 lists the reported implied volatilities (VAEX) and the
average Parkinson (1980) volatility estimate over all respondents.
Consider for instance the results for survey 1. On that day, the
reported implied volatility estimate (VAEX) after market closure
was 24.86%. The equally weighted average over the Parkinson
(1980) volatility estimates of the respondents was 15.78%. The
fourth column heading ‘‘Hit ratio’’ is the ratio over all respondents
that estimated a lower volatility than the implied volatility (VAEX).
Apparently, a significant 81.94%6 of the respondents in survey
1 estimated a volatility level that was lower than the implied
volatility estimate on that day.
The results from the table reveal clear signs of overconfidence
relative to a benchmark volatility obtained from quoted option
prices. For all surveys, except for survey 9, the average over the
volatility estimates from the investors was lower than the implied
volatility observed at the time the survey was sent out. In 19 out
of the 21 surveys, significantly more than 50% of the investors
expected volatility to be lower than the implied volatility at that
time. Over the total of 2405 responses obtained from all surveys,
72.27% of the individual investor’s volatility forecasts were lower
than the implied volatility; a result that is significantly different
from 50%.
3 Having 26 two-week periods in a year.
4 For that matter, Martens and van Dijk (2007) confirm the potential of this
measure in the presence of microstructure noise.
5 Information and data can be downloaded from www.euronext.com. The VAEX
follows the VIX methodology for the US market based on S&P500 Index option
prices listed on CBOE.
6 Significantly different from 50%.
R. Huisman et al. / Economics Letters 114 (2012) 69–71
71
Table 1
Summary of the surveys.
Survey t
Survey date
Forecast date
St
Average Et (St +1 )
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
12-18-2009
12-31-2009
1-15-2010
1-29-2010
2-12-2010
2-26-2010
3-12-2010
3-26-2010
4-9-2010
4-23-2010
5-7-2010
5-21-2010
6-4-2010
6-18-2010
7-2-2010
7-16-2010
8-13-2010
8-27-2010
9-10-2010
9-24-2010
10-8-2010
12-31-2009
1-15-2010
1-29-2010
2-12-2010
2-26-2010
3-12-2010
3-26-2010
4-9-2010
4-23-2010
5-7-2010
5-21-2010
6-4-2010
6-18-2010
7-2-2010
7-16-2010
7-30-2010
8-27-2010
9-10-2010
9-24-2010
10-8-2010
10-22-2010
324.63
335.33
337.99
327.90
315.74
317.74
339.57
343.81
355.89
353.38
312.35
313.41
321.22
336.06
308.20
323.99
323.92
317.04
334.96
337.85
336.49
327.16
335.69
338.78
330.53
317.36
319.34
341.25
345.99
355.43
356.83
320.75
318.84
319.85
337.44
312.48
323.99
326.45
322.01
338.73
340.00
341.64
216
194
179
154
129
119
131
128
116
103
87
82
81
87
69
87
83
104
85
88
83
Table 2
Volatilities.
the Pearson–Tukey measure are even lower than those from the
Parkinson measure.
Survey t
VAEX
Parkinson’s estimate
Hit ratio
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
24.86
24.16
20.07
24.86
27.41
21.76
18.19
18.76
16.51
19.31
37.68
41.25
32.35
24.10
30.27
24.38
26.65
26.02
21.89
21.55
17.62
15.78
20.74
19.05
18.43
19.94
27.12
18.22
15.33
17.23
15.32
30.11
23.29
24.89
17.95
23.07
20.07
18.59
19.96
17.58
17.61
16.56
81.94**
70.62**
64.25**
79.87**
81.40**
65.56**
57.25*
75.00**
48.28
72.82**
72.41**
90.24**
79.01**
82.76**
73.91**
71.26**
80.72**
76.92**
69.41**
71.59**
55.42
*
**
Refers to significance at 5% level.
Refers to significance at the 1% level.
Table 1 shows that the number of respondents decreases
over time and more or less stabilized from survey 11. Survey
11 had 87 respondents and the number of respondents stays
approximately at this level in later surveys. There is no apparent
reason why the number of respondents decreased, perhaps
some investors lost interest. To test whether this might have
influenced our results, we also examine overconfidence starting
from survey 11. Over the 936 remaining responses, a significant
74.89% of the investor’s volatility forecasts were lower than
the implied volatility. As this number is even somewhat higher
than obtained from all responses, we therefore believe that our
result is robust with respect to developments in the sample of
investors.
The results are also robust to the volatility measure. We
calculated the volatilities using the Pearson and Tuckey (1965)
measure, which assumes the 95% theoretical confidence bounds.7
The results indicate that the expected volatilities resulting from
7 Results available upon request.
5. Concluding remarks
In this paper, we introduce a new measurement method for
investor overconfidence and test it on a new and unique data
set. We test whether a group of individual investors, clients
from one of the biggest Dutch banks, is overconfident in their
stock market predictions. Confidence measures are drawn from
a repeated survey in which we asked the investors to forecast
the price of a stock index at a future time and the maximum
and minimum price that could be obtained. Based on these
predictions of highest and lowest bounds, we directly estimate
their volatility expectations and compare these with VIX-like
implied volatility used as an objective market-based expected
volatility benchmark. Our results confirm that surveyed retail
investors exhibit a significant overconfidence bias.
Acknowledgements
We would like to thank the editor and an anonymous referee
for helpful comments. The usual disclaimer applies.
References
Barber, B., Odean, T., 2001. Boys will be boys: gender, overconfidence, and common
stock investments. Quarterly Journal of Economics 141, 261–292.
Daniel, K., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and
security market under-and overreactions. Journal of Finance 53 (6), 1839–1885.
DeBondt, W.F.M., 1998. A portrait of the individual investor. European Economic
Review 42, 831–844.
DeBondt, W.F.M., Thaler, R.H., 1995. Financial decision making in markets and firms:
a behavioral perspective. In: Jarrow, R.A., Maksimovic, V., Ziemba, W.T. (Eds.),
Finance, Handbooks in Operational Research and Management Science, vol. 9.
North Holland, Amsterdam, pp. 385–410.
Glaser, M., Weber, M., 2007. Overconfidence and trading volume. Geneva Risk and
Insurance Review 32, 1–36.
Graham, J.R., Harvey, C.R., 2005. The long-run equity risk premium. Finance
Research Letters 2, 185–194.
Martens, M., van Dijk, D., 2007. Measuring volatility with the realized range. Journal
of Econometrics 138, 181–207.
Parkinson, M., 1980. The extreme value method for estimating the variance of the
rate of return. Journal of Business 53, 61–65.
Pearson, E.S., Tuckey, J.W., 1965. Approximate means and standard deviations based
on distances between percentage points of frequency curves. Biometrika 52,
533–546.
Yu, W.W., Lui, E.C.K., Wang, J.W., 2010. The predictive power of the implied volatility
of options traded otc and on exchanges. Journal of Banking & Finance 34 (1),
1–11.