Directory UMM :Data Elmu:jurnal:J-a:Journal Of Banking And Finance:Vol24.Issue8.2000:
Journal of Banking & Finance 24 (2000) 1275±1287
www.elsevier.com/locate/econbase
Trading volume and autocorrelation: Empirical
evidence from the Stockholm Stock Exchange
Patrik Safvenblad
*
Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83, Stockholm, Sweden
Received 16 July 1998; accepted 9 June 1999
Abstract
In accordance with studies for other markets, Swedish index returns exhibit high
autocorrelation, (a) after days of above average performance of the stock market, (b)
after low absolute returns, (c) when trading volume is low, and (d) following Fridays.
Contrary to the non-synchronous trading and the transaction cost hypotheses, all
results extend to individual stock returns. It is concluded that autocorrelation patterns
are related to the trading patterns of individual investors, and not the cross-security
information processing of the market. In particular, the observed autocorrelation
structure corresponds to feedback trading. Ó 2000 Elsevier Science B.V. All rights
reserved.
JEL classi®cation: G14
Keywords: Return autocorrelation; Trading volume; Feedback trading
1. Introduction
It has been well documented that high frequency stock index returns are
positively autocorrelated. Several theoretical explanations have been put forward, most prominently non-synchronous trading, transaction costs,
*
Tel.: +46-8-736-9161; fax: +46-8-312327.
E-mail address: ®npsa@hhs.se
0378-4266/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 0 7 1 - 0
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afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
time-varying expected returns and feedback trading. Several empirical papers
test the predictions of the various models on data.
So far, the empirical tests are inconclusive; Atchison et al. (1987) reject nonsynchronous trading, Mech (1993) and Ogden (1997) favour trading costs or
information frictions while Boudoukh et al. (1994) argue that special patterns
of non-trading may explain the observed levels of autocorrelation.
This paper introduces a new element to the analysis: the return autocorrelation of individual stocks. As all theoretical models of index return autocorrelation include assumptions about the (absence of) autocorrelation of
individual stock returns, it is possible to draw conclusions on the likely origin
of index return autocorrelation based on the autocorrelation of individual
stock returns. To the best of the author's knowledge, this possibility has so far
not been used in the literature on index return autocorrelation.
The empirical study uses data from the Stockholm Stock Exchange (SSE), a
market not widely studied in this context, thus reducing data-snooping biases.
The small number of traded stocks makes it easier to have full control over the
creation of index returns. In addition, SSE is a limit order market, eliminating
specialist trading strategies as the source of observed autocorrelation. The
properties of index return autocorrelation are similar to those found for other
stock markets. It is thus likely that the key empirical results will carry over to
other markets.
Index return autocorrelation on the SSE is high, and depends on (among
other things) realised return, volatility, trading volume and day-of-the-week.
The same patterns are found for individual stock returns. This is inconsistent
with popular explanations of index return autocorrelation and therefore it is
concluded that the observed autocorrelation patterns are best explained as the
result of trading strategies such as feedback trading.
2. Some earlier empirical evidence
Table 1 gives a sample from the rich earlier empirical evidence of autocorrelation in daily stock returns. Index return autocorrelation is predominantly
positive, regardless of country or sample period. 1
The evidence of autocorrelation in individual stock returns is less consistent.
US studies report average autocorrelations close to zero (e.g. Atchison et al.,
1987). Later work shows that the level of autocorrelation is increasing in ®rm
1
Empirical evidence is given by, e.g., Koutmos (1997). Positive index return autocorrelation is
also observed for other return frequencies, from intraday to monthly returns. See, for example,
Stoll and Whaley (1990) for intraday returns and Lo and MacKinlay (1990) for weekly and
monthly returns.
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1277
Table 1
Selected empirical evidence on autocorrelation in daily stock and index returnsa
Source
Series
Sample period
Index
returns
Atchison et al. (1987)
Berglund and
Liljeblom (1988)
Chan (1993)
CRSP
Helsinki
1978±81
1977±82
0.17
0.49
Smallest N Y S E decile
Largest N Y S E decile
C R S P small stocks
1980±89
1980±89
1962±87
0.05
0.35
C R S P large stocks
Tel Aviv
Paris small stocks
Paris large stocks
Stockholm small stocks
Stockholm large stocks
1962±87
1987
1991±95
1991±95
1980±95
1980±95
Lo and MacKinlay
(1990)
Ronen (1998)
Safvenblad (1997b)
Comparison: this paper
Stock
returns
0.02
0.32
)0.09
0.35
0.04
0.16
0.24
0.30
0.15
)0.12
0.07
0.08
0.15
a
Estimates and signi®cance levels as reported in cited articles. Where signi®cance levels were not
reported, they were calculated using asymptotic standard errors.
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
size and signi®cantly positive for larger stocks (Chan, 1993; Sias and Starks,
1997). Safvenblad (1997a) reports similar results for French stocks.
In less liquid markets, positive return autocorrelation for stocks has been
documented in several markets, including Austria (Huber, 1997), Finland
(Berglund and Liljeblom, 1988), Israel (Ronen, 1998), Malaysia and Singapore
(Laurence, 1986).
3. Data
The sample consists of daily returns and trading volume for 62 major stocks
traded on the SSE over the period 1980±1995. The stocks were selected from all
traded stocks based on sample length (more than ten years) and trading volume
(highest), including all listed share classes of each company. The sample covers
approximately 90% of total trading volume on the exchange. Data series were
collected from Findata. Details on individual stocks are available in Safvenblad (1997b).
Stocks are split into three groups, Large, Medium and Small, according to
average trading volume. For each of these groups, results are reported for the
average of individual stocks as well as for an equally weighted index. Results
are also reported for All, the average of all stocks and a corresponding index.
For individual stocks, non-trading and ex-dividend days (annual) have been
omitted and only closing traded prices are used. For index returns, non-trading
1278
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
days are ®lled in with the closing bid quote and dividends are reinvested
without transaction costs. 2
4. Possible explanations of return autocorrelation
Swedish index returns are strongly positively correlated. Table 2 reports an
index return autocorrelation of 0.345 for the All portfolio. For individual
stocks, autocorrelation is signi®cantly positive and much higher than reported
in studies on US data. As for French and US stocks, autocorrelation is increasing in trading volume; the average autocorrelation for the stocks in Small
is 0.084, and 0.153 for the stocks in Large.
This result indicates that Swedish stock returns are generally positively
autocorrelated, but that larger bid±ask spreads induce negative return autocorrelation for smaller stocks. The positive autocorrelation is incompatible
with most models of price formation, including non-synchronous trading,
time-varying expected returns and transaction costs. Models of limit order
markets, such as that of Kyle (1989), can only accommodate negative return
autocorrelation for individual securities. This result thus provides support for
the feedback trading hypothesis.
4.1. Non-synchronous trading
The most prominent explanation of index return autocorrelation is nonsynchronous trading (Fischer, 1966; Scholes and Willams, 1977). In a pure
non-synchronous trading model, it is assumed that stock returns are continuous processes sampled whenever the stocks are traded. As all stocks do not
trade simultaneously (synchronously), there will be some outdated stock prices
whenever a stock index is compiled. This measurement delay will result in
positive return autocorrelation. Lo and MacKinlay (1990) show that the
autocorrelation in daily index returns will be roughly equal to the average daily
non-trading of component stocks. 3 Non-synchronous trading adds to the
measured index return autocorrelation, but the extant literature suggests that
non-synchronous trading can explain only parts of the observed autocorrelation. This conclusion is reached by Atchison et al. (1987), Lo and MacKinlay
2
Filling in the individual stock price series with bid quotes will introduce negative return
autocorrelation in the index return series (Berglund and Liljeblom, 1988). This problem is relatively
minor for the index series, and ®lling in the index series with bid quotes does not change any of the
conclusions of the paper.
3
Boudoukh et al. (1994) show that higher autocorrelation may be obtained if non-trading is
concentrated to, e.g., high volatility stocks. There are no indications of such trading patterns in the
Swedish sample.
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P. S
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Table 2
First autocorrelation of stock returnsa
Sample
Index returns
b^1 c
Td
Stock returns
b^1 e
Tf
Number
of stocks
Large
0.301
(0.024)
0.302
(0.025)
0.238
(0.027)
0.345
(0.024)
0.153
(0.036)
0.096
(0.025)
0.084
(0.027)
0.110
(0.017)
2659
20
5.7
2419
20
13.4
1710
22
24.6
2245
62
14.6
Medium
Small
All
3671
3672
3691
3677
Non-trading
(%)b
a
Regression model: rt b0 b1 rtÿ1 et . Regressions use least squares estimation with asymptotic
White standard errors (in parentheses). Sample period 1 January 1980±31 December 1995. The
reported number of observations also apply to Table 3.
b
Average daily non-trading.
c
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
d
Number of daily observations.
e
Average of individual regression estimates. Sample standard error of mean in parentheses.
f
Average number of daily observations.
**
Signi®cantly dierent from zero at the 0.05 level.
(1990), Ogden (1997) and Sias and Starks (1997) for US data and Berglund and
Liljeblom (1988) for Finnish data.
The same conclusion holds for the Swedish data. Measured autocorrelation
is signi®cantly higher than that predicted by the level of non-trading. The
autocorrelation of the Small portfolio is seemingly in accordance with the nontrading probabilities of component stocks (non-trading 24.6%, autocorrelation
0.238), but if the index is created without ®lling in bid-quotes for non-trading
days, autocorrelation rises to 0.386. For the portfolio Large the discrepancy
between non-trading and autocorrelation is quite large; autocorrelation is
0.301 while non-trading is 5.7%, much too low to credibly explain the observed
index return autocorrelation. 4
4.2. Time-varying expected returns
According to the hypothesis of time-varying expected returns, the observed
autocorrelation can be attributed to systematically varying risk premia (for
4
That the portfolio Large has higher return autocorrelation than the portfolio Small contrasts
®ndings of Boudoukh et al. (1994) and McQueen et al. (1996), who ®nd signi®cantly higher
autocorrelation for portfolios of smaller US stocks. There is positive cross-autocorrelation between
portfolio returns, therefore the portfolio All has higher return autocorrelation than the subportfolios.
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
example Campbell et al., 1993; Conrad, 1988). Time-varying expected returns
could account for the similarity between autocorrelation in stock returns and
stock index returns. However, as concluded by Ogden (1997), Sias and Starks
(1997), and McQueen et al. (1996), the model cannot credibly explain the
observed levels of autocorrelation in daily returns. The high autocorrelation
will, for example, imply highly negative risk premia after days of negative stock
returns.
4.3. Transaction costs
Cohen et al. (1980), Mech (1993) and Ogden (1997) argue that transaction
and information costs can lead market makers to base their quotes on a limited
information set, for example only the ``own'' order ¯ow. Quotes will be inef®cient, but the market makers' losses are limited by the spread which reduces
the possible pro®ts other market participants can make from arbitrage.
Transaction costs can result in autocorrelated index returns. However, the
hypothesis does not address the issue of autocorrelation in individual stock
returns.
The transaction cost argument has not been analysed theoretically for the
auction market setting. However, there are two reasons to believe that transaction costs are less likely to cause autocorrelated index returns in an auction
market. First, traders are not only passive price takers, they are also de facto
market makers (whenever they submit limit orders). The spread ``earned'' when
submitting limit orders will balance the spread ``paid'' when submitting market
orders, reducing average transaction costs. Second, there are no specialists with
predetermined single-stock trading strategies. All market participants have
similar access to information and can submit market and limit orders for all
stocks. 5
4.4. Feedback trading
In the non-synchronous trading model, prices are explicitly modelled as
ecient, and returns on individual stocks are therefore not serially correlated.
The most common type of trading model leading to such prices is a competitive
rational expectations equilibrium, REE (Hellwig, 1980; Kyle, 1985). In the case
of a non-competitive REE market, prices will exhibit ``bid±ask bounce'', resulting in negative return autocorrelation (Kyle, 1989). The negative return
5
Short term price ineciencies arise even in a frictionless auction market. If securities trade
exactly simultaneously, information revealed in the price will be used to update prices of other
securities. Depending on assumptions, this can result in both positive and negative index return
autocorrelation (S
afvenblad, 1997a).
P. S
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1281
autocorrelation imposes transaction costs on non-informational trades, increasing returns to liquidity provision. Although trade-to-trade returns are
negatively autocorrelated, so-called ``feedback trading'' can introduce positive
autocorrelation in returns measured over longer intervals (Sentana and Wadhwani, 1992).
Feedback trading includes several well-known trading strategies, such as
pro®t taking, herding, contrarian investment and dynamic portfolio reallocation. 6 If the structure of feedback trading is consistent across stocks, similar
autocorrelation patterns will result in both stock and index returns. In the case
of positive feedback trading, traders buy after price increases (similar to
herding), while in the case of negative feedback trading, traders sell after price
increases (similar to pro®t taking). Positive feedback trading results in negative
return autocorrelation while negative feedback trading results in positive return
autocorrelation. 7 The autocorrelation observed in the Swedish market could
thus be the result of negative feedback trading.
5. Further empirical evidence
5.1. Autocorrelation conditional on past returns
An observed regularity in index return autocorrelation is that autocorrelation tends to be high following on positive returns. This has been documented
for index returns from the US (Sentana and Wadhwani, 1992), Australia,
Belgium, Germany and Japan (Koutmos, 1997) 8 and France (Safvenblad,
1997b). The asymmetry is also present in the Swedish sample. For the portfolio
All autocorrelation is 0:330 following a day of high returns, but only 0:118
following a day of low returns (Panel a, Table 3). The pattern is similar for
individual stocks, with an average autocorrelation of 0:126 following high
returns and ÿ0:015 following low returns. These observations are consistent
with asymmetric feedback trading; pro®t taking following on prices increases,
but not on price declines. Since net stock holdings are positive, there will be
more ``winners'' after a day of good stock market performance and most pro®t
6
That individual investors engage in feedback trading is documented by e.g. Sias and Starks
(1997), Gompers and Metrick (1998) and Odean (1998).
7
The following example gives the intuition. After a day of strong market performance, a number
of traders are left with positive positions and pro®ts that they wish to close before the trading day
ends. This selling, negative feedback trading, will lead to a price pressure that will lead closing
prices to be biased downward relative to public information. This bias will be recovered the
following day, resulting in positive expected returns conditional on positive returns, that is, positive
return autocorrelation.
8
Koutmos (1997) rejects asymmetry for Italy and the UK.
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P. S
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Table 3
Autocorrelation conditional on preceding day's return, trading volume and day-of-the-week
Index returns
b^1 b low
b^2 b high
Panel a: Following on low or high return
Large
0.083
0.319
(0.053)
(0.043)
0.278
Medium
0.052
(0.090)
(0.051)
Small
)0.023
0.249
(0.083)
(0.048)
All
0.118
0.330
(0.077)
(0.046)
b^1 ÿ b^1 b
Stock returns
b^1 c low
b^2 c high
b^1 ÿ b^1 c
)0.236
(0.068)
)0.226
(0.103)
)0.272
(0.096)
)0.212
(0.090)
0.021
(0.015)
)0.024
(0.014)
)0.040
(0.027)
)0.015
(0.011)
0.190
(0.044)
0.111
(0.027)
0.083
(0.027)
0.126
(0.019)
)0.168
(0.042)
)0.135
(0.034)
)0.123
(0.046)
)0.141
(0.024)
0.244
(0.056)
0.211
(0.054)
0.243
(0.070)
0.233
(0.035)
0.104
(0.025)
0.040
(0.013)
0.014
(0.013)
0.052
(0.010)
0.139
(0.034)
0.171
(0.047)
0.229
(0.069)
0.181
(0.030)
trading volume
0.180
0.159
(0.060)
(0.037)
0.242
0.074
(0.083)
(0.023)
0.111
0.041
(0.098)
(0.023)
0.210
0.090
(0.083)
(0.016)
0.077
(0.020)
0.020
(0.011)
0.008
(0.015)
0.034
(0.009)
0.082
(0.021)
0.055
(0.019)
0.033
(0.024)
0.056
(0.012)
Panel b: Following on low or high absolute return
Large
0.402
0.193
0.209
(0.071)
(0.028)
(0.076)
Medium
0.341
0.161
0.180
(0.071)
(0.042)
(0.082)
Small
0.300
0.106
0.194
(0.066)
(0.042)
(0.078)
All
0.543
0.210
0.333
(0.073)
(0.037)
(0.082)
Panel c: Following on low or high market
Large
0.299
0.119
(0.045)
(0.039)
Medium
0.291
0.049
(0.054)
(0.063)
Small
0.161
0.050
(0.078)
(0.060)
All
0.328
0.118
(0.064)
(0.053)
a
a
Regression model: rt b0 b1 D1;tÿ1 b2 D2;tÿ1 rtÿ1 et . D1;t (D2;t ) is a dummy variable for low
(high) returns/absolute returns/market trading volume. Panel c: Trading volume uses logarithms of
daily trading volume, detrended using a centred 20 trading day moving average.
b
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
c
Average of individual regression estimates. Reported signi®cance levels test whether the mean is
dierent from zero using the sample standard deviation (in parentheses).
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
taking should be expected after such days. As a result, autocorrelation in
measured returns would tend to be more positive after price increases. Such
trading patterns have been documented empirically by Odean (1998), and can
also be motivated by the predictions of prospect theory (Kahneman and
Tversky, 1979).
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1283
5.2. Autocorrelation conditional on absolute returns
When volatility is high, index return autocorrelation can be expected to be
low. The cost of pricing errors will be high, and, as trading volume tends to be
high, non-trading is low. That autocorrelation is lower conditional on high
volatility has been observed for most major stock markets (cf. Sentana and
Wadhwani, 1992; Koutmos, 1997). Swedish index returns exhibit similar
characteristics (panel b, Table 3). For All autocorrelation is 0:543 following a
low volatility day but only 0:210 following a high volatility day.
The more interesting result is, however, that a similar pattern is obtained for
individual stocks. Average autocorrelation for the stocks in All is 0:233 following a low volatility day and 0:052 following a high volatility day. This result
cannot be explained by the transaction cost hypothesis. Interpreted within the
feedback trading model, the results imply uninformed buying after large
market rises and uninformed selling after large market declines.
5.3. Autocorrelation conditional on trading volume
In REE models, such as Admati and P¯eiderer (1988), trading volume is a
measure of the amount of information revealed in trading. 9 Therefore, prices
realised in high trading volume tend to be better estimates of the underlying, or
``true'', value of securities. In the same vein, Foster and Viswanathan (1993)
show that trading volume is positively correlated with the precision of the
informed trader's signal, and the resulting price precision. Similarly, in the
model of Campbell et al. (1993), high trading volume makes the aggregate risk
aversion more easily observable. The same prediction is also made by the nonsynchronous trading hypothesis. High trading volume reduces the non-synchronicity of prices and resulting index return autocorrelation.
The prediction is supported by the results in panel c of Table 3. Autocorrelation after high volume days is signi®cantly lower for all investigated index
series. 10 For the portfolio All, autocorrelation is 0:328 following a low volume
day, but only 0:118 following a high volume day. Again, a similar pattern is
observed for individual stocks, in particular for the most liquid stocks. For the
stocks in Large, average autocorrelation is 0:159 following a low volume day,
but only 0:077 following a high volume day. These results are qualitatively
similar to those reported by Campbell et al. (1993) for US data.
9
Other sources of trading volume, such as portfolio rebalancing or liquidity trading, will
generally only contribute small portions of total trading volume. Particularly, as non-informational
demand ``attracts'' informed trading (Admati and P¯eiderer, 1988).
10
Following Campbell et al. (1993) the market trading volume is used.
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
5.4. Autocorrelation conditional on day-of-the-week
Several authors have documented that index return autocorrelation is particularly high between Friday and Monday returns. 11 This eect is interesting
since it is unrelated to the non-synchronous trading or transaction cost hypotheses of return autocorrelation. The upcoming weekend implies a period of
non-trading, but this should not aect trading volume or transaction costs. The
high Friday autocorrelation is con®rmed for all four portfolios (Table 4).
Autocorrelation for the All portfolio is 0:466 following a Friday compared to
0:175 following other days. 12 The same pattern extends to individual stock
returns, 54 out of the 62 stocks exhibit higher autocorrelation on Fridays, on
average 0:130 compared to 0:039 for other days.
The results further strengthen the conclusion that the same factors drive
autocorrelation in index returns and individual stock returns. In particular, the
results strengthen the case for negative feedback trading as it is reasonable to
believe that traders who follow a pro®t taking strategy want to close their
positions before the weekend.
6. Conclusion
This paper relates the time series properties of index return autocorrelation
to that of individual stocks. The data used is from a relatively small stock
exchange, with a fairly high degree of non-trading. This may be the reason why
Swedish index returns exhibit higher autocorrelation than, for example, US
returns. Still, the return, volatility, trading volume and day-of-the-week dependence of autocorrelation is similar to that observed in US and other markets. This makes it more likely that the results carry over to other markets.
The four speci®cations studied in this paper yield similar results for both
types of autocorrelation. Non-synchronous trading and transaction costs add
to the observed level of index return autocorrelation but cannot address the
autocorrelation properties of individual stock returns. Therefore these hypotheses are rejected.
The observed patterns of autocorrelation have sensible explanations within
the feedback trading framework. Therefore, the paper supports feedback
trading as the cause of index return autocorrelation. This suggests that future
11
See Boudoukh et al. (1994) for US data, S
afvenblad (1997b) for French data and Norden
(1992) for Swedish data.
12
The results in Table 4 are qualitatively similar when controls are made for trading volume,
returns and volatility.
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1285
Table 4
Autocorrelation conditional on day-of-the-weeka
Index returns
b^ b Mon:±Thu:
1
Large
Medium
Small
xAll
0.159
(0.029)
0.116
(0.045)
0.084
(0.045)
0.175
(0.040)
b^2 b Fri:
b^1 ÿ b^1 b
0.420
(0.063)
0.437
(0.075)
0.248
(0.075)
0.466
(0.068)
)0.261
(0.069)
)0.321
(0.087)
)0.164
(0.087)
)0.291
(0.079)
Stock returns
b^ c Mon:±Thu:
1
0.088
(0.022)
0.026
(0.012)
0.007
(0.013)
0.039
(0.009)
b^2 c Fri:
b^1 ÿ b^1 c
)0.114
(0.030)
)0.096
(0.032)
)0.065
(0.030)
)0.091
(0.018)
0.202
(0.048)
0.123
(0.035)
0.072
(0.032)
0.130
(0.022)
a
Regression model: rt b0 b1 D1;tÿ1 b2 D2;tÿ1 rtÿ1 et .D1;t (D2;t ) is a dummy variable for
Monday±Thursday (Friday).
b
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
c
Average of individual regression estimates. Reported signi®cance levels test whether the mean is
dierent from zero using the sample standard deviation (in parentheses).
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
empirical work on return autocorrelation could focus on the trading and
ownership patterns of investors groups.
Acknowledgements
The paper has bene®tted from comments made by Clas Bergstr
om, Magnus
Dahlquist, Yrj
o Koskinen, Lars Norden, G
oran Robertsson, David Smith,
Staan Viotti, two anonymous referees, seminar participants at the Stockholm
School of Economics, at the ``Nordic Symposium on Corporate and Institutional Finance'', in Oslo, and at the ``Arne Ryde Workshop on Asset Pricing'',
in Lund. I gratefully acknowledge research funding from Bankforskningsinstitutet and Jan Wallanders och Tom Hedelius' stiftelse.
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www.elsevier.com/locate/econbase
Trading volume and autocorrelation: Empirical
evidence from the Stockholm Stock Exchange
Patrik Safvenblad
*
Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83, Stockholm, Sweden
Received 16 July 1998; accepted 9 June 1999
Abstract
In accordance with studies for other markets, Swedish index returns exhibit high
autocorrelation, (a) after days of above average performance of the stock market, (b)
after low absolute returns, (c) when trading volume is low, and (d) following Fridays.
Contrary to the non-synchronous trading and the transaction cost hypotheses, all
results extend to individual stock returns. It is concluded that autocorrelation patterns
are related to the trading patterns of individual investors, and not the cross-security
information processing of the market. In particular, the observed autocorrelation
structure corresponds to feedback trading. Ó 2000 Elsevier Science B.V. All rights
reserved.
JEL classi®cation: G14
Keywords: Return autocorrelation; Trading volume; Feedback trading
1. Introduction
It has been well documented that high frequency stock index returns are
positively autocorrelated. Several theoretical explanations have been put forward, most prominently non-synchronous trading, transaction costs,
*
Tel.: +46-8-736-9161; fax: +46-8-312327.
E-mail address: ®npsa@hhs.se
0378-4266/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 4 2 6 6 ( 9 9 ) 0 0 0 7 1 - 0
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
time-varying expected returns and feedback trading. Several empirical papers
test the predictions of the various models on data.
So far, the empirical tests are inconclusive; Atchison et al. (1987) reject nonsynchronous trading, Mech (1993) and Ogden (1997) favour trading costs or
information frictions while Boudoukh et al. (1994) argue that special patterns
of non-trading may explain the observed levels of autocorrelation.
This paper introduces a new element to the analysis: the return autocorrelation of individual stocks. As all theoretical models of index return autocorrelation include assumptions about the (absence of) autocorrelation of
individual stock returns, it is possible to draw conclusions on the likely origin
of index return autocorrelation based on the autocorrelation of individual
stock returns. To the best of the author's knowledge, this possibility has so far
not been used in the literature on index return autocorrelation.
The empirical study uses data from the Stockholm Stock Exchange (SSE), a
market not widely studied in this context, thus reducing data-snooping biases.
The small number of traded stocks makes it easier to have full control over the
creation of index returns. In addition, SSE is a limit order market, eliminating
specialist trading strategies as the source of observed autocorrelation. The
properties of index return autocorrelation are similar to those found for other
stock markets. It is thus likely that the key empirical results will carry over to
other markets.
Index return autocorrelation on the SSE is high, and depends on (among
other things) realised return, volatility, trading volume and day-of-the-week.
The same patterns are found for individual stock returns. This is inconsistent
with popular explanations of index return autocorrelation and therefore it is
concluded that the observed autocorrelation patterns are best explained as the
result of trading strategies such as feedback trading.
2. Some earlier empirical evidence
Table 1 gives a sample from the rich earlier empirical evidence of autocorrelation in daily stock returns. Index return autocorrelation is predominantly
positive, regardless of country or sample period. 1
The evidence of autocorrelation in individual stock returns is less consistent.
US studies report average autocorrelations close to zero (e.g. Atchison et al.,
1987). Later work shows that the level of autocorrelation is increasing in ®rm
1
Empirical evidence is given by, e.g., Koutmos (1997). Positive index return autocorrelation is
also observed for other return frequencies, from intraday to monthly returns. See, for example,
Stoll and Whaley (1990) for intraday returns and Lo and MacKinlay (1990) for weekly and
monthly returns.
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1277
Table 1
Selected empirical evidence on autocorrelation in daily stock and index returnsa
Source
Series
Sample period
Index
returns
Atchison et al. (1987)
Berglund and
Liljeblom (1988)
Chan (1993)
CRSP
Helsinki
1978±81
1977±82
0.17
0.49
Smallest N Y S E decile
Largest N Y S E decile
C R S P small stocks
1980±89
1980±89
1962±87
0.05
0.35
C R S P large stocks
Tel Aviv
Paris small stocks
Paris large stocks
Stockholm small stocks
Stockholm large stocks
1962±87
1987
1991±95
1991±95
1980±95
1980±95
Lo and MacKinlay
(1990)
Ronen (1998)
Safvenblad (1997b)
Comparison: this paper
Stock
returns
0.02
0.32
)0.09
0.35
0.04
0.16
0.24
0.30
0.15
)0.12
0.07
0.08
0.15
a
Estimates and signi®cance levels as reported in cited articles. Where signi®cance levels were not
reported, they were calculated using asymptotic standard errors.
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
size and signi®cantly positive for larger stocks (Chan, 1993; Sias and Starks,
1997). Safvenblad (1997a) reports similar results for French stocks.
In less liquid markets, positive return autocorrelation for stocks has been
documented in several markets, including Austria (Huber, 1997), Finland
(Berglund and Liljeblom, 1988), Israel (Ronen, 1998), Malaysia and Singapore
(Laurence, 1986).
3. Data
The sample consists of daily returns and trading volume for 62 major stocks
traded on the SSE over the period 1980±1995. The stocks were selected from all
traded stocks based on sample length (more than ten years) and trading volume
(highest), including all listed share classes of each company. The sample covers
approximately 90% of total trading volume on the exchange. Data series were
collected from Findata. Details on individual stocks are available in Safvenblad (1997b).
Stocks are split into three groups, Large, Medium and Small, according to
average trading volume. For each of these groups, results are reported for the
average of individual stocks as well as for an equally weighted index. Results
are also reported for All, the average of all stocks and a corresponding index.
For individual stocks, non-trading and ex-dividend days (annual) have been
omitted and only closing traded prices are used. For index returns, non-trading
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
days are ®lled in with the closing bid quote and dividends are reinvested
without transaction costs. 2
4. Possible explanations of return autocorrelation
Swedish index returns are strongly positively correlated. Table 2 reports an
index return autocorrelation of 0.345 for the All portfolio. For individual
stocks, autocorrelation is signi®cantly positive and much higher than reported
in studies on US data. As for French and US stocks, autocorrelation is increasing in trading volume; the average autocorrelation for the stocks in Small
is 0.084, and 0.153 for the stocks in Large.
This result indicates that Swedish stock returns are generally positively
autocorrelated, but that larger bid±ask spreads induce negative return autocorrelation for smaller stocks. The positive autocorrelation is incompatible
with most models of price formation, including non-synchronous trading,
time-varying expected returns and transaction costs. Models of limit order
markets, such as that of Kyle (1989), can only accommodate negative return
autocorrelation for individual securities. This result thus provides support for
the feedback trading hypothesis.
4.1. Non-synchronous trading
The most prominent explanation of index return autocorrelation is nonsynchronous trading (Fischer, 1966; Scholes and Willams, 1977). In a pure
non-synchronous trading model, it is assumed that stock returns are continuous processes sampled whenever the stocks are traded. As all stocks do not
trade simultaneously (synchronously), there will be some outdated stock prices
whenever a stock index is compiled. This measurement delay will result in
positive return autocorrelation. Lo and MacKinlay (1990) show that the
autocorrelation in daily index returns will be roughly equal to the average daily
non-trading of component stocks. 3 Non-synchronous trading adds to the
measured index return autocorrelation, but the extant literature suggests that
non-synchronous trading can explain only parts of the observed autocorrelation. This conclusion is reached by Atchison et al. (1987), Lo and MacKinlay
2
Filling in the individual stock price series with bid quotes will introduce negative return
autocorrelation in the index return series (Berglund and Liljeblom, 1988). This problem is relatively
minor for the index series, and ®lling in the index series with bid quotes does not change any of the
conclusions of the paper.
3
Boudoukh et al. (1994) show that higher autocorrelation may be obtained if non-trading is
concentrated to, e.g., high volatility stocks. There are no indications of such trading patterns in the
Swedish sample.
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
Table 2
First autocorrelation of stock returnsa
Sample
Index returns
b^1 c
Td
Stock returns
b^1 e
Tf
Number
of stocks
Large
0.301
(0.024)
0.302
(0.025)
0.238
(0.027)
0.345
(0.024)
0.153
(0.036)
0.096
(0.025)
0.084
(0.027)
0.110
(0.017)
2659
20
5.7
2419
20
13.4
1710
22
24.6
2245
62
14.6
Medium
Small
All
3671
3672
3691
3677
Non-trading
(%)b
a
Regression model: rt b0 b1 rtÿ1 et . Regressions use least squares estimation with asymptotic
White standard errors (in parentheses). Sample period 1 January 1980±31 December 1995. The
reported number of observations also apply to Table 3.
b
Average daily non-trading.
c
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
d
Number of daily observations.
e
Average of individual regression estimates. Sample standard error of mean in parentheses.
f
Average number of daily observations.
**
Signi®cantly dierent from zero at the 0.05 level.
(1990), Ogden (1997) and Sias and Starks (1997) for US data and Berglund and
Liljeblom (1988) for Finnish data.
The same conclusion holds for the Swedish data. Measured autocorrelation
is signi®cantly higher than that predicted by the level of non-trading. The
autocorrelation of the Small portfolio is seemingly in accordance with the nontrading probabilities of component stocks (non-trading 24.6%, autocorrelation
0.238), but if the index is created without ®lling in bid-quotes for non-trading
days, autocorrelation rises to 0.386. For the portfolio Large the discrepancy
between non-trading and autocorrelation is quite large; autocorrelation is
0.301 while non-trading is 5.7%, much too low to credibly explain the observed
index return autocorrelation. 4
4.2. Time-varying expected returns
According to the hypothesis of time-varying expected returns, the observed
autocorrelation can be attributed to systematically varying risk premia (for
4
That the portfolio Large has higher return autocorrelation than the portfolio Small contrasts
®ndings of Boudoukh et al. (1994) and McQueen et al. (1996), who ®nd signi®cantly higher
autocorrelation for portfolios of smaller US stocks. There is positive cross-autocorrelation between
portfolio returns, therefore the portfolio All has higher return autocorrelation than the subportfolios.
1280
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
example Campbell et al., 1993; Conrad, 1988). Time-varying expected returns
could account for the similarity between autocorrelation in stock returns and
stock index returns. However, as concluded by Ogden (1997), Sias and Starks
(1997), and McQueen et al. (1996), the model cannot credibly explain the
observed levels of autocorrelation in daily returns. The high autocorrelation
will, for example, imply highly negative risk premia after days of negative stock
returns.
4.3. Transaction costs
Cohen et al. (1980), Mech (1993) and Ogden (1997) argue that transaction
and information costs can lead market makers to base their quotes on a limited
information set, for example only the ``own'' order ¯ow. Quotes will be inef®cient, but the market makers' losses are limited by the spread which reduces
the possible pro®ts other market participants can make from arbitrage.
Transaction costs can result in autocorrelated index returns. However, the
hypothesis does not address the issue of autocorrelation in individual stock
returns.
The transaction cost argument has not been analysed theoretically for the
auction market setting. However, there are two reasons to believe that transaction costs are less likely to cause autocorrelated index returns in an auction
market. First, traders are not only passive price takers, they are also de facto
market makers (whenever they submit limit orders). The spread ``earned'' when
submitting limit orders will balance the spread ``paid'' when submitting market
orders, reducing average transaction costs. Second, there are no specialists with
predetermined single-stock trading strategies. All market participants have
similar access to information and can submit market and limit orders for all
stocks. 5
4.4. Feedback trading
In the non-synchronous trading model, prices are explicitly modelled as
ecient, and returns on individual stocks are therefore not serially correlated.
The most common type of trading model leading to such prices is a competitive
rational expectations equilibrium, REE (Hellwig, 1980; Kyle, 1985). In the case
of a non-competitive REE market, prices will exhibit ``bid±ask bounce'', resulting in negative return autocorrelation (Kyle, 1989). The negative return
5
Short term price ineciencies arise even in a frictionless auction market. If securities trade
exactly simultaneously, information revealed in the price will be used to update prices of other
securities. Depending on assumptions, this can result in both positive and negative index return
autocorrelation (S
afvenblad, 1997a).
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1281
autocorrelation imposes transaction costs on non-informational trades, increasing returns to liquidity provision. Although trade-to-trade returns are
negatively autocorrelated, so-called ``feedback trading'' can introduce positive
autocorrelation in returns measured over longer intervals (Sentana and Wadhwani, 1992).
Feedback trading includes several well-known trading strategies, such as
pro®t taking, herding, contrarian investment and dynamic portfolio reallocation. 6 If the structure of feedback trading is consistent across stocks, similar
autocorrelation patterns will result in both stock and index returns. In the case
of positive feedback trading, traders buy after price increases (similar to
herding), while in the case of negative feedback trading, traders sell after price
increases (similar to pro®t taking). Positive feedback trading results in negative
return autocorrelation while negative feedback trading results in positive return
autocorrelation. 7 The autocorrelation observed in the Swedish market could
thus be the result of negative feedback trading.
5. Further empirical evidence
5.1. Autocorrelation conditional on past returns
An observed regularity in index return autocorrelation is that autocorrelation tends to be high following on positive returns. This has been documented
for index returns from the US (Sentana and Wadhwani, 1992), Australia,
Belgium, Germany and Japan (Koutmos, 1997) 8 and France (Safvenblad,
1997b). The asymmetry is also present in the Swedish sample. For the portfolio
All autocorrelation is 0:330 following a day of high returns, but only 0:118
following a day of low returns (Panel a, Table 3). The pattern is similar for
individual stocks, with an average autocorrelation of 0:126 following high
returns and ÿ0:015 following low returns. These observations are consistent
with asymmetric feedback trading; pro®t taking following on prices increases,
but not on price declines. Since net stock holdings are positive, there will be
more ``winners'' after a day of good stock market performance and most pro®t
6
That individual investors engage in feedback trading is documented by e.g. Sias and Starks
(1997), Gompers and Metrick (1998) and Odean (1998).
7
The following example gives the intuition. After a day of strong market performance, a number
of traders are left with positive positions and pro®ts that they wish to close before the trading day
ends. This selling, negative feedback trading, will lead to a price pressure that will lead closing
prices to be biased downward relative to public information. This bias will be recovered the
following day, resulting in positive expected returns conditional on positive returns, that is, positive
return autocorrelation.
8
Koutmos (1997) rejects asymmetry for Italy and the UK.
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
Table 3
Autocorrelation conditional on preceding day's return, trading volume and day-of-the-week
Index returns
b^1 b low
b^2 b high
Panel a: Following on low or high return
Large
0.083
0.319
(0.053)
(0.043)
0.278
Medium
0.052
(0.090)
(0.051)
Small
)0.023
0.249
(0.083)
(0.048)
All
0.118
0.330
(0.077)
(0.046)
b^1 ÿ b^1 b
Stock returns
b^1 c low
b^2 c high
b^1 ÿ b^1 c
)0.236
(0.068)
)0.226
(0.103)
)0.272
(0.096)
)0.212
(0.090)
0.021
(0.015)
)0.024
(0.014)
)0.040
(0.027)
)0.015
(0.011)
0.190
(0.044)
0.111
(0.027)
0.083
(0.027)
0.126
(0.019)
)0.168
(0.042)
)0.135
(0.034)
)0.123
(0.046)
)0.141
(0.024)
0.244
(0.056)
0.211
(0.054)
0.243
(0.070)
0.233
(0.035)
0.104
(0.025)
0.040
(0.013)
0.014
(0.013)
0.052
(0.010)
0.139
(0.034)
0.171
(0.047)
0.229
(0.069)
0.181
(0.030)
trading volume
0.180
0.159
(0.060)
(0.037)
0.242
0.074
(0.083)
(0.023)
0.111
0.041
(0.098)
(0.023)
0.210
0.090
(0.083)
(0.016)
0.077
(0.020)
0.020
(0.011)
0.008
(0.015)
0.034
(0.009)
0.082
(0.021)
0.055
(0.019)
0.033
(0.024)
0.056
(0.012)
Panel b: Following on low or high absolute return
Large
0.402
0.193
0.209
(0.071)
(0.028)
(0.076)
Medium
0.341
0.161
0.180
(0.071)
(0.042)
(0.082)
Small
0.300
0.106
0.194
(0.066)
(0.042)
(0.078)
All
0.543
0.210
0.333
(0.073)
(0.037)
(0.082)
Panel c: Following on low or high market
Large
0.299
0.119
(0.045)
(0.039)
Medium
0.291
0.049
(0.054)
(0.063)
Small
0.161
0.050
(0.078)
(0.060)
All
0.328
0.118
(0.064)
(0.053)
a
a
Regression model: rt b0 b1 D1;tÿ1 b2 D2;tÿ1 rtÿ1 et . D1;t (D2;t ) is a dummy variable for low
(high) returns/absolute returns/market trading volume. Panel c: Trading volume uses logarithms of
daily trading volume, detrended using a centred 20 trading day moving average.
b
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
c
Average of individual regression estimates. Reported signi®cance levels test whether the mean is
dierent from zero using the sample standard deviation (in parentheses).
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
taking should be expected after such days. As a result, autocorrelation in
measured returns would tend to be more positive after price increases. Such
trading patterns have been documented empirically by Odean (1998), and can
also be motivated by the predictions of prospect theory (Kahneman and
Tversky, 1979).
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1283
5.2. Autocorrelation conditional on absolute returns
When volatility is high, index return autocorrelation can be expected to be
low. The cost of pricing errors will be high, and, as trading volume tends to be
high, non-trading is low. That autocorrelation is lower conditional on high
volatility has been observed for most major stock markets (cf. Sentana and
Wadhwani, 1992; Koutmos, 1997). Swedish index returns exhibit similar
characteristics (panel b, Table 3). For All autocorrelation is 0:543 following a
low volatility day but only 0:210 following a high volatility day.
The more interesting result is, however, that a similar pattern is obtained for
individual stocks. Average autocorrelation for the stocks in All is 0:233 following a low volatility day and 0:052 following a high volatility day. This result
cannot be explained by the transaction cost hypothesis. Interpreted within the
feedback trading model, the results imply uninformed buying after large
market rises and uninformed selling after large market declines.
5.3. Autocorrelation conditional on trading volume
In REE models, such as Admati and P¯eiderer (1988), trading volume is a
measure of the amount of information revealed in trading. 9 Therefore, prices
realised in high trading volume tend to be better estimates of the underlying, or
``true'', value of securities. In the same vein, Foster and Viswanathan (1993)
show that trading volume is positively correlated with the precision of the
informed trader's signal, and the resulting price precision. Similarly, in the
model of Campbell et al. (1993), high trading volume makes the aggregate risk
aversion more easily observable. The same prediction is also made by the nonsynchronous trading hypothesis. High trading volume reduces the non-synchronicity of prices and resulting index return autocorrelation.
The prediction is supported by the results in panel c of Table 3. Autocorrelation after high volume days is signi®cantly lower for all investigated index
series. 10 For the portfolio All, autocorrelation is 0:328 following a low volume
day, but only 0:118 following a high volume day. Again, a similar pattern is
observed for individual stocks, in particular for the most liquid stocks. For the
stocks in Large, average autocorrelation is 0:159 following a low volume day,
but only 0:077 following a high volume day. These results are qualitatively
similar to those reported by Campbell et al. (1993) for US data.
9
Other sources of trading volume, such as portfolio rebalancing or liquidity trading, will
generally only contribute small portions of total trading volume. Particularly, as non-informational
demand ``attracts'' informed trading (Admati and P¯eiderer, 1988).
10
Following Campbell et al. (1993) the market trading volume is used.
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P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
5.4. Autocorrelation conditional on day-of-the-week
Several authors have documented that index return autocorrelation is particularly high between Friday and Monday returns. 11 This eect is interesting
since it is unrelated to the non-synchronous trading or transaction cost hypotheses of return autocorrelation. The upcoming weekend implies a period of
non-trading, but this should not aect trading volume or transaction costs. The
high Friday autocorrelation is con®rmed for all four portfolios (Table 4).
Autocorrelation for the All portfolio is 0:466 following a Friday compared to
0:175 following other days. 12 The same pattern extends to individual stock
returns, 54 out of the 62 stocks exhibit higher autocorrelation on Fridays, on
average 0:130 compared to 0:039 for other days.
The results further strengthen the conclusion that the same factors drive
autocorrelation in index returns and individual stock returns. In particular, the
results strengthen the case for negative feedback trading as it is reasonable to
believe that traders who follow a pro®t taking strategy want to close their
positions before the weekend.
6. Conclusion
This paper relates the time series properties of index return autocorrelation
to that of individual stocks. The data used is from a relatively small stock
exchange, with a fairly high degree of non-trading. This may be the reason why
Swedish index returns exhibit higher autocorrelation than, for example, US
returns. Still, the return, volatility, trading volume and day-of-the-week dependence of autocorrelation is similar to that observed in US and other markets. This makes it more likely that the results carry over to other markets.
The four speci®cations studied in this paper yield similar results for both
types of autocorrelation. Non-synchronous trading and transaction costs add
to the observed level of index return autocorrelation but cannot address the
autocorrelation properties of individual stock returns. Therefore these hypotheses are rejected.
The observed patterns of autocorrelation have sensible explanations within
the feedback trading framework. Therefore, the paper supports feedback
trading as the cause of index return autocorrelation. This suggests that future
11
See Boudoukh et al. (1994) for US data, S
afvenblad (1997b) for French data and Norden
(1992) for Swedish data.
12
The results in Table 4 are qualitatively similar when controls are made for trading volume,
returns and volatility.
P. S
afvenblad / Journal of Banking & Finance 24 (2000) 1275±1287
1285
Table 4
Autocorrelation conditional on day-of-the-weeka
Index returns
b^ b Mon:±Thu:
1
Large
Medium
Small
xAll
0.159
(0.029)
0.116
(0.045)
0.084
(0.045)
0.175
(0.040)
b^2 b Fri:
b^1 ÿ b^1 b
0.420
(0.063)
0.437
(0.075)
0.248
(0.075)
0.466
(0.068)
)0.261
(0.069)
)0.321
(0.087)
)0.164
(0.087)
)0.291
(0.079)
Stock returns
b^ c Mon:±Thu:
1
0.088
(0.022)
0.026
(0.012)
0.007
(0.013)
0.039
(0.009)
b^2 c Fri:
b^1 ÿ b^1 c
)0.114
(0.030)
)0.096
(0.032)
)0.065
(0.030)
)0.091
(0.018)
0.202
(0.048)
0.123
(0.035)
0.072
(0.032)
0.130
(0.022)
a
Regression model: rt b0 b1 D1;tÿ1 b2 D2;tÿ1 rtÿ1 et .D1;t (D2;t ) is a dummy variable for
Monday±Thursday (Friday).
b
Regression estimates from least squares estimation with asymptotic White standard errors (in
parentheses).
c
Average of individual regression estimates. Reported signi®cance levels test whether the mean is
dierent from zero using the sample standard deviation (in parentheses).
*
Signi®cantly dierent from zero at the 0.05 level.
**
Signi®cantly dierent from zero at the 0.01 level.
empirical work on return autocorrelation could focus on the trading and
ownership patterns of investors groups.
Acknowledgements
The paper has bene®tted from comments made by Clas Bergstr
om, Magnus
Dahlquist, Yrj
o Koskinen, Lars Norden, G
oran Robertsson, David Smith,
Staan Viotti, two anonymous referees, seminar participants at the Stockholm
School of Economics, at the ``Nordic Symposium on Corporate and Institutional Finance'', in Oslo, and at the ``Arne Ryde Workshop on Asset Pricing'',
in Lund. I gratefully acknowledge research funding from Bankforskningsinstitutet and Jan Wallanders och Tom Hedelius' stiftelse.
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