The dispersion effect in international stock returns

EMPFIN-00759; No of Pages 12 Journal of Empirical Finance xxx (2014) xxx–xxx

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Journal of Empirical Finance journal homepage: www.elsevier.com/locate/jempfin

The dispersion effect in international stock returns☆ Markus Leippold ⁎, Harald Lohre ⁎ a b

University of Zurich, Department of Banking and Finance, Plattenstrasse 14, 8032 Zurich, Switzerland Deka Investment GmbH, Quantitative Products, Mainzer Landstr. 16, 60325 Frankfurt/Main, Germany

a r t i c l e

i n f o

Article history: Received 12 October 2011 Received in revised form 26 July 2014 Accepted 1 September 2014 Available online xxxx JEL classification: G12 G14 G15 Keywords: International dispersion effect Information uncertainty Liquidity

a b s t r a c t We find that stocks exhibiting high dispersion in analysts' earnings forecasts not only underperform in the U.S. but also in some European countries. Investigating the abnormal returns generated by the dispersion strategy around the world for the 1990–2008 sample period, we observe that the returns of the strategy are uneven, with large abnormal returns realized during the mid-to-late 1990s and the 2000–2003 period. In particular, we document that the dispersion effect is most profitable in a very narrow time frame around the burst of the technology bubble. As a consequence, the dispersion hedge strategy would have been rather difficult to implement, especially given that the highest mispricing obtains for stocks characterized by high arbitrage costs. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Earnings estimates of financial analysts serve as a timely measure for assessing a company's current value. Condensing the expertise of different analysts, the Institutional Brokers' Estimate System (I/B/E/S) provides a consensus estimate, which is the mean value of all available earnings forecasts for a given company. To judge the credibility of the earnings signal, one can resort to additional information embedded in the distribution of the analysts' earnings forecasts. Especially, the latter's second moment is a natural candidate to capture the dispersion of the analysts' earnings forecasts. Intuitively, one may well expect companies with a higher dispersion in the analysts' earnings forecasts to earn higher returns, thus compensating investors for bearing uncertain earnings prospects. However, empirical evidence for the U.S. is at odds with dispersion's being a priced risk factor. Even more so, Diether et al. (2002) document that low dispersion stocks significantly outperform high dispersion stocks.

☆ We are grateful to Tim Adam, Yakov Amihud, Nur Ata, Naohiko Baba, Andrea Buraschi, Lucía Cuadro-Sáez, Volker Flögel, Levent Güntay, Satadru Hore, Thomas Kieselstein, Stefan Klein, Peter Lückoff, Ivelina Pavlova, Georg Pflug, Andrea Vedolin, Michael Wolf, Bo Zhao, and the seminar participants at the World Finance Conference in Rhodes, the 2009 FMA Annual Meeting in Reno, the 3rd Annual Risk Management Conference in Singapore, the 2009 Conference of the Swiss Society for Financial Market Research in Geneva, the 2008 Frontiers of Finance Conference in Belize, the 11th Symposium on Finance, Banking, and Insurance in Karlsruhe, the 2008 Meeting of the Spanish Finance Association in Barcelona, the 2008 International Conference on Price, Credit, and Liquidity Risks in Konstanz, the 2008 Meeting of the Euro Working Group on Financial Modelling in London, and Northfield's 22nd Annual Research Conference in Venice for helpful comments and suggestions. Note that this paper expresses the authors' views that do not have to coincide with those of Deka Investment GmbH. Markus Leippold gratefully acknowledges the financial support of the Swiss National Science Foundation (NCCR FINRISK). ⁎ Corresponding authors. E-mail addresses: [email protected] (M. Leippold), [email protected] (H. Lohre).

http://dx.doi.org/10.1016/j.jempfin.2014.09.001 0927-5398/© 2014 Elsevier B.V. All rights reserved.

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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M. Leippold, H. Lohre / Journal of Empirical Finance xxx (2014) xxx–xxx

In rationalizing this striking result, Diether et al. (2002) contend that dispersion may not be viewed as a risk factor, but rather as a metric for differences of opinion. Invoking an argument of Miller (1977), they suggest that prices tend to reflect the view of the optimistic investors whenever there is disagreement about a stock's value, since the pessimistic investors' views are often not revealed due to short-sale constraints. In fact, Boehme et al. (2006) show that the dispersion effect is most prominent among short-sale constrained firms. Of course, the high dispersion stocks' prices are bound to fall once the uncertainty is resolved. We wonder whether this dispersion effect is common to various markets or whether it is unique to the U.S. Testing for an analogous price pattern in other markets, we provide original evidence of dispersion effects in some European countries. However, a simple analysis of the time series nature of the dispersion effect reveals that the positive European return differentials occur in a very narrow time frame of three years, out of a total sample period of almost twenty years. On the other hand, the U.S. dispersion effect provides a more favorable return pattern, providing consistent abnormal returns most of the time. Still, the U.S. and the European dispersion strategy have a common characteristic in that they both have been very effective in hedging against the market downturn following the burst of the technology bubble. This hedging characteristic also holds at the end of our sample period, which coincides with the beginning of the financial crisis following the collapse of Lehman Brothers. However, we question the practicability of such a hedge strategy, because capturing these abnormal returns would have required short-selling firms way before their stock price peaked. Hence, most investors following the dispersion strategy would have been squeezed out of the market by margin calls just before the strategy would have become profitable. In further shaping one's intuition as to the dispersion effect's nature, we find it to be particularly pronounced among high and low dispersion stocks characterized by high information uncertainty as measured by analyst coverage or total stock volatility. In a related vein, Avramov et al. (2009) find the U.S. dispersion effect to be only profitable among the worst rated firms, while it is non-existent for higher rated firms. Likewise, Sadka and Scherbina (2007) show that analyst disagreement is closely related to trading costs in the U.S. In particular, the mispricing is most severe for less liquid stocks. We corroborate this argument by documenting the highest mispricing when limiting the sample to stocks with high idiosyncratic volatility or to stocks subject to high illiquidity. This observation suggests that high arbitrage costs additionally deter investors from exploiting the dispersion effect. This paper's structure is as follows. Section 1 presents the data we use for our study. In Section 2, we screen for the dispersion effect in various developed equity markets. Section 3 seeks to foster an understanding of the economic rationale governing the dispersion effect. First, we consider its evolution over time. Second, we examine its interaction with distinct information uncertainty environments. Finally, we establish a link between the dispersion effect and liquidity. Section 4 concludes.

Table 1 Country overview. The table contains descriptive information on the companies that have been domestically traded in the sample period (1990–2009). The screening of country lists sketches the evolution of the countries' samples. First, we give the Total size of the country lists followed by the number of companies surviving the first screen for Major listings. The column headed Region contains the number of companies surviving the screen eliminating regional listings and the like. The final screen excludes companies which exhibit free-floating market value below 10 million USD. We further describe this final sample giving the number of a country's dead companies (#Dead) and the number of companies with at least two I/B/E/S estimates in the sample period (#I/B/E/S), along with respective percentage values (%-Dead and %-I/B/E/S). The table provides information for the U.S. in Panel A, while Panel B covers European countries. Country

Sample: FMV N 10

Screening of country lists Total

Major

Region

Panel A: USA USA

36,659

20,030

7279

Panel B: Europe Europe

29,266

10,522

Austria Belgium Denmark Finland France Germany Greece Italy Netherlands Norway Portugal Spain Sweden Switzerland United Kingdom

360 1000 685 341 2643 10,740 523 794 791 585 296 311 1203 1130 7677

All Top 5

65,738 58,922

FMV N 10

#Dead

%Dead

#Return

%Return

#I/B/E/S

%I/B/E/S

6272

2554

40.7%

6180

98.5%

4641

74.0%

9383

7019

1996

28.4%

6901

98.3%

4101

58.4%

177 288 365 190 1458 1833 393 390 272 328 146 204 549 387 3444

161 263 230 180 1368 1525 360 365 250 284 134 180 441 316 3232

119 206 197 159 945 1017 338 345 201 254 92 170 346 277 2268

31 40 55 42 258 228 57 95 77 98 48 51 109 49 732

26.1% 19.4% 27.9% 26.4% 27.3% 22.4% 16.9% 27.5% 38.3% 38.6% 52.2% 30.0% 31.5% 17.7% 32.3%

115 200 197 155 917 991 338 345 199 252 91 168 344 274 2232

96.6% 97.1% 100.0% 97.5% 97.0% 97.4% 100.0% 100.0% 99.0% 99.2% 98.9% 98.8% 99.4% 98.9% 98.4%

80 129 146 132 603 630 195 229 180 166 62 155 237 213 944

67.2% 62.6% 74.1% 83.0% 63.8% 61.9% 57.7% 66.4% 89.6% 65.4% 67.4% 91.2% 68.5% 76.9% 41.6%

30,454 27,314

16,568 13,845

13,206 10,848

4524 3881

34.3% 35.8%

12,998 10,664

98.4% 98.3%

8742 7055

65.8% 65.0%

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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2. Data 2.1. Sample selection We use a comprehensive sample of companies domiciled in 16 equity markets, 15 European markets and the U.S., covering the period from July 1990 to March 2009. All data has been gathered from Datastream including I/B/E/S earnings revisions data. Table 1 contains the descriptive characteristics of the sample countries classified by region. We collected companies for each country by merging the live and dead research lists provided by Datastream and thereby obtained a total number of 65,738 companies. To arrive at our final sample, we have pruned the initial country research lists as follows. First, we adjusted each country list for secondary issues and cross-country listings to prevent double-counting. In particular, we extracted 30,454 companies. Hence, one-half of the initial list does refer to major listings.1 Second, we screened for non-equity issues, i.e., we excluded investment trusts, ADRs, and the like. Third, we also excluded OTC stocks and stocks that are only listed on regional exchanges. These two screenings resulted in 16,568 companies. We further excluded those companies with a market capitalization of less than 10 million USD, which leaves us with a final sample of 12,998 companies. Almost one-half are U.S. companies and the biggest five markets make up around 80%. To avoid survivorship bias, the sample includes 4524 “dead” companies, i.e., one-third of the whole sample, ranging from 16.9% for Greece to 52.2% for Portugal. The label “dead” applies to companies in extreme distress and to those being merged, delisted, or converted. Since we aim to investigate the dispersion effect, we additionally check the coverage of return and earnings revisions data.2 Unsurprisingly, the coverage for return data is close to 100% in each country, on average 98.4% of the companies do exhibit at least one return observation over the course of the sample period. On the other hand, the earnings estimates figures are more fragmentary. However, the average coverage still amounts to 65.8% spanning a range from 41.6% (U.K.) to 91.2% (Spain). Note that our sample contains a certain amount of penny stocks that will not be included in the investment strategies. We do not discard these stocks right away, since being a penny stock is not a static firm characteristic. In particular, we do not invest in companies with stock price below 5 USD at the beginning of a given month. 2.2. Return data We consider monthly stock returns in local currency inclusive of dividends by employing total return figures. To represent the respective markets, we chose broad market indices as compiled by Datastream. Short-term government issues serve as a proxy for the risk-free rate. Ince and Porter (2006) show that the well-known price momentum effect cannot be detected in the U.S. when naïvely using raw Datastream data, an observation that we find extends to other international markets as well. To cure these data issues, Ince and Porter (2006) propose two major adjustments. One is to remove non-common equity from the country research lists and the other is to screen for irregular return patterns. Since the former has already been dealt with when deleting secondary issues, we merely have to address the quality of the return data. We follow Ince and Porter (2006) in adjusting the return data to allow for reasonable statistical and economic inferences. Interestingly, we find our comprehensive sample to be little confounded by erroneous return data. For instance, the U.S. only requires changing 161 return observations, which corresponds to 0.01% of all observations. This fraction is even smaller for Europe, for which we adjusted 69 observations across all 15 countries. We assume that Datastream has significantly corrected the database in response to the objections of Ince and Porter (2006).3 Still, the remaining issues might severely affect statistical inferences and weeding them out makes us even more comfortable with the quality of the data. 3. Testing for the dispersion effect 3.1. Risk and return We implement the dispersion strategy as in Diether et al. (2002), defining dispersion as the standard deviation of earnings forecasts over the absolute value of its mean. Based on the previous month's dispersion, we assign stocks monthly into five quintiles. Unfortunately, building quintile portfolios is not viable in some countries: the number of eligible stocks in Austria, Belgium, Finland, Greece, Norway, or Portugal is too small to provide sufficiently diversified test portfolios for the dispersion effect.4 Therefore, these countries are dropped when testing for country-specific dispersion effects. Nevertheless, the companies of the dropped countries add to the European sample used for assessing the aggregate European dispersion effect.5 Adopting a holding period of one month, the dispersion 1 To assign cross-listed stocks to a single market we checked the unique Datastream identifier “MAJOR” which indicates whether the current issue is a major listing. See Schmidt et al. (2011) for a comprehensive guide to screening Datastream country research lists. 2 Note that our analysis relies on the unadjusted data file of I/B/E/S. 3 In fact, according to an employee of Thomson Financial Services, the return time series is constantly screened for possible glitches in the price, dividend, and adjustment factor history. In particular, the history of several U.S. OTC stocks has been fixed recently, which presumably accounted for a lot of the issues detected by Ince and Porter (2006). 4 For a country to be considered it is required to have at least 25 eligible stocks in any given month of the sample period. Note that this choice will not give rise to overly volatile dispersion portfolios in each country, see Table 4. 5 To test for dispersion effects in the dropped countries one might consider tercile instead of quintile portfolios. However, tercile portfolios most likely will not generate return differentials of the same magnitude as quintile portfolios because the difference in the average level of analyst forecast dispersion will be smaller.

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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Table 2 Country universes by year. The table gives the number of companies to be considered for the dispersion strategy averaged over the months of a given year. In a given month a country's eligible stocks are tracked and the table gives yearly figures averaged over all months. Panel A covers the U.S. and Panel B covers European countries. Year

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

Panel A: USA USA

937

1006

1133

1290

1411

1614

1862

2070

2152

2341

2197

1926

1772

1999

2092

2186

2222

2068

1499

Panel B: European countries Europe 885 965

1024

1075

1186

1366

1464

1626

1739

1920

1801

1464

1214

1355

1419

1614

1790

1823

1267

93 152 156 35 94 65 37 95 160

56 160 165 31 95 64 38 96 190

59 179 177 36 99 67 46 94 188

67 204 179 42 109 68 63 99 219

72 233 179 41 113 68 78 104 263

80 254 204 55 118 79 101 111 290

80 272 207 65 130 90 119 118 279

79 300 264 68 137 96 132 126 327

77 306 269 75 124 91 116 132 268

52 271 200 68 101 83 77 128 206

39 242 151 61 87 74 61 108 171

44 242 160 66 88 77 76 107 247

61 237 163 75 85 74 82 104 291

61 258 195 99 85 79 92 128 319

58 278 233 114 87 84 96 132 366

62 285 265 102 85 79 100 141 350

48 234 200 64 61 59 65 127 174

Denmark France Germany Italy Netherlands Spain Sweden Switzerland UK

77 131 114 38 91 76 34 94 140

89 146 134 40 94 71 36 92 158

strategy is to go long stocks with low dispersion and to go short stocks with high dispersion in analysts' earnings forecasts. Table 2 gives the number of companies eligible for the dispersion over time. We observe the U.S. and the European aggregate to build on a similarly large number of companies. Even though some European countries, such as Italy and Sweden, exhibit rather small samples at the beginning—starting with 38 and 34 companies, respectively—their coverage increases over time. Table 3 gives average monthly buy-and-hold returns and volatility figures of dispersion-based portfolios by country. First, we assess the profitability of the dispersion hedge strategy by considering the return differential—low dispersion minus high dispersion stocks—along with its t-statistic. For the U.S., we confirm prior evidence of Diether et al. (2002) and Avramov et al. (2009). We obtain a monthly hedge return of 49 basis points at a monthly volatility of 4.15%, which give rise to a t-statistic of 1.77. Note that the returns of the dispersion-based portfolios decrease monotonically with increasing dispersion, while their volatility is positively related to dispersion. The aggregate European hedge strategy provides a similar return of 51 basis points per month, but at a considerably lower volatility of 2.87%, corresponding to a t-statistic of 2.65. Further, using the t-statistic metric, we identify Germany, Italy, the Netherlands, and Spain as having anomalous returns at the 5%-level. If we relax the significance level to 10%, France and Denmark appear to be anomalous as well. All of the remaining countries exhibit positive return differentials as well. While the low dispersion portfolio sometimes contributes significantly to the return spread, we note that the lion's share is typically due to the high dispersion portfolio. Given this preliminary evidence of international dispersion effects, we seek to further characterize the involved dispersion portfolios by examining their descriptive statistics in Table 4. First of all, inspecting the average dispersion of the available dispersion-based portfolios suggests that the dispersion in analysts' earnings forecasts follows a heavily right-skewed distribution. Especially the average dispersion of the high dispersion portfolio is rather large. For instance, while the fourth U.S. quintile portfolio has an average dispersion of 7.31%, the high dispersion portfolio figure amounts to 55.51%. Note that this pattern is even more pronounced for the European countries. Just consider the high dispersion portfolio of the European strategy, which has a mean dispersion of 100.53%, indicating considerable disagreement among the analysts.6 On the other hand, the low dispersion portfolio has a mean dispersion of 2.51%, which is indicative of a strong consensus among the analysts. Note that the European countries are not completely homogenous in terms of the average dispersion numbers. For the European dispersion strategy, this observation translates into a country bias with respect to the U.K. Relative to the total sample, the European low dispersion portfolio tends to be overweighted in U.K. stocks, whereas the high dispersion portfolio is underweight U.K. stocks. Other than this, we do not detect significant country biases.7 Moreover, across all countries, the dispersion-based portfolios' volatility increases with dispersion, which indicates that these portfolios might differ in terms of their market betas. To clarify this, we compute the betas according to the classical regression Rit −RFt ¼ α i þ βi ðRMt −RFt Þ þ εit ;

ð1Þ

where Rit denotes the gross return of quintile i, RFt is the country-specific risk-free rate, and RMt is the country's market return.8 The beta of the dispersion-based portfolios also increases with dispersion. Moreover, in all countries the highest betas obtain for the high dispersion quintile. Also, while the remaining portfolios with lower dispersion have rather homogenous size characteristics,

6

Note that a high dispersion could be either due to high forecast dispersion or the average earnings forecast being close to zero. In unreported results, we observe that the performance evolution of the low and high dispersion portfolios corresponding to a country-neutral implementation almost coincides with that of the original strategy. In particular, the corresponding dispersion hedge strategy returns 46 bp per month at a volatility of 2.55% which compares to the original strategy with 51 bp return at 2.87%. As a result, the corresponding t-statistics are almost identical, 2.72 for the country-neutral strategy versus 2.65 for the original strategy. 8 We use a GDP-weighted risk-free rate of the country-specific rates for the European aggregate. 7

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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Table 3 Return of dispersion portfolios. The table gives average monthly buy-and-hold returns of quintile portfolios that are built monthly dependent on the level of dispersion. We give the return differential of the respective hedge strategies along with the according t-statistic. The second column gives the average number of stocks eligible for a given country's dispersion hedge strategy. All figures refer to the period from July 1990 to March 2009. Country

USA Europe Denmark France Germany Italy Netherlands Spain Sweden Switzerland UK

#Stocks

1777.7 1420.9 66.7 233.4 193.7 63.8 100.4 77.1 78.1 113.2 251.7

Portfolio dispersion ranking Low

2

3

4

High

Low–high

t-statistic

1.25 0.83 0.86 0.83 0.45 0.48 0.99 1.16 1.20 0.75 0.89

0.85 0.75 0.59 0.81 0.29 0.56 0.99 0.96 0.97 0.73 0.79

0.90 0.66 0.56 0.68 0.26 0.51 0.72 0.61 0.89 0.59 0.79

0.86 0.55 0.43 0.59 0.02 0.20 0.68 0.83 1.03 0.29 0.77

0.76 0.32 0.33 0.34 −0.22 −0.11 0.19 0.52 0.95 0.66 0.65

0.49 0.51 0.53 0.48 0.67 0.59 0.80 0.64 0.25 0.09 0.23

1.77 2.65 1.74 1.78 2.58 2.00 2.62 2.19 0.71 0.34 0.95

Table 4 Descriptive statistics of dispersion portfolios. The table gives mean values of dispersion (in %), volatility (in %), beta and log-size over the whole period. Quintile portfolios are built monthly dependent on the level of dispersion. We consider the quintile portfolios' betas (arising from a standard CAPM) and size is measured as the average of log (market value). Country

USA

Europe

Denmark

France

Germany

Italy

Netherlands

Spain

Sweden

Switzerland

UK

Portfolio dispersion ranking

Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size Dispersion Volatility Beta Size

Low

2

3

4

High

Low–high

0.64 4.82 0.78 20.69 2.51 4.06 0.88 22.02 3.53 5.15 1.01 21.47 3.17 4.95 0.96 20.19 3.37 5.28 1.09 20.21 4.46 6.25 0.87 20.71 2.35 4.86 0.84 20.18 3.53 5.09 0.78 20.87 3.82 5.79 0.64 22.17 3.52 4.55 0.94 20.67 1.61 3.89 0.66 24.67

2.00 5.01 0.82 20.84 5.83 4.45 0.97 21.68 7.75 4.95 0.95 21.75 6.51 5.36 1.07 20.61 7.33 5.56 1.12 20.59 9.02 6.84 0.92 20.89 4.81 4.94 0.90 20.23 7.13 5.56 0.86 20.99 7.82 5.94 0.66 22.55 7.30 5.31 1.11 20.90 3.17 4.38 0.73 25.09

3.64 5.62 0.95 20.56 9.70 4.83 1.05 21.24 13.10 5.56 1.03 21.55 10.23 5.76 1.16 20.42 11.96 5.93 1.25 20.54 13.14 6.70 0.95 20.81 7.72 5.43 0.97 20.09 10.87 5.85 0.92 20.62 12.71 6.32 0.70 22.40 11.69 5.90 1.22 20.79 4.87 4.60 0.74 25.23

7.31 6.34 1.09 20.26 16.91 5.14 1.14 20.76 22.29 5.89 1.15 21.42 17.14 6.17 1.26 20.17 21.58 6.09 1.28 20.26 19.61 6.83 0.99 20.49 13.23 5.77 1.07 19.88 16.88 6.71 1.08 20.34 21.89 7.38 0.79 22.20 19.65 5.99 1.25 20.53 7.75 4.82 0.81 25.36

55.51 7.59 1.30 19.91 100.53 6.03 1.33 20.17 131.10 6.41 1.28 20.96 116.98 7.29 1.52 19.63 121.91 7.69 1.61 19.73 64.15 8.08 1.17 20.15 97.24 6.93 1.27 19.12 72.21 7.30 1.16 19.65 121.06 8.12 0.97 21.91 112.77 6.80 1.38 19.97 42.20 6.02 1.03 25.07

−54.87 4.15 −0.52 0.78 −98.02 2.87 −0.46 1.85 −127.57 4.55 −0.27 0.51 −113.81 4.07 −0.56 0.56 −118.54 3.90 −0.52 0.48 −59.69 4.42 −0.30 0.56 −94.89 4.56 −0.42 1.06 −68.68 4.37 −0.39 1.22 −117.24 5.27 −0.34 0.26 −109.25 4.02 −0.44 0.70 −40.59 3.71 −0.37 −0.40

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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the high dispersion portfolio is different. In particular, measuring size in terms of the logarithm of market value, we find that the high dispersion portfolio is mostly populated by small caps, which may in turn explain its conspicuous market exposure. Finally, turning to the hedge strategy, we almost always observe considerable negative exposure to the market portfolio, suggesting a distinct hedge potential with respect to market risk. 3.2. Time-series regressions Some of the examined long–short dispersion strategies are highly volatile: thus, we wonder whether their high returns solely compensate for the risks involved. To check whether the long–short portfolio returns can be attributed to common risk factors, one usually adopts the standard approach of Fama and French (1993) and estimates a regression model of the form RLt −RSt ¼ α þ βðRMt −RFt Þ þ γRSMBt þ δRHMLt þ εt ;

ð2Þ

where RLt − RSt is the return difference of the respective hedge strategy, i.e., the long leg minus the short leg. For each country, we compute the country-specific factors as follows: a country's broad market index represents its market return RMt while the size and value factor are computed according to the methodology of Fama and French (1993). For the European aggregate, we apply the very same methodology to the whole universe of European companies. Thus, we did not aggregate country-specific Fama–French factors of the European countries but computed direct Fama–French factors for Europe.9 Given the factor structure in (2), we can identify the hedge strategy's alpha net of common risk factors. In addition to the Fama–French factors, one commonly considers price momentum as a further factor to control for. Given that prior research has documented price and earnings momentum to be fairly closely connected, see Leippold and Lohre (2012), one might deem the earnings momentum factor to be likewise meaningful when testing for the dispersion effect. In fact, given that dispersion is the second moment of the earnings estimate distribution, it seems natural to adjust the dispersion strategies' returns for earnings momentum, which derives from the first moment of this distribution. Therefore, we conjecture earnings momentum to be more closely related to the dispersion effect than price momentum.10 Indeed, in untabulated results, we find earnings momentum and the dispersion effect to be highly correlated in terms of returns and Fama–French alphas. While a high return correlation may simply be picking up systematic risk factor tilts shared by both anomalies, the high correlation in Fama–French alphas suggests that there is a common unsystematic component at work as well. Hence, when testing for the dispersion effect, we extend the Fama–French setting of Eq. (2) to a four-factor model by adding an earnings momentum factor: RLt −RSt ¼ α þ βðRMt −RFt Þ þ γRSMBt þ δRHMLt þ ζ RPMNt þ εt ;

ð3Þ

where RPMNt refers to the returns of the earnings momentum strategy (positive minus negative earnings revisions). In computing the earnings momentum factor, we follow the standard methodology of Chan et al. (1996). Table 5 displays the results of the four-factor regression for dispersion-based portfolios according to Eq. (3), which uses 225 monthly returns spanning the period from July 1990 to March 2009. First, we examine the results for the U.S. We observe that the risk factors explain most of the variation in the excess returns of both legs of the dispersion strategy. In particular, the low dispersion portfolio heavily loads to the market and size factors and exhibits a positive exposure to earnings momentum, rendering the remaining alpha of 9 basis points insignificant. On the other hand, the high dispersion portfolio generally behaves like growth stocks with a significant negative earnings momentum loading. Still, an unexplained alpha of −68 basis points remains: thus, the long–short strategy earns a highly significant monthly alpha of 77 basis points. Interestingly, while this alpha is large, the statistical fit of the regression is fairly good considering the fact that one is analyzing a long–short strategy. Almost two-thirds of the variation in the dispersion strategy's excess returns is captured by the four-factor model. In particular, we confirm the considerable negative market exposure together with a negative loading on size. Finally, we identify a close positive relation between earnings momentum and the dispersion effect. However, the dispersion effect is not subsumed by earnings momentum, suggesting that they represent distinct phenomena. By and large, these observations extend to other countries as well. However, among the 9 European countries, we find the Spanish alpha to be significant at the 5%-level and the Italian one at the 10%-level. Also, it appears to be a stylized fact that the alpha of the dispersion effect is governed by the underperformance of the high dispersion portfolio. While the adjusted R2 for the European strategies usually do not reach the level of the U.S. strategy, we still observe remarkably high values. With the exception of Denmark, all of the regressions for the long–short strategies have adjusted R2s in excess of 30%. These figures are quite sizeable, given that the typical values for meaningful long–short strategies are in the single digits. Interestingly, the returns for the aggregate European strategy are fully captured by the common factor controls.11 To further examine the evolution of both hedge strategies over time, we compute the related country alphas via trailing four-factor regressions according to Eq. (3). We use a 36-month window and plot the resulting alphas in Fig. 1 for the U.S. and Europe. To also visualize the importance of adjusting for the earnings momentum factor, we plot the alphas arising from a Fama–French regression according to Eq. (2). For gauging the statistical significance of the four-factor alpha we plot corresponding 95%-confidence intervals.12 9

For details on the construction of the European Fama–French factors, we refer the reader to Schmidt et al. (2011). For the relation between dispersion and earnings momentum see also Berkman et al. (2009) and Scherbina (2008). 11 In unreported results we find standard Fama–French-Momentum regressions building on price momentum to give similar results. However, supporting our choice of momentum factor, the statistical fit is slightly worse when using price instead of earnings momentum as a common factor control. 12 Note that the estimated alpha is shifted forward relative to the actual period because of using trailing three-year windows to estimate alphas. 10

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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7

Table 5 Time-series-regressions of dispersion portfolios. The table gives the results of a regression according to Eq. (3) using 225 monthly returns ranging from July 1990 to March 2009 along with the according t-statistics. 4-factor Fama–French-Earnings Momentum Model

USA

Europe

Denmark

France

Germany

Italy

Netherlands

Spain

Sweden

Switzerland

UK

Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high Low High Low–high

α

t(α)

β

t(β)

γ

t(γ)

δ

t(δ)

ζ

t(ζ)

Adj. R2

0.09 −0.68 0.77 −0.03 −0.11 0.09 0.13 −0.23 0.36 −0.17 −0.43 0.26 −0.06 −0.30 0.24 −0.01 −0.42 0.41 0.17 −0.14 0.31 0.17 −0.29 0.46 0.12 0.04 0.08 −0.01 0.19 −0.21 0.34 0.46 −0.11

0.79 −4.36 4.47 −0.30 −0.93 0.60 0.66 −1.02 1.21 −1.13 −2.85 1.29 −0.39 −1.42 1.14 −0.03 −2.17 1.67 1.09 −0.79 1.31 1.20 −1.63 2.06 0.55 0.17 0.27 −0.13 1.19 −1.03 2.94 2.32 −0.54

0.93 1.25 −0.32 0.95 1.30 −0.35 1.05 1.27 −0.22 1.00 1.40 −0.40 1.04 1.50 −0.45 0.91 1.13 −0.22 0.91 1.16 −0.25 0.85 1.10 −0.25 0.72 0.98 −0.27 0.98 1.24 −0.26 0.81 1.14 −0.33

39.32 39.63 −9.09 47.73 47.16 −10.52 23.40 23.86 −3.21 30.22 41.38 −8.70 28.87 30.64 −9.37 30.31 36.16 −5.63 25.69 29.95 −4.79 32.78 34.11 −6.24 23.27 29.06 −6.47 34.03 30.27 −5.03 30.72 25.68 −6.94

−0.32 −0.04 −0.28 −0.33 −0.28 −0.06 −0.19 −0.03 −0.16 −0.32 −0.18 −0.13 −0.32 −0.33 0.02 −0.20 −0.18 −0.03 −0.14 −0.01 −0.12 −0.19 −0.04 −0.15 −0.26 −0.28 0.03 −0.07 −0.04 −0.03 −0.35 −0.33 −0.02

−10.70 −1.02 −6.32 −12.65 −7.57 −1.28 −2.75 −0.36 −1.51 −9.66 −5.48 −2.97 −7.17 −5.62 0.32 −4.15 −3.44 −0.41 −2.99 −0.26 −1.81 −5.66 −0.99 −2.81 −5.82 −5.84 0.45 −2.08 −0.78 −0.55 −11.06 −6.29 −0.28

0.01 −0.19 0.20 0.07 −0.11 0.18 −0.05 −0.04 −0.01 −0.07 −0.07 0.00 −0.03 −0.12 0.09 −0.05 −0.07 0.02 0.01 0.05 −0.04 −0.09 −0.05 −0.04 0.04 −0.01 0.04 −0.01 0.03 −0.04 −0.08 −0.04 −0.04

0.18 −3.69 3.45 1.99 −2.31 3.09 −1.30 −0.94 −0.12 −2.05 −1.99 −0.01 −0.70 −2.40 1.89 −1.28 −1.64 0.33 0.30 1.44 −0.85 −2.94 −1.36 −0.79 1.31 −0.16 1.10 −0.52 0.73 −0.88 −1.96 −0.64 −0.50

0.17 −0.27 0.44 0.26 −0.37 0.63 0.02 −0.20 0.22 0.06 −0.57 0.63 0.05 −0.48 0.53 0.19 −0.35 0.53 0.26 −0.39 0.65 0.18 −0.29 0.46 0.22 −0.27 0.48 0.15 −0.53 0.69 0.17 −0.38 0.55

3.33 −3.86 5.73 5.09 −5.21 7.34 0.46 −3.78 3.21 1.08 −9.45 7.80 0.71 −5.42 6.00 3.23 −5.77 6.94 5.85 −7.95 9.75 4.47 −5.83 7.47 4.15 −4.69 6.91 3.93 −9.79 10.11 3.42 −4.50 6.15

88.4 91.7 65.8 92.7 93.6 58.4 71.0 73.6 10.4 83.2 92.0 52.8 82.8 85.1 42.7 80.9 87.5 31.8 78.9 87.4 45.7 83.5 87.5 44.0 70.8 81.9 35.1 87.2 88.5 48.5 81.4 78.1 34.7

First of all, we note that the inclusion of the earnings momentum factor is relevant, since the Fama–French alpha is thus considerably reduced. Also, while this reduction typically is present throughout the whole sample period, it appears to be weakest at the turn of the century. Second, the U.S. strategy exhibits the most sizeable alpha, which is positive for the whole sample period and often significantly greater than zero. Third, the evolution of the European alpha appears downward shifted when compared to the U.S. As a result, the four factor alpha is hardly deemed to be significantly positive within the sample period.

400 350

400

Fama−French Four−Factor 95%−CI

350 300

250

250

200

200 Alpha (bps)

Alpha (bps)

300

USA

150 100 50

Fama−French Four−Factor 95%−CI

150 100 50

0

0

−50

−50

−100

−100

−150 1993

Europe

1996

1999

2002

2006

2009

−150 1993

1996

1999

2002

2006

2009

Fig. 1. Trailing alpha of the dispersion effect. We plot trailing dispersion strategy alphas arising from Eqs. (2) and (3) using an estimation window of 36 months, thus the results cover July 1993 to March 2009. The dashed line gives the Fama–French alpha and the solid line is the corresponding four-factor alpha. The shaded area depicts the 95%-confidence interval (CI) of the four-factor alpha.

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

8

M. Leippold, H. Lohre / Journal of Empirical Finance xxx (2014) xxx–xxx USA

Europe

Dispersion Market

Dispersion Market 6

Cumulative Return

Cumulative Return

6

4

2

0 1990

4

2

1994

1997

Time

2001

2005

2009

0 1990

1994

1997

Time

2001

2005

2009

Fig. 2. Cumulative returns: dispersion versus market portfolio. The figure gives cumulative returns of the dispersion hedge portfolio (solid line) and of a broad market index (dashed line). The left chart gives results for the U.S. strategy, and the right chart gives results for the European aggregate strategy. The sample period is from July 1990 to March 2009.

4. Rationalizing the dispersion effect In the following, we seek to delve into the economic nature of the dispersion effect. First, we consider the evolution of the related strategies over time. Second, we will analyze the interaction of the dispersion effect with measures of information uncertainty. Third, we examine the profitability of dispersion strategies in the presence of varying levels of liquidity.

4.1. The dispersion effect over time In the following, we seek to sharpen our intuition about the time series nature of the dispersion effect. Therefore, Fig. 2 depicts the cumulative return for the U.S. and the European strategies. A striking common pattern emerges: following a steady build-up of wealth until the end of 1998, we observe a severe drawdown. For example, the U.S. strategy erodes all of its accumulated wealth within the subsequent year. The decline in performance is reversed for almost all countries in March 2000. Even more so, the dispersion strategy soars to a new height within the next three years. While the subsequent period is typically characterized by rather flat return paths across countries, we observe that the sharp correction of the markets during the financial crisis again proves to be fertile a ground for the dispersion strategies' profitability. Note that the general evolution of the European dispersion effect only resembles that of the U.S. for the second half of the sample period. While the U.S. dispersion effect amasses significant wealth in the first half of the sample period, the positive European return differentials mainly derive from a narrow time frame, namely March 2000 to March 2003. Comparing the dispersion strategy performance to the evolution of a broad market index, it indeed appears that the dispersion strategy would have been a quite effective hedge against the market downturn following the burst of the technology bubble at the beginning of the century.13 To further disentangle the performance drivers of the dispersion effect, we investigate the performance of the low dispersion and the high dispersion portfolios in Fig. 3. Focusing on the time frame March 2000 to March 2003, we find the U.S. low dispersion portfolio significantly accumulating wealth, while the high dispersion portfolio is eroding wealth. On the other hand, the European low dispersion portfolios' movements are rather flat in the same period. Hence, the resulting dispersion effects are solely driven by a severe underperformance of the short legs. This observation is quantified by the subperiod analysis conducted in Table 6. In particular, we focus on the subperiod March 2000 to March 2003 and the two surrounding subperiods August 1990 to February 2000 and April 2003 to March 2009. The choice of breakpoints is motivated as follows: Except for the U.S. most countries exhibit a rather flat return pattern outside the 2000–2003 window. Especially, the strategies experience a decline in performance at the end of the nineties. This pattern of declining performance ends for almost all countries in March 2000, defining the first breakpoint. The following three years are marked by significant outperformance of the dispersion strategy reaching a global peak in April 2003, defining the second breakpoint. 13 This finding does not imply that the dispersion strategy represents a bet against the technology bubble. In unreported results we document that the share of technology stocks in the high dispersion portfolio was increasing at the end of the 1990s. Focusing on the average industry allocation from April 1998 to March 2003 (when the dispersion effects proved to be most profitable) we indeed observe a significant active bet against technology stocks implicit in the dispersion hedge strategy. However, excluding technology stocks from the sample reduces the dispersion effects' returns by 6 bp per month on average which hardly impairs the significance of return differentials and time series regression alphas.

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

M. Leippold, H. Lohre / Journal of Empirical Finance xxx (2014) xxx–xxx

25

USA

15

Market Low Dispersion High Dispersion

9 Europe

Market Low Dispersion High Dispersion

Cumulative Return

Cumulative Return

20

15

10

10

5

5

0 1990

1994

1997

Time

2001

2005

2009

0 1990

1994

1997

Time

2001

2005

2009

Fig. 3. Cumulative returns: dispersion legs versus market portfolio. The figure gives cumulative returns of the long and short legs of the dispersion hedge strategy. The dotted line is for the low dispersion portfolio, the dashed line is for the high dispersion portfolio, and the solid line is for the market portfolio. The left chart gives results for the U.S. strategy, and the right chart gives results for the European aggregate strategy. The sample period is from July 1990 to March 2009.

For the 1990–2000 decade, we note that the hedge return differentials are hardly significant. Considering the subperiod 2000–2003 in Table 6, the resulting return differentials are more sizeable than those of the whole sample period, given that the European countries have rather flat return patterns outside the 3 year subperiod. The declining performance of the dispersion hedge strategy prior 2000 is almost always due to the extraordinary performance of the short leg. With the technology bubble bursting in March 2000, these high dispersion stocks then suffered extremely negative returns that more than outweighed the dispersion strategies' previous losses. In fact, half of the European country strategies exhibit significant return differentials in the 2000–2003 period. However, the corresponding four-factor alphas, collected in Panel B of Table 6, are insignifcant relating to their elevated exposure to common risk factors, viz. the market risk factor. While the U.S. dispersion strategy is also exposed to a considerable amount of systematic risk—its adjusted R2 amounts to 83.4%—the corresponding alpha is the only one to be deemed highly significant in that 3-year period. Still, being short high dispersion companies would have been a favorable thing to do. However, we conjecture that any real-world implementation would have been rather unfeasible—just think of the up-tick rule. Of course, one may argue that most of the involved shorts could have already been in place at the beginning of 1999. However, with stock prices subsequently reaching unwarranted levels, one would have had trouble meeting the according margin calls. Thus, many investors would have not been able to follow the dispersion strategy when it was really profitable. To summarize: prior to 1999, only the U.S. dispersion effect has consistently provided abnormal returns. On the other hand, the most sizeable part of the effect derives from a narrow time frame of three years. Hence, to really capture those excess returns would have required a rather patient investor, equipped with 10 years waiting time, who is not wiped out of this strategy following the violent swing in 1999.

4.2. The dispersion effect and information uncertainty In this section, we will analyze the interaction of the dispersion effect with information uncertainty. Presumably, the respective price drift should be higher in more opaque information environments for which information diffusion is slowest. In fact, the dispersion of analysts' earnings forecasts is a common proxy for information uncertainty. Besides this metric, Zhang (2006) provides evidence that the U.S. price momentum strategy is more effective when limited to high uncertainty stocks as measured by size, firm age, analyst coverage, stock volatility, or cash flow volatility. If the dispersion effect is confined to a highly uncertain information environment, investors would certainly be less prone to follow such a strategy. Hence, we will examine dispersion effect profits for different degrees of information uncertainty. We consider four measures to monthly proxy for information uncertainty: analyst coverage, size, total stock volatility, and idiosyncratic volatility. Total stock volatility and idiosyncratic volatility (arising from a standard Fama–French regression) are estimated monthly using a given stock's daily returns pertaining to the respective month. Panel A of Table 7 gives the according results using a similar sorting procedure as in the previous section. In particular, we first sort stocks into five quintiles based on dispersion. For each quintile the stocks are further sorted into three terciles based on one of the three information uncertainty proxies. Note that we report the results for the two extreme terciles and the corresponding return differential. Also, we provide the results of a t-test checking for significance in the differences between both terciles. Obviously, the double-sorting procedure requires a sufficient number of companies in a given country to deliver meaningful results. Hence, we focus on the U.S. and the European aggregate. Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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M. Leippold, H. Lohre / Journal of Empirical Finance xxx (2014) xxx–xxx

Table 6 Dispersion effect: subperiod analysis. The table gives average monthly buy-and-hold returns (Panel A) and four-factor alphas according to Eq. (3) (Panel B) of extreme quintile portfolios that are built monthly dependent on the level of dispersion. In Panel A, Volatility figures are given below return figures, both referring to the periods August 1990 to February 2000, March 2000 to March 2003, and April 2003 to March 2009. We give the return differential of the respective hedge strategies, Lo–Hi, along with the according t-statistic. In Panel B, we give four-factor alphas are given above the corresponding t-statistics. The table also reports the adjusted R2 arising from the hedge strategies' time series regressions. Country

1990–2000 Low

Panel A: Returns USA Europe Denmark France Germany Italy Netherlands Spain Sweden Switzerland UK

1.76 4.31 1.23 3.57 0.95 4.46 1.28 4.93 0.79 4.09 0.75 6.98 1.39 4.06 1.28 5.94 1.84 6.09 1.04 4.38 1.18 3.64

Panel B: Four-Factor Alpha USA −0.19 −1.33 Europe 0.00 −0.03 Denmark 0.02 0.10 France 0.11 0.58 Germany −0.18 −1.20 Italy −0.27 −0.89 Netherlands 0.32 1.89 Spain 0.01 0.06 Sweden 0.26 0.79 Switzerland −0.19 −1.18 UK −0.08 −0.50

2000–2003 High

Lo–Hi

1.49 5.59 1.07 4.97 0.37 4.98 0.84 5.94 0.60 4.96 0.72 8.05 0.91 5.47 0.77 8.52 1.66 8.22 1.18 5.70 1.38 5.00

0.27 2.87 0.17 2.43 0.58 3.64 0.44 3.20 0.19 2.38 0.04 4.33 0.48 3.77 0.51 5.09 0.17 5.64 −0.14 2.95 −0.20 3.12

−0.42 −2.39 −0.19 −1.24 −0.23 −0.94 −0.16 −0.91 −0.03 −0.15 −0.31 −1.12 0.00 −0.01 −0.17 −0.57 −0.14 −0.41 0.05 0.26 0.28 1.38

0.23 1.30 0.18 0.94 0.25 0.77 0.27 1.09 −0.15 −0.79 0.04 0.11 0.32 1.07 0.18 0.52 0.40 0.89 −0.24 −1.00 −0.36 −1.36

t-stat 1.00 0.75 1.69 1.47 0.85 0.09 1.36 1.08 0.33 −0.52 −0.70

64.1 42.8 16.3 35.5 33.2 23.0 34.2 51.2 33.7 30.4 30.1

2003–2009

Low

High

Lo–Hi

0.80 4.51 −0.39 4.45 0.21 5.13 −0.42 5.21 −1.21 7.56 −0.75 6.52 −0.45 4.65 0.93 4.02 −0.11 6.04 −0.80 4.63 0.02 4.22

−0.80 11.13 −2.59 7.66 −0.43 7.54 −1.65 10.42 −3.99 12.12 −2.14 9.32 −2.23 9.35 −0.11 6.41 −2.21 10.25 −2.62 7.89 −1.92 7.70

1.60 7.88 2.20 4.26 0.64 6.17 1.23 6.84 2.78 6.47 1.39 5.31 1.79 6.66 1.04 4.14 2.10 6.54 1.83 5.83 1.94 5.19

0.26 0.73 0.26 0.96 0.15 0.26 −0.78 −1.65 1.37 2.89 0.24 0.64 −0.01 −0.02 0.39 1.32 0.86 1.16 0.26 0.79 1.10 4.28

−2.21 −3.45 0.35 0.98 −0.28 −0.40 −0.77 −1.43 0.56 0.79 −0.77 −1.26 0.81 1.56 −0.38 −0.93 0.81 1.22 0.31 0.63 0.20 0.32

2.47 3.97 −0.09 −0.18 0.43 0.43 −0.01 −0.01 0.81 1.01 1.01 1.31 −0.83 −1.04 0.77 1.39 0.05 0.07 −0.05 −0.08 0.90 1.43

t-stat 1.23 3.15 0.63 1.09 2.61 1.59 1.63 1.53 1.95 1.90 2.28

83.4 71.9 18.2 70.5 52.5 32.3 62.3 38.4 63.3 65.9 55.5

Low

High

Lo–Hi

0.67 5.66 0.81 4.48 1.04 6.14 0.75 4.79 0.75 5.47 0.67 4.72 1.09 5.95 1.08 4.10 0.85 5.06 1.08 4.67 0.87 4.09

0.39 8.08 0.63 6.26 0.64 7.73 0.58 7.27 0.39 7.93 −0.38 7.32 0.30 7.39 0.45 5.48 1.42 6.27 1.50 7.40 0.81 6.27

0.28 2.97 0.18 2.36 0.40 4.94 0.17 3.40 0.37 3.83 1.05 4.00 0.80 4.40 0.63 3.12 −0.57 3.49 −0.42 4.20 0.06 3.48

0.00 −0.03 −0.20 −1.27 −0.18 −0.53 −0.43 −1.92 −0.63 −1.59 0.54 2.23 −0.29 −0.92 0.28 1.50 −0.17 −0.53 0.03 0.18 0.58 2.76

−0.40 −1.98 −0.14 −0.75 −0.40 −0.94 −0.63 −2.69 −0.99 −2.11 −0.35 −1.44 −0.40 −1.17 −0.41 −1.80 0.47 1.19 0.17 0.58 0.77 2.37

0.40 2.14 −0.06 −0.35 0.21 0.36 0.20 0.67 0.36 0.84 0.89 2.64 0.11 0.32 0.69 2.23 −0.64 −1.46 −0.14 −0.39 −0.18 −0.56

t-stat 0.81 0.66 0.69 0.42 0.82 2.23 1.55 1.73 −1.40 −0.85 0.14

74.8 67.4 9.3 60.5 42.3 52.2 56.2 31.0 9.1 53.0 38.9

Our findings are as follows. First, the dispersion effect is indeed more pronounced for small stocks. This difference between small and large stocks is significant for the European strategy. Second, while the U.S. dispersion strategy is confined to stocks with low analyst coverage, this screen is rather indiscriminate for Europe. Third, analyzing the dispersion effect by different degrees of volatility we find the U.S. strategy to be only effective for high volatility stocks, be it total or idiosyncratic. Both differences in return differentials are highly significant. While this striking finding does not translate to the European strategy, we nevertheless conclude that the U.S. dispersion effect would have been difficult to arbitrage. In fact, a stock's idiosyncratic volatility is a common proxy for arbitrage costs, thus preventing rational investors from exploiting the U.S. dispersion effect. 4.3. The dispersion effect and liquidity In further elaborating on the above argument, we next examine the role of liquidity when implementing dispersion strategies. In fact, Sadka and Scherbina (2007) evidence that high dispersion companies happen to entail high trading cost. Also, the authors Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

M. Leippold, H. Lohre / Journal of Empirical Finance xxx (2014) xxx–xxx

11

Table 7 Dispersion effect versus information uncertainty and liquidity. The table gives return differentials of the dispersion hedge strategy by terciles of different information uncertainty and liquidity metrics. We first sort stocks into five quintiles based on the prior month's dispersion in analysts' earnings forecasts. In Panel A, for each quintile the stocks are further sorted into three terciles based on analyst coverage, size, total stock volatility and idiosyncratic volatility. Below the return differentials we give t-statistics in parentheses. For each information uncertainty metric, we compute the difference in the dispersion effect between extreme terciles and plot the according t-statistic below the return differential. Panel B gives analogous results for the liquidity metrics dollar volume, share turnover, the ILLIQ measure of Amihud (2002), and Liu's measure. Differentials are in bold face if significant on a 5%-level or in italics if significant on a 10%-level. Panel A: Information Uncertainty Country

USA Europe

Analyst coverage

Size

Volatility

Low

High

Lo–Hi

Low

High

0.56 (2.41) 0.40 (2.28)

0.28 (0.78) 0.44 (1.71)

0.28 (0.98) −0.04 (−0.17)

0.79 (3.01) 0.90 (4.60)

0.41 (1.26) 0.41 (1.65)

Lo–Hi 0.38 (1.38) 0.49 (2.33)

Idiosyncratic

Low

High

Hi–Lo

0.15 (0.74) 0.61 (4.80)

0.88 (3.44) 0.34 (1.52)

0.74 (3.32) −0.27 (−1.19)

Hi–Lo

Low 0.14 (0.68) 0.58 (4.50)

High

Hi–Lo

bf0.77 (2.95) 0.42 (1.87)

0.63 (2.71) −0.17 (−0.76)

High

Hi–Lo

Panel B: Liquidity Country

USA Europe

Dollar volume

Share turnover

ILLIQ

Liu measure

Low

High

Lo–Hi

Low

High

Lo–Hi

Low

High

0.52 (2.22) 0.63 (3.62)

0.56 (1.63) 0.29 (1.16)

−0.04 (−0.14) 0.34 (1.73)

0.45 (1.89) 0.56 (3.56)

0.54 (1.72) 0.40 (1.71)

−0.09 (−0.40) 0.15 (0.83)

0.35 (1.09) 0.30 (1.28)

0.55 (2.17) 0.64 (3.71)

0.20 (0.88) 0.34 (1.89)

Low ct 0.61 (1.93) 0.63 (2.37)

0.69 (3.09) 0.62 (4.41)

0.08 (0.31) −0.01 (−0.05)

observe the highest mispricing for the less liquid stocks, suggesting that trading costs erode all of the potential profits, thus rendering the arbitrage opportunity an illusion. Hence, we expect liquidity to also play a crucial role in inhibiting profitable execution of European dispersion strategies. To operationalize this conjecture, we will analyze the profitability of the dispersion strategies when restricted to high and low dispersion stocks characterized by different degrees of liquidity. Liu (2006) aptly describes liquidity “as the ability to trade large quantities quickly at low cost with little price impact”. To take into account these distinct dimensions of liquidity, we compute different metrics. A stock's dollar volume or its turnover allow capturing the trading quantity dimension. As for the price impact dimension, we resort to the ILLIQ measure of Amihud (2002), which is the absolute daily return over the associated dollar volume. To obtain an aggregate monthly value of ILLIQ, we simply compute its mean over the corresponding daily values. The fourth measure is the one introduced by Liu (2006), designed to capture multiple dimensions of liquidity, such as trading speed and trading quantity. Its definition is

Liu Measure ¼ Number of No  Trading Days over the prior 12 months þ

1=Turnover ; 1; 000; 000

ð4Þ

where Turnover is the average daily turnover over the prior 12 months. This measure addresses the trading speed dimension of liquidity since it very well captures lock-in-risk, i.e., the danger of being locked in a certain position that cannot be sold.14 Panel B of Table 7 displays the profitability of dispersion strategies restricted to high and low dispersion stocks characterized by different degrees of liquidity. In particular, we first sort stocks into five quintiles based on the dispersion in analysts' earnings forecasts. For each quintile the stocks are further sorted into three terciles based on one of the four liquidity measures. The general pattern for the U.S. is that the largest dispersion effects occur for the least liquid stocks and that profitability increases with illiquidity. For instance, the U.S. dispersion effect is only significant for the least liquid stocks—measuring liquidity by dollar volume, ILLIQ, or the measure of Liu (2006). The pattern of profitability's decreasing with liquidity can also be observed for the aggregate European strategy. Judging by dollar volume, share turnover, and ILLIQ, the strategy is only useful for the most illiquid stocks. Given that illiquidity is a common proxy for financial distress, our results complement the finding of Avramov et al. (2009) that the U.S. dispersion effect is confined to the worst rated companies. All in all, this evidence questions the possibility of a successful implementation of the examined dispersion effect. 5. Conclusion Examining the time series evolution of the international dispersion effects, we document that most of the associated returns to occur within a rather narrow time frame: three years. Moreover, we find the dispersion effect to be most pronounced among high and low dispersion portfolios characterized by high information uncertainty. Likewise, the highest hedge returns are obtained with the least liquid stocks, hence, high arbitrage costs will most likely deter investors from exploiting a given dispersion mispricing. 14

Note that while the first three measures only take into account the stocks' liquidity over the preceding month, the Liu measure hinges on data of the preceding year.

Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001

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Please cite this article as: Leippold, M., Lohre, H., The dispersion effect in international stock returns, J. Empir. Finance (2014), http://dx.doi.org/10.1016/j.jempfin.2014.09.001