1 Introduction
Allowing private investors to interact, social trading—also referred to as copy trading—is a financial innovation which has been surfaced through modern-day financial markets. There are various platforms offering differentiated forms of social trading as an integral part of their business model.1 All forms of social trading exhibit a distinction between signal providers and signal followers as a common defining feature. Regarding signal providers, social trading platforms enable visibility and traceability, i.e. their trading strategy specifications, conducted transactions, and resulting returns are published. Platform users can freely access the published information and subsequently subscribe to one or several signal providers. By delegating their investment decisions to another (mostly non-professional) trader, platform users become signal followers (Doering et al. 2015; Oehler et al. 2016).
Social trading involves severe asymmetries regarding the distribution of economic consequences between signal providers and signal followers. When an administered portfolio performs well, the corresponding signal provider is remunerated via performance fees. Furthermore, portfolios with good past performance are placed at the top of the platforms’ selection lists and thus generate attention2—the increased attention leading to higher inflows and, in consequence, a continued eligibility for remuneration (Röder and Walter 2019). On the other hand, a failing portfolio barely bears any (monetary) consequences for the signal provider (Schneider and Oehler 2021).
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Considering the present asymmetries, signal providers are exposed to a range of incentives which, in different contexts, have been shown to impact trading behavior. As elaborated by Carpenter (2000), portfolio managers face option-like (or convex) incentives, and thus may be led to increase risk after performing poorly.3 Furthermore, even though signal provider compensation may not be directly linked to a corresponding ranking, social trading compensation schemes indirectly impose tournament incentives as administered accounts have to occupy a relative position reasonably suited for generating attention from followers.4 In the presence of tournament incentives, there is empirical evidence that risk-taking is increased by underperforming traders (Kirchler et al. 2018). In the context of social trading, evidence that signal providers face convex incentives and thus increase risk when approaching their high watermark is provided by Doering and Jonen (2018).
Motivated by the present asymmetries, we assess whether signal provider transactions involving stocks which exhibit lottery characteristics (Bali et al. 2011; Kumar 2009) are driven by the relative past performance of their corresponding operated portfolios. By trading lottery-like stocks, signal providers expose their (perhaps unknowing) followers to a lottery-like return structure, i.e. trigger gambling. Regarding social trading, we are the first to our knowledge to explicitly analyze signal provider gambling with stocks.
Within the spectrum of social trading providers, the wikifolio platform seems most suitable to analyze stock gambling for several reasons. On the wikifolio platform, signal providers can choose from an extensive investment universe including stocks, funds, ETFs, investment certificates, and leverage products. However, when creating a portfolio (referred to as wikifolio), signal providers can choose to generally exclude leverage products from their trading activities; wikifolios which do not categorically exclude leverage products are permanently tagged with a warning label. Since leverage products are excluded within the vast majority of available wikifolios, stocks are being left as the only potential asset category for employing a lottery-like return structure.
There are social trading platforms like Zulutrade that primarily offer foreign exchange trading (Glaser and Risius 2018; Schneider and Oehler 2021) and thus cannot be employed to examine signal provider stock gambling. Other major social trading platforms like ayondo and eToro offer trading via Contracts for Difference (CFD) which in turn may be vastly levered (Berger et al. 2018; Dorfleitner et al. 2018; Pelster and Hofmann 2018). Hence, on platforms where every asset can be levered, it is unlikely that signal providers choose stocks to generate lottery-like payoffs, i.e. a relatively small probability of a large return (Bali et al. 2011; Kumar 2009).
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First, we assess whether the monthly number of transactions within an administered wikifolio, as well as the respective transaction volume, depends on a corresponding wikifolio’s relative past performance. We provide empirical evidence for a U-shaped relation between trading activity within a corresponding wikifolio and previous peer performance.
Subsequently, in the course of our main analysis, we examine the factors that have an impact on signal provider gambling as depicted by the relative monthly share of transactions involving lottery-like stocks. By assessing signal provider trading behavior regarding lottery-like stocks, we add a new aspect to the relatively new research area on social trading. Our results indicate that signal providers tend to increase the traded relative share of lottery-like stocks within an administered wikifolio when being placed at one of the extreme ends of the relative performance spectrum. These results are in line with Schneider and Oehler (2021), who report a similar pattern for traded currency pairs which exhibit extreme past daily returns. Furthermore, we provide empirical evidence that signal providers administering wikifolios with more moderate peer performance are more likely to trade nonlottery stocks, i.e. stocks exhibiting low idiosyncratic volatility and low idiosyncratic skewness.
As our previous results do not allow to derive a statement about the net exposure towards lottery-like return characteristics, we assess whether the net lottery flow—measured as the cumulative net investment into lottery-like stocks—is impacted by relative past wikifolio performance. The results from our analysis suggest that underperforming signal providers increase the net position of lottery-like stocks and therefore trigger gambling for their corresponding followers.
The present paper makes several contributions to pre-existing research. In the context of social trading, we are the first to our knowledge to analyze stock gambling, i.e. trading behavior regarding lottery-like stocks. Social trading forms a novel, information rich, and interactive digital environment—previously labeled as scopic regime (Gemayel and Preda 2018a, b). By linking behavioral patterns of traders, i.e. signal providers, in a social trading framework to pre-existing research in behavioral finance, we add to a more comprehensive understanding of actions, underlying motives, and aggregated outcomes. Signal providers on social trading platforms are subject to a limited monetary downside, as they may (partly) trade with virtual money. We discuss asymmetries regarding the distribution of economic consequences between signal providers and signal followers as well as how common social trading design features may drive signal providers to gamble—in turn triggering gambling for signal followers. When considering an investment in social trading, signal followers should be aware of the implied incentive structure and potential behavioral patterns displayed by signal providers. When introducing or adjusting design features, platform operators should carefully consider the resulting incentive structure for signal providers and the resulting consequences for signal followers.
The rest of the paper is structured as follows. In Sect. 2 we provide a short review on literature concerning stock market gambling as well as on social trading. The employed data and methodology are described in Sect. 3. Subsequently, in Sect. 4 we present and discuss our obtained results. In Sect. 5 we conduct and describe several tests regarding the robustness of our main results. Section 6 concludes.
2 Literature review
There are many similarities between lottery players and stock traders (Dorn et al. 2015; Statman 2002). Barberis and Huang (2008) show that under the assumption of investors behaving in accordance with Tversky and Kahneman’s (1992) cumulative prospect theory, the skewness of a security can be priced—positive skewness being a key characteristic with regard to lottery-like payoffs (Kumar 2009). The idea that certain stocks are perceived and employed as lotteries is introduced by Kumar (2009). In this context, Kumar (2009) shows that individual investors, at the aggregate level, exhibit a preference for stocks with lottery features. Furthermore, Kumar (2009) documents that lottery-like stocks underperform. In the context of stocks as lotteries, Bali et al. (2011) examine the role of extreme positive daily returns with regard to cross-sectional stock pricing. The evidence provided by Bali et al. (2011) suggests that investors may be willing to pay more for stocks with extreme positive returns, causing these stocks to exhibit lower returns in the future.5 Barinov (2018) argues that lottery-like stocks may act as insurance against unexpected increases in market volatility, and thus offers a rational explanation for the respective documented low expected returns. Bali et al. (2017) go so far as to suggest that the well documented beta anomaly (Black 1972; Black et al. 1972) is strongly driven by investors’ demand for lottery-like stocks.6
There are several reasons why studying gambling behavior in the context of social trading, a financial innovation facilitating the interaction of private investors, is particularly interesting. One of the defining features of social trading is the distinction between signal providers and signal followers. The respective social trading platform enables visibility and traceability with regard to signal provider trading decisions and returns. Thus, social trading offers a population of majorly private traders to publicly display their investing abilities, a feature formerly reserved to professional asset managers. Based on the published information, platform users can subscribe to one or several signal providers and thereby become signal followers (Doering et al. 2015; Oehler et al. 2016). Motivated by private investor preferences for lottery-like stocks (Bali et al. 2011; Kumar 2009), we study gambling behavior in a context where traders, i.e. signal providers, can be observed by their peers as well as by (potential) followers.
Furthermore, in the face of relative performance-based selection lists composed by social trading platforms, signal providers have to compete for the attention of signal followers. As followers are prerequisite for receiving compensation (see Sect. 3.4), social trading indirectly exposes signal providers to tournament incentives (Kirchler et al. 2018). Considering this dynamic between attention and remuneration, we study when signal providers utilize lottery-like stocks, which offer an unlikely but possible major return and, thus, may catapult an administered account to the top.
Studies by Oehler et al. (2016) and Dorfleitner et al. (2018) show that, on average, social trading participants do not outperform the market.
Venturing into the behavioral finance paradigm, Glaser and Risius (2018) note that signal providers on social trading platforms are subject to behavioral biases (Tversky and Kahneman 1974)—in this regard, signal providers do not differ from other (private) investors. Oehler et al. (2016) argue that the signal followers’ role on social trading platforms represents herding behavior. Gemayel and Preda (2018b) argue that a scopic information-rich environment, as given by a social trading platform, produces excess and perpetual herding behavior.7 With regard to signal providers on social trading platforms, Glaser and Risius (2018) and Pelster and Hofmann (2018) assess the disposition effect (Shefrin and Statman 1985) and the impact of receiving attention from signal followers. Pelster and Hofmann (2018) report an increase of the disposition effect with the number of investors copying a signal provider’s trading strategy. Glaser and Risius (2018) provide evidence that the disposition effect intensifies with the amount of capital entrusted to a signal provider. In contrast, Gemayel and Preda (2018a) find evidence of a weaker disposition effect among signal providers compared to traders in a traditional setting. Addressing trader visibility, Pelster and Breitmayer (2019) suggest that signal providers receiving attention from their peers exhibit increased trading activity and are more prone to take risks. Doering and Jonen (2018) argue that signal providers face convex incentives (Carpenter 2000) and thus increase risk when approaching their high watermark.8
Pelster and Breitmayer (2019) relate social trading to research on private investor (stock) trading driven by excitement (Dorn and Sengmueller 2009; Taffler 2018) as well as the desire to gamble (Dorn et al. 2015; Gao and Lin 2015; Kumar 2009). Using a social trading framework, Schneider and Oehler (2021) study gambling behavior with currency pairs. In the context of this paper, we are the first to our knowledge to explicitly combine research on social trading and stock gambling. We argue that the unique environment for traders established by social trading may have an impact on gambling behavior and, in this regard, assess the factors that affect signal provider stock gambling. Based on the incentive structure that signal providers face (Doering and Jonen 2018), we analyze if signal provider transactions involving stocks with lottery characteristics (Bali et al. 2011; Kumar 2009) are driven by the relative past performance of their administered portfolios. When investing in lottery-like stocks, signal providers expose their followers to a lottery-like return structure. Thus, our analysis yields valuable implications for investors delegating their investment decisions via social trading.
3 Data and methodology
3.1 Platform selection
Out of the spectrum of social trading providers, the wikifolio platform seems most suitable to analyze stock gambling. Signal providers on the wikifolio platform can choose from an extensive investment universe including stocks, funds, ETFs, investment certificates, and leverage products. When creating a wikifolio, most signal providers choose to generally exclude leverage products, thereby communicating mitigated portfolio risk to potential followers. The initial decision regarding the inclusion of leverage products is final and may not be adjusted during the life cycle of a corresponding wikifolio. Moreover, wikifolios which do not categorically exclude leverage products are permanently tagged with a warning label, even when all funds are temporarily allocated to non-leveraged investments. Thus, for the majority of signal providers, stocks are left as the only potential assets for employing a lottery-like return structure.
The wikifolio platform contains several further design peculiarities which make it an interesting research subject for studying stock gambling behavior: Administered signal provider portfolios are purely virtual, i.e. signal providers do not actually hold the corresponding assets. In consequence, transactions are not executed as in traditional market environments. Thus, signal providers are not subject to any transaction costs and therefore do not reduce returns by (excessive) trading (Barber and Odean 2000; 2001; Odean 1999). Furthermore, signal providers are compensated via performance fees which are self-imposed when creating the wikifolio. Performance fees are calculated depending on the high watermark principle, i.e. signal providers may only receive remuneration if a corresponding wikifolio reaches a new high. Hence, signal provider compensation is not substantially different to the remuneration of hedge fund managers and commodity trading advisors (Ackermann et al. 1999; Brown et al. 2001). As a further specification, signal providers are only eligible for remuneration when the capital invested by followers in a corresponding wikifolio exceeds a certain threshold. Finally, signal providers may simultaneously administer several wikifolios which can be closed—and potentially replaced—at any time. In combination with the depicted remuneration scheme, the option to simultaneously administer several wikifolios and close unsuccessful projects without consequences may have a severe impact on signal provider behavior, especially with regard to gambling.
3.2 Wikifolio data
We obtain data on signal provider portfolios, i.e. wikifolios, from the wikifolio platform. For each wikifolio daily prices as well as transaction data regarding all conducted transactions are freely accessible.
Wikifolios go through different life cycle stages9: Test, Published, Investable, Closing, and Closed. When reaching the status Closed, wikifolios remain visible on the profile of their corresponding signal provider, however, they no longer appear when using the platform’s search function. We therefore download the names of all signal providers who manage wikifolios which appear on the dashboard, i.e. signal providers who can be found using the search function. Afterwards, we assess each signal provider’s profile and download data for all accessible wikifolios. Thus, we include all Closed wikifolios associated to signal providers who manage at least one wikifolio exhibiting the status Published, Investable, or Closing. Closed wikifolios associated to signal providers who are not active anymore, i.e. their corresponding wikifolios have all been closed, are not accessible and thus cannot be included in our analysis. We download wikifolio data at the beginning of February 2019 which leads to a comprehensive dataset of 30,279—divided by status into 15,341 Published, 7696 Investable, 55 Closing, and 7187 Closed—wikifolios.
As data for signal providers who have completely disappeared from the platform is not available, the composed dataset is subject to a certain survivorship bias. When exhibiting good peer performance, there is no apparent incentive for signal providers to cease activities (see Sect. 3.4). Therefore, signal providers who have altogether vanished from the platform had likely been administering underperforming wikifolios, placing them at the lower end of the performance spectrum.
In the further course of our analysis, we limit the dataset to wikifolios which encompass data over at least six months; the dataset is thereupon reduced to 24,101 entities. The earliest data points go back to December 2011. Data after February 2019 is not included.
Volatility and skewness characteristics of wikifolios included in our analysis are displayed in Table 1. Idiosyncratic volatility (\(IVol\)) and idiosyncratic skewness (\(ISkew2F\)) are computed following Kumar (2009) and Harvey and Siddique (2000). In addition, we compute idiosyncratic skewness (\(ISkew3F\)) following Boyer et al. (2010). For the computation of idiosyncratic volatility and idiosyncratic skewness, we use regional daily factors obtained from the Kenneth French Data Library (KFDL).10
Table 1
Characteristics wikifolios
Measurement period | 1 Month | 6 Months | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
\(TVol\) | \(IVol\) | \(TSkew\) | \(ISkew2F\) | \(ISkew3F\) | \(TVol\) | \(IVol\) | \(TSkew\) | \(ISkew2F\) | \(ISkew3F\) | |
Panel A: Mean wikifolio characteristics USD | ||||||||||
All wikifolios | 1.688 | 1.301 | −0.032 | 0.012 | −0.004 | 1.891 | 1.703 | −0.072 | 0.044 | 0.026 |
Leverage | 2.978 | 2.347 | −0.014 | 0.017 | 0.002 | 3.608 | 3.352 | −0.048 | 0.040 | 0.013 |
w/o Leverage | 1.177 | 0.887 | −0.039 | 0.010 | −0.006 | 1.231 | 1.069 | −0.081 | 0.045 | 0.031 |
Published | 1.523 | 1.179 | −0.022 | 0.025 | 0.007 | 1.725 | 1.562 | −0.050 | 0.070 | 0.042 |
Investable | 1.598 | 1.223 | −0.048 | −0.003 | −0.020 | 1.836 | 1.640 | −0.098 | 0.020 | 0.004 |
Closing | 3.241 | 2.560 | −0.008 | 0.036 | 0.003 | 3.404 | 3.059 | 0.083 | 0.165 | 0.173 |
Closed | 2.764 | 2.153 | 0.010 | 0.043 | 0.035 | 2.911 | 2.672 | −0.001 | 0.082 | 0.093 |
Panel B: Monthly mean wikifolio characteristics USD | ||||||||||
All wikifolios | 1.574 | 1.200 | 0.015 | 0.062 | 0.045 | 1.725 | 1.540 | −0.046 | 0.065 | 0.055 |
Leverage | 2.598 | 2.019 | 0.030 | 0.062 | 0.045 | 3.017 | 2.788 | 0.029 | 0.109 | 0.093 |
w/o Leverage | 1.186 | 0.888 | 0.007 | 0.059 | 0.042 | 1.242 | 1.076 | −0.060 | 0.059 | 0.051 |
Published | 1.445 | 1.101 | 0.026 | 0.066 | 0.049 | 1.590 | 1.422 | −0.040 | 0.079 | 0.059 |
Investable | 1.469 | 1.114 | 0.002 | 0.064 | 0.038 | 1.652 | 1.464 | −0.045 | 0.071 | 0.060 |
Closing | 2.606 | 2.044 | 0.017 | 0.065 | 0.032 | 2.784 | 2.479 | 0.023 | 0.150 | 0.145 |
Closed | 2.678 | 2.128 | 0.019 | 0.066 | 0.058 | 3.189 | 2.958 | −0.023 | 0.050 | 0.058 |
We further estimate monthly wikifolio alphas, \(\alpha\), using the Fama and French (1993) three-, the Carhart (1997) four-, the Fama and French (2015) five-, and the Fama and French (2018) six-factor model:\({R}_{i,t}\) denotes the return of portfolio (i.e. wikifolio) \(i\), \({R}_{F,t}\) is the risk-free return, and \({RMRF}_{t}\) represents the return of the market portfolio net of the risk-free return regarding period (i.e. month) \(t\). \({SMB}_{t}\) and \({HML}_{t}\) reflect the size and book-to-market factors as describes by Fama and French (1993). \({WML}_{t}\) is a factor capturing momentum as identified by Jegadeesh and Titman (1993). \({RMW}_{t}\) and \({CMA}_{t}\) respectively represent the profitability and investment factor (Fama and French 2015). Regional monthly factors are obtained from the KFDL. The results are displayed in Panel A and Panel B of Table 2.
$$R_{i,t} - R_{F,t} = \beta_{1} *RMRF_{t} + \beta_{2} *SMB_{t} + \beta_{3} *HML_{t} + \alpha ,$$
(1)
$$R_{i,t} - R_{F,t} = \beta_{1} *RMRF_{t} + \beta_{2} *SMB_{t} + \beta_{3} *HML_{t} + \beta_{4} *WML_{t} + \alpha ,$$
(2)
$$R_{i,t} - R_{F,t} = \beta_{1} *RMRF_{t} + \beta_{2} *SMB_{t} + \beta_{3} *HML_{t} + \beta_{4} *RMW_{t} + \beta_{5} *CMA_{t} + \alpha ,$$
(3)
$$R_{i,t} - R_{F,t} =\; \beta_{1} *RMRF_{t} + \beta_{2} *SMB_{t} + \beta_{3} *HML_{t} + \beta_{4} *RMW_{t} + \beta_{5} *CMA_{t} + \beta_{6} *WML_{t} + \alpha .$$
(4)
Table 2
Performance wikifolios
Panel A: Raw returns USD | Panel B: Panel regression estimates USD | ||||||||
|---|---|---|---|---|---|---|---|---|---|
\(\alpha\) | \(RMRF\) | \(SMB\) | \(HML\) | \(RMW\) | \(CMA\) | \(WML\) | \(R^{2}\) | ||
All wikifolios | |||||||||
Mean | 0.5076 | 0.0948 | 0.5543*** | −0.0836 | −0.2484 | 0.0013 | |||
Median | 0.2083 | (0.28) | (6.51) | (−0.48) | (−1.30) | ||||
SD | 51.0441 | 0.1151 | 0.5470*** | −0.0821 | −0.2782 | −0.0489 | 0.0013 | ||
(0.35) | (6.47) | (−0.47) | (−1.40) | (−0.38) | |||||
0.1520 | 0.5225*** | −0.1589 | −0.2943 | −0.2792 | −0.1515 | 0.0014 | |||
(0.43) | (5.33) | (−0.95) | (−1.30) | (−0.93) | (−0.56) | ||||
0.1787 | 0.5144*** | −0.1590 | −0.3434 | −0.2952 | −0.1340 | −0.0581 | 0.0014 | ||
(0.54) | (5.34) | (−0.95) | (−1.49) | (−1.00) | (−0.48) | (−0.44) | |||
Leverage | |||||||||
Mean | 0.3756 | 0.0085 | 0.5749*** | −0.1450 | −0.0435 | 0.0004 | |||
Median | −0.0364 | (0.02) | (6.16) | (−0.59) | (−0.17) | ||||
SD | 95.2699 | 0.0224 | 0.5676*** | −0.1437 | −0.0703 | −0.0400 | 0.0004 | ||
(0.05) | (6.08) | (−0.58) | (−0.28) | (−0.22) | |||||
0.1267 | 0.5352*** | −0.2840 | −0.2789 | −0.5917 | 0.0032 | 0.0004 | |||
(0.26) | (5.08) | (−1.44) | (−1.13) | (−1.14) | (0.01) | ||||
0.1556 | 0.5225*** | −0.2846 | −0.3434 | −0.6124 | 0.0220 | −0.0724 | 0.0004 | ||
(0.32) | (4.87) | (−1.44) | (−1.13) | (−1.14) | (0.06) | (−0.37) | |||
w/o Leverage | |||||||||
Mean | 0.5600 | 0.1306 | 0.5492*** | −0.0623 | −0.3254 | 0.0971 | |||
Median | 0.3042 | (0.39) | (6.02) | (−0.37) | (−1.70) | ||||
SD | 6.0386 | 0.1507 | 0.5428*** | −0.0608 | −0.3522 | −0.0457 | 0.0974 | ||
(0.47) | (5.85) | (−0.36) | (−1.78) | (−0.34) | |||||
0.1681 | 0.5203*** | −0.1168 | −0.3063 | −0.1715 | −0.2047 | 0.0988 | |||
(0.48) | (5.10) | (−0.67) | (−1.28) | (−0.60) | (−0.77) | ||||
0.1907 | 0.5143*** | −0.1167 | −0.3448 | −0.1841 | −0.1901 | −0.0466 | 0.0990 | ||
(0.58) | (5.06) | (−0.67) | (−1.50) | (−0.67) | (−0.70) | (−0.35) | |||
Published | |||||||||
Mean | 0.3981 | −0.0025 | 0.5256*** | −0.0854 | −0.2730 | 0.0204 | |||
Median | 0.1904 | (−0.01) | (5.86) | (−0.50) | (−1.44) | ||||
SD | 12.4578 | 0.0090 | 0.5216*** | −0.0845 | −0.2896 | −0.0277 | 0.0204 | ||
(0.03) | (5.60) | (−0.49) | (−1.45) | (−0.20) | |||||
0.0229 | 0.4957*** | −0.1307 | −0.2078 | −0.1054 | −0.2510 | 0.0208 | |||
(0.07) | (4.95) | (−0.76) | (−0.85) | (−0.36) | (−0.95) | ||||
0.0339 | 0.4924*** | −0.1307 | −0.2276 | −0.1118 | −0.2445 | −0.0241 | 0.0208 | ||
(0.11) | (4.86) | (−0.76) | (−0.96) | (−0.39) | (−0.92) | (−0.18) | |||
Investable | |||||||||
Mean | 0.5917 | 0.1516 | 0.5824*** | −0.1387 | −0.3405* | 0.0018 | |||
Median | 0.2536 | (0.44) | (7.05) | (−0.82) | (−1.79) | ||||
SD | 48.0254 | 0.1537 | 0.5816*** | −0.1385 | −0.3435* | −0.0052 | 0.0018 | ||
(0.47) | (7.27) | (−0.82) | (−1.71) | (−0.04) | |||||
0.1977 | 0.5661*** | −0.1924 | −0.4328* | −0.2496 | −0.0162 | 0.0018 | |||
(0.57) | (5.91) | (−1.16) | (−1.96) | (−0.93) | (−0.06) | ||||
0.2056 | 0.5636*** | −0.1925 | −0.4470* | −0.2544 | −0.0116 | −0.0177 | 0.0018 | ||
(0.62) | (6.11) | (−1.16) | (−1.90) | (−0.96) | (−0.04) | (−0.14) | |||
Closing | |||||||||
Mean | 0.4536 | −0.2782 | 1.2438*** | 0.6929 | 0.1242 | 0.0188 | |||
Median | 0.4765 | (−0.35) | (4.27) | (1.28) | (0.26) | ||||
SD | 31.2105 | 0.0118 | 1.1162*** | 0.7405 | −0.4283 | −0.8894 | 0.0217 | ||
(0.02) | (4.67) | (1.38) | (−0.81) | (−1.64) | |||||
−0.5721 | 1.2280*** | 0.9744 | 1.4049 | 1.7762 | -1.2576 | 0.0214 | |||
(−0.71) | (3.87) | (1.57) | (1.26) | (1.14) | (−1.02) | ||||
−0.2797 | 1.1191*** | 0.9869 | 0.7512 | 1.5678 | -1.0808 | −0.7902 | 0.0236 | ||
(−0.38) | (3.98) | (1.65) | (0.77) | (1.04) | (−0.91) | (−1.60) | |||
Closed | |||||||||
Mean | 0.5162 | 0.1909 | 0.5003*** | 0.1765 | 0.4884 | 0.0002 | |||
Median | 0.0361 | (0.26) | (3.27) | (0.39) | (0.81) | ||||
SD | 117.6044 | 0.3020 | 0.4579*** | 0.1852 | 0.3036 | −0.2295 | 0.0002 | ||
(0.37) | (3.04) | (0.40) | (0.64) | (−0.80) | |||||
0.6669 | 0.3302** | −0.3856 | −0.0727 | -1.7022 | −0.0681 | 0.0004 | |||
(0.65) | (2.26) | (−1.25) | (−0.22) | (−1.16) | (−0.13) | ||||
0.8442 | 0.2834* | −0.3832 | −0.4516 | -1.8187 | 0.1367 | −0.3282 | 0.0004 | ||
(0.73) | (1.72) | (−1.24) | (−0.82) | (−1.18) | (0.19) | (−0.85) | |||
Panel C: Raw returns EUR | Panel D: Panel regression estimates EUR | ||||||
|---|---|---|---|---|---|---|---|
\(\alpha\) | \(RMRF\) | \(SMB\) | \(HML\) | \(WML\) | \(R^{2}\) | ||
All wikifolios | |||||||
Mean | 0.3788 | 0.1530 | 0.4264*** | −0.1439* | −0.0956 | 0.0013 | |
Median | 0.2127 | (0.65) | (7.18) | (−1.86) | (−0.58) | ||
SD | 51.7708 | 0.3004 | 0.4584*** | −0.0801 | −0.1036 | −0.1657** | 0.0014 |
(1.21) | (7.57) | (−0.99) | (−0.66) | (−2.09) | |||
Leverage | |||||||
Mean | 0.2571 | 0.0300 | 0.3990*** | −0.1560 | 0.0985 | 0.0004 | |
Median | −0.0487 | (0.08) | (4.43) | (−1.13) | (0.29) | ||
SD | 96.7035 | 0.1658 | 0.4317*** | −0.0822 | 0.0892 | −0.1735 | 0.0004 |
(0.40) | (5.22) | (−0.67) | (0.27) | (−1.32) | |||
w/o Leverage | |||||||
Mean | 0.4272 | 0.2003 | 0.4374*** | −0.1389* | −0.1741 | 0.1134 | |
Median | 0.3292 | (0.91) | (7.37) | (−1.89) | (−1.56) | ||
SD | 5.6197 | 0.3532 | 0.4695*** | −0.0781 | −0.1816* | −0.1643** | 0.1184 |
(1.56) | (7.74) | (−0.99) | (−1.73) | (−2.25) | |||
Published | |||||||
Mean | 0.2701 | 0.0728 | 0.4201*** | −0.1388* | −0.1738 | 0.0220 | |
Median | 0.1700 | (0.34) | (7.36) | (−1.78) | (−1.47) | ||
SD | 12.2547 | 0.2187 | 0.4530*** | −0.0729 | −0.1817 | −0.1673** | 0.0231 |
(0.97) | (7.79) | (−0.89) | (−1.62) | (−2.38) | |||
Investable | |||||||
Mean | 0.4812 | 0.2332 | 0.4854*** | −0.1051 | −0.2065* | 0.0018 | |
Median | 0.2997 | (1.02) | (7.83) | (−1.34) | (−1.76) | ||
SD | 48.5424 | 0.3348 | 0.5080*** | −0.0560 | −0.2107* | −0.1223 | 0.0019 |
(1.45) | (7.73) | (−0.65) | (−1.87) | (−1.49) | |||
Closing | |||||||
Mean | 0.3622 | 0.0489 | 1.0187*** | −0.3227 | −0.6806* | 0.0193 | |
Median | 0.4191 | (0.06) | (4.12) | (−1.03) | (−1.74) | ||
SD | 31.0383 | 0.8001 | 1.2253*** | 0.2611 | −0.7041** | -1.1890** | 0.0268 |
(1.12) | (4.52) | (0.63) | (−2.02) | (−2.08) | |||
Closed | |||||||
Mean | 0.2913 | 0.0581 | 0.1423 | −0.3639 | 0.8070 | 0.0004 | |
Median | −0.0287 | (0.09) | (0.83) | (−1.61) | (1.06) | ||
SD | 119.7828 | 0.3622 | 0.1901 | −0.2997 | 0.7743 | −0.2340 | 0.0004 |
(0.45) | (1.30) | (−1.52) | (1.05) | (−1.26) | |||
As the model fit is rather weak, the applied regional KFDL factors may not be an appropriate benchmark for analyzing wikifolios. Signal providers strongly focus on assets which have been issued in Germany (see Sect. 3.4). Thus, using local German factors may produce a more sound model (Hollstein 2021). We therefore match EUR-denominated wikifolio data with local German factors obtained from Richard Stehle's homepage.11 As Dirkx and Peter (2020) conclude that the profitability and investment factor (Fama and French 2015) have limited relevance with regard to the German market, we estimate alphas using the Fama and French (1993) three- and the Carhart (1997) four-factor model. The results are reported in Panel C and Panel D of Table 2. Applying local German factors does not substantially increase the model fit. We attribute the rather poor model fit to the variety of non-equity instruments which are included in the considered wikifolios.12
Contrary to Oehler et al. (2016), the conducted performance analyses do not yield significantly negative alphas, α, for the analyzed signal provider portfolios. Our results suggest that wikifolios neither under- nor outperform the equity benchmark. Differences in the performance of wikifolios depicted in Oehler et al. (2016) and our reported results may be caused by a longer observation period as well as a much broader data basis.13
3.3 Transaction data
Signal providers can choose from an extensive investment universe. Main groups of tradable assets are stocks, funds, ETFs, investment certificates, and leverage products. An overview of traded instrument categories is displayed in Appendix Table 7 When creating a wikifolio, signal providers can choose if they want to have access to the entire investment universe provided by the wikifolio platform or exclude leverage products from their trading activities. The tag Attention: Might contain leverage products—included in the summary information which appears when using the search function on the platform’s front page as well as on the front page of the respective individual wikifolios—informs signal followers whether leverage products are potentially traded.
The number of conducted transactions is not evenly distributed among all administered wikifolios. There is a vast number of wikifolios where no transaction is conducted for several continuous months, indicating that the corresponding signal providers pursue a plain buy-and-hold strategy or have abandoned the administered wikifolio without closing. On the other hand, there are wikifolios continuously exhibiting a great number of monthly transactions. To account for abandoned or inactive wikifolios, we drop wikifolio-month observations after the signal provider has conducted the last transaction within a corresponding wikifolio. Table 3 provides an overview regarding the distribution of transactions after accounting for inactive entities.
For each transaction, the International Securities Identification Number (ISIN), the change in quantity, and the price of the respective traded asset is provided by the wikifolio platform. In order to provide an overview of signal providers’ geographical preferences with regard to traded assets, we sort the obtained transaction data on the two initial letters of each transaction ISIN which indicate the issuing country. The analysis reveals that signal providers strongly focus on assets which have been issued in Germany. Results are displayed in Appendix Table 8. 70 percent of all transactions conducted by signal providers involve assets issued in Germany. Regarding transaction volume, the focus on German assets is even more severe, accounting for a total share of 87 percent. The results indicate that, when considered together, wikifolios lack international diversification. However, missing spatial diversification might be caused by the peculiarities of the wikifolio platform; about 85 percent of assets which are available to signal providers have been issued in Germany. Thus, the selection process of signal providers might be biased by the (wide yet spatially pooled) range of available assets.
3.4 Compensation of signal providers
As described by Gemayel and Preda (2018a), the monetary incentive structure established by a social trading platform may have a substantial impact on signal provider behavior. Generally, there is no restriction on who can become a signal provider on the wikifolio platform. The majority of signal providers is composed of private traders. Furthermore, there are labels indicating if an asset manager or a media company, i.e. a professional trader, is in charge of the wikifolio. Regarding private traders, the maximum number of simultaneously administered wikifolios is limited to eight, on the other hand, asset managers and media companies may simultaneously manage any given number.
The portfolios which underlie the wikifolio certificates, regardless of their assigned status, are purely virtual, i.e. signal providers do not actually hold the corresponding assets. In order to directly mirror the performance of their own administered wikifolios, signal providers need to buy corresponding wikifolio certificates (which is in accordance with the copy-trading approach of signal followers on the wikifolio platform). Wikifolios can obtain the label Real Money when a certain amount is invested in the corresponding wikifolio certificates by the administering signal provider.
Signal providers are compensated via performance fees—ranging from 5 to 30 percent—which are self-imposed when creating the wikifolio. Receivable performance fees are calculated depending on the high watermark principle, meaning that signal providers only become eligible for remuneration if their corresponding wikifolio reaches a new high for the year, i.e. a new high watermark is set. The basis for calculating the performance fee is the return of the administered wikifolio, i.e. the difference between the current and the last peak of the wikifolio equivalent value.14 High watermarks are reset to the current index level of each wikifolio at the end of each calendar year. Contingent on the amount of capital invested in a respective wikifolio via certificates, signal providers are (only) entitled to claim a pre-defined share of the amount derived from value appreciation and performance fee. The maximum share signal providers may receive is 50 percent.15 Signal providers trading wikifolios of wikifolios are compensated differently—since their respective wikifolios are not included in our main analysis, we do not elaborate the corresponding approach.
3.5 Sorting criteria for wikifolios
By default, wikifolios are sorted on so-called wikifolio points which are calculated from twelve criteria. In addition to risk and return, the respective underlying criteria are meant to reflect the wikifolio’s popularity, as well as the corresponding signal provider’s activity and commitment. A complete breakdown regarding the calculation method of wikifolio points as described on the wikifolio platform is provided in Appendix Table 8. Furthermore, platform users may sort available wikifolios on the following 14 individual criteria: Date created, Date of issuance, Performance ever, Performance since first issuance, Performance YTD, Performance 12 months, Performance 6 months, Performance 3 months, Performance 1 month, Sharpe Ratio (365 Days), Maximum loss (to date), Invested capital, Reservations,16 and Risk factor.17
3.6 Stock market data and definition of lottery-like stocks
We employ all stocks that are included within the wikifolio investment universe, i.e. stocks that can be traded by signal providers, as benchmark for the classification of lottery-like stocks. This leads to a dataset of 7308 stocks which are henceforth used as benchmark. Following Kumar (2009), we classify stocks in the lowest kth stock price percentile (measured in the previous month), highest kth idiosyncratic volatility percentile, and highest kth idiosyncratic skewness percentile as lottery-like stocks. For the conducted analysis, we set \(k=50\).18 Volatility and skewness characteristics with regard to the sorted portfolios are displayed in Appendix Table 9.
We compute idiosyncratic volatility and idiosyncratic skewness as in Kumar (2009). Accordingly, idiosyncratic volatility is determined as the standard deviation of the residuals obtained by fitting a four-factor model—comprising the market, size, book-to-market (Fama and French 1993), and momentum (Carhart 1997) factors—to a time-series of daily stock returns. Idiosyncratic skewness is measured as the third moment of the residuals obtained by regressing daily stock returns on a two-factor model employing the market excess return and the square of the market excess return as respective factors (Harvey and Siddique 2000). The regressions providing the residuals for the computation of idiosyncratic volatility and idiosyncratic skewness are run for each respective stock-month combination, employing daily stock returns of the corresponding previous six months (i.e., months \(t-6\) to \(t-1\)). Different definitions of lottery-like stocks are applied as part of the robustness checks in Sect. 5. For all stocks included in the wikifolio investment universe, the corresponding regional daily factors—Fama and French (1993) factors and momentum factor (Jegadeesh and Titman 1993)—are obtained from the KFDL; stocks issued from countries which cannot be sorted into regions with available factors are paired with the Developed ex US factors from the KFLD.
3.7 Regression model
3.7.1 Selection of main independent variables
Regarding signal providers, the incentive structure stems from the wikifolio platform’s established incentive scheme. As described in Sect. 3.4, signal provider compensation depends on the success of the administered wikifolio, i.e. attainment of new high watermarks, and the amount of capital invested in the corresponding wikifolio's certificates. In order to generate invested capital, wikifolios need to be visible, i.e. obtain good positions on the lists which are presented to signal followers (Jacobs and Hillert 2016). The default sorting criteria, as well as seven out of the 14 additional sorting options which may be selected, directly depend on past wikifolio performance (see Sect. 3.5). In this regard, it is interesting to assess if the number/volume of transactions conducted by signal providers is related to the past performance of their administered wikifolios. Additionally, within the elaborated conditions set by the wikifolio platform, past wikifolio returns may affect signal providers’ intention to engage in gambling. In this context, we assess whether the relative transaction number/volume with regard to lottery-like stocks relates to past wikifolio returns.
We set the wikifolio raw return of the previous month as well as the average monthly wikifolio raw returns over the previous six months as past performance measures. For each of the employed performance measures, each wikifolio is then assigned a number from 1 to 10, indicating its according relative monthly performance ranking.19 The variables are depicted as follows:
$$RR_{i,t - 1} /R\overline{R}_{i,t - 6}^{t - 1} .$$
(5)
All variables included in the regression analyses are displayed and described in Appendix Table 11.
The independent variable of interest, the relative performance ranking, is based on raw returns instead of abnormal returns (alphas). In the context of social trading, Röder and Walter (2019) provide evidence that investment flows follow raw returns instead of factor model alphas. Hence, basing the independent variable of interest on raw returns seems to be the coherent approach.
3.7.2 Monthly transactions
At first, we assess whether the monthly transaction volume generated by a signal provider for an administered wikifolio, as well as the corresponding number of transactions, depend on the wikifolio’s past performance. The according relevant dependent variables are the monthly number/volume of assets traded within each wikifolio (\({T}_{i,t}^{num}/{T}_{i,t}^{vol}\)). Even when eliminating abandoned or inactive wikifolios as described in Sect. 3.3, there is a substantial number of wikifolio-month observations in the dataset where no transaction is conducted. Consequently, for these cases the respective variables take the value zero. Deriving from that, the dependent variables are highly positively skewed. Thus, for our regression analyses we transform the dependent variables as follows:
$$lnT_{i,t}^{num} = {\text{ln}}\left( {1 + T_{i,t}^{num} } \right)/lnT_{i,t}^{vol} = {\text{ln}}\left( {1 + T_{i,t}^{vol} } \right).$$
(6)
By adding the constant \(1\) to the initial variables before applying the natural logarithm, we assure that wikifolio-month observations with no respective transactions can be included into the regression analyses. As described in the previous section, relative past wikifolio performance (\({RR}_{i, t-1}/{R\overline{R} }_{i,t-6}^{t-1}\)) depicts the relevant independent variable. The baseline regression model is as follows:\(DV\) is a stand-in for the dependent variable reflecting the number (\({T}_{i.t}^{num}\))/volume (\({T}_{i,t}^{vol}\)) of transactions conducted within wikifolio \(i\) in month \(t\). \(RR\) is a stand-in for the relative past return variable of the wikifolio, measured over the previous month (\({RR}_{i,t-1}\))/previous six months (\({R\overline{R} }_{i,t-6}^{t-1}\)).\(Controls\)20 depicts a vector of control variables. All variables are described in Appendix Table 11.
$$DV = \alpha + \beta_{1} \times RR + Controls + \in$$
(7)
3.7.3 Monthly relative transactions lottery-like stocks
As main analysis, we assess the impact of past wikifolio performance on relative lottery-like stock transactions. We set the relative monthly number/volume of lottery-like stocks traded (\({RTL}_{i,t}^{num}/{RTL}_{i,t}^{vol}\)) as the according dependent variable. The variables are defined as follows:\({TL}_{i,t}^{num}/{TL}_{i,t}^{vol}\) denote the monthly number/volume of lottery-like stocks traded. Since we employ relative shares of traded lottery-like stocks, all wikifolio-month observations with no conducted transaction—indicating abandoned wikifolios or the implementation of a plain buy-and-hold strategy—are excluded. In order to establish coherence, we transform the introduced dependent variables for the constituent regression analyses by adding the constant \(1\) and then applying the natural logarithm:
$$RTL_{i,t}^{num} = \frac{{TL_{i,t}^{num} }}{{T_{i,t}^{num} }}/RTL_{(i,t)}^{vol} = \frac{{TL_{(i,t)}^{vol} }}{{T_{(i,t)}^{vol} }},$$
(8)
$${{lnRTL_{i,t}^{num} = ln\left( {1 + RTL_{i,t}^{num} } \right)} \mathord{\left/ {\vphantom {{lnRTL_{i,t}^{num} = ln\left( {1 + RTL_{i,t}^{num} } \right)} {lnRTL_{(i,t)}^{vol} = ln(1 + RTL_{(i,t)}^{vol} ).}}} \right. \kern-\nulldelimiterspace} {lnRTL_{i,t}^{vol} = ln\left(1 + RTL_{i,t}^{vol}\right).}}$$
(9)
Relative past wikifolio performance (\({RR}_{i,t-1}\)/\({R\overline{R} }_{i,t-6}^{t-1}\)) depicts the relevant independent variable. The baseline regression model is depicted in Eq. 7. As before, \(DV\) is a stand-in for the dependent variable reflecting the relative number (\({lnRTL}_{i.t}^{num}\))/volume (\({lnRTL}_{i,t}^{vol}\)) of lottery-like stock transactions conducted within wikifolio \(i\) in month \(t\). \(RR\) is a stand-in for the relative past return variable of the wikifolio, measured over the previous month (\({RR}_{i,t-1}\))/previous six months (\({R\overline{R} }_{i,t-6}^{t-1}\)).\(Controls\)21 depicts a vector of control variables. Appendix Table 11 displays and describes all variables employed in the regression analyses.
4 Results and discussion
4.1 Monthly transactions
The initial results obtained from the regression analysis are ambiguous. The regression models where standard errors are simultaneously clustered by month and wikifolio as well as by month and signal provider do not indicate a statistically significant relationship between relative past performance and the number or volume of conducted transactions. When including fixed effects,22 all regression specifications yield significantly positive coefficients for the relative performance variable. In order to determine whether a non-linear model describes the relation between trading activity and relative past performance more appropriately, we include squared terms of the established relative return variables: \({(RR}_{i,t-1})^{2}\) and \(({R\overline{R} }_{i,t-6}^{t-1})^{2}\). Estimating regression models including squared terms indicates a U-shaped relation between relative past performance and trading activity which is statistically significant in the specifications including clustered standard errors and within the contrived fixed effects models. Regression results corresponding to the quadratic model are displayed in Appendix Table 12.23
Regarding the upper end of the relative performance spectrum, i.e. signal providers who have previously outperformed their peers, an increase in trading activity seems to be in line with previous research. Gervais and Odean (2001), Odean (1999), and Statman et al. (2006) provide evidence that past returns have a positive impact on investor overconfidence, and thus on trading activity. Within the framework of a social trading platform, performing well relative to peers might induce a surge in signal provider overconfidence which causes increased trading activity. Since portfolios on the wikifolio platform are virtual, and thus there are no transaction costs for signal providers, the effect might be particularly pronounced.24 As described, the considered independent variables, \({RR}_{i,t-1}\) and \({R\overline{R} }_{i,t-6}^{t-1}\), capture the relative performance of all wikifolios for which data could be attained; literature on overconfidence primarily focuses on absolute performance. Although based on performance relative to peers, the composed variable covers absolute performance, it is reasonable to assume that outperforming peers is connected to generating net profits. Measuring relative performance over the previous month, in less two percent of all wikifolio-month observations a negative return is generated when the wikifolio is assigned to one of the top three percentiles. Measuring relative performance over a 6-month period leads to positive returns in more than 99.5 percent of all wikifolio-month observations when the wikifolio has outperformed 70 percent of its peers.
Apart from overconfidence, excitement may be cited as an explanation for the reported results. The role of excitement in investing is elaborated by Taffler (2018). Trading as entertainment has been depicted by Dorn and Sengmueller (2009).
In the context of social trading, Pelster and Breitmayer (2019) show that signal providers who receive attention (from signal followers) increase their trading activity due to increased levels of excitement. Furthermore, Pelster and Breitmayer (2019) provide evidence, that past performance is the main determinant for a signal provider to be followed. Performing well relative to peers might boost signal provider attractiveness which will lead to a larger number of signal followers investing in the corresponding wikifolio. The enhanced excitement which is caused by additional followers may encourage signal providers to be more active, i.e. increase their trading activity.
Regarding the lower end of the relative performance spectrum, i.e. underperforming signal providers, an increase in trading activity may be caused by traders trying to restructure their losing wikifolios. The incentive to restructure a losing entity might be amplified by the lack of transaction costs and the very limited monetary downside risk for signal providers. Restructuring a wikifolio may be implemented by including new assets. Furthermore, contrary to what is suggested by the disposition effect (Shefrin and Statman 1985), signal providers may decide to get rid of losing positions. So far, regarding the occurrence and magnitude of the disposition effect in social trading, there is contradictory evidence (Gemayel and Preda 2018a; Glaser and Risius 2018; Pelster and Hofmann 2018).
Table 3
Deciles distribution transactions
\(D1\) | \(D2\) | \(D3\) | \(D4\) | \(D5\) | \(D6\) | \(D7\) | \(D8\) | \(D9\) | \(D10\) | |
|---|---|---|---|---|---|---|---|---|---|---|
Number | 7 | 16 | 26 | 39 | 58 | 87 | 136 | 230 | 460 | 3,085 |
Volume | 1 | 3 | 7 | 12 | 21 | 37 | 67 | 102 | 210 | 50,552 |
4.2 Transactions lottery-like stocks
As depicted in Sect. 3.7.3, we conduct regression analyses for dependent variables reflecting the relative share of transactions involving lottery-like stocks: monthly relative number of traded lottery-like stocks (\({lnRTL}_{i.t}^{num}\)) and monthly relative volume of traded lottery-like stocks (\({lnRTL}_{i.t}^{vol}\)). Our regression analysis does not yield a statistically significant relation between relative past wikifolio performance and the traded share of lottery-like stocks. In order to determine whether there is a non-linear relation between the relative share of transactions involving lottery-like stocks and previous performance, we include squared terms of the respective performance measures: \({(RR}_{i,t-1})^{2}\) and \(({R\overline{R} }_{i,t-6}^{t-1})^{2}\). Results are displayed in Table 4 (Panel A and Panel C).
Table 4
Relative share lottery-like stocks
Panel A: Number lottery | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | 0.0541*** | 0.0541*** | 0.0551*** | 0.0319*** | 0.0362*** | 0.0352*** | 0.0383*** | 0.0589*** | 0.0589*** | 0.0593*** | 0.0330*** | 0.0389*** | 0.0363*** | 0.0408*** |
(19.42) | (17.75) | (63.40) | (37.16) | (33.56) | (44.59) | (34.01) | (19.97) | (18.03) | (67.42) | (36.96) | (35.32) | (43.64) | (35.56) | |
\(RR\) | −0.0098*** | −0.0098*** | −0.0095*** | −0.0006** | −0.0031*** | −0.0006** | −0.0030*** | −0.0116*** | −0.0116*** | −0.0112*** | −0.0010*** | −0.0040*** | −0.0010*** | −0.0039*** |
(−13.43) | (−12.23) | (−34.49) | (−2.13) | (−11.02) | (−2.20) | (−10.88) | (−14.18) | (−12.79) | (−39.95) | (−3.41) | (−13.75) | (−3.37) | (−13.46) | |
\({RR}^{2}\) | 0.0009*** | 0.0009*** | 0.0009*** | 0.0001*** | 0.0003*** | 0.0001*** | 0.0003*** | 0.0010*** | 0.0010*** | 0.0010*** | 0.0001*** | 0.0004*** | 0.0001*** | 0.0004*** |
(14.19) | (12.94) | (36.96) | (3.36) | (12.40) | (3.45) | (12.34) | (14.81) | (13.43) | (41.48) | (4.11) | (14.23) | (4.11) | (14.04) | |
\(Leverage\) | 0.0023* | 0.0023* | 0.0027*** | −0.0024*** | −0.0025*** | 0.0018 | 0.0018 | 0.0022*** | −0.0027*** | −0.0028*** | ||||
(1.90) | (1.80) | (5.00) | (−3.25) | (−3.40) | (1.53) | (1.45) | (4.20) | (−3.62) | (−3.74) | |||||
\(RealMoney\) | 0.0081*** | 0.0081*** | 0.0080*** | 0.0074*** | 0.0075*** | 0.0079*** | 0.0079** | 0.0077*** | 0.0072*** | 0.0073*** | ||||
(3.01) | (2.65) | (9.86) | (5.26) | (5.36) | (2.92) | (2.58) | (9.51) | (5.15) | (5.23) | |||||
\(Investable\) | −0.0034*** | −0.0034*** | −0.0020*** | −0.0002 | 0.0009 | −0.0035*** | −0.0035*** | −0.0021*** | −0.0002 | 0.0008 | ||||
(−3.46) | (−3.01) | (−4.64) | (−0.21) | (1.27) | (−3.51) | (−3.06) | (−4.96) | (−0.33) | (1.11) | |||||
\(Closing\) | −0.0133** | −0.0133** | −0.0132*** | −0.0125*** | −0.0116*** | −0.0136*** | −0.0136** | −0.0136*** | −0.0127*** | −0.0118*** | ||||
(−2.58) | (−2.48) | (−4.37) | (−3.11) | (−2.88) | (−2.68) | (−2.58) | (−4.51) | (−3.15) | (−2.93) | |||||
\(Closed\) | −0.0078*** | −0.0078*** | −0.0050*** | −0.0024*** | −0.0008 | −0.0078*** | −0.0078*** | −0.0051*** | −0.0025*** | −0.0009 | ||||
(−6.14) | (−5.44) | (−7.67) | (−2.79) | (−0.87) | (−6.07) | (−5.38) | (−7.84) | (−2.90) | (−1.01) | |||||
\(Fee\) | 0.0106* | 0.0106 | 0.0109*** | 0.0221*** | 0.0213*** | 0.0098 | 0.0098 | 0.0101*** | 0.0215*** | 0.0208*** | ||||
(1.76) | (1.47) | (4.25) | (4.95) | (4.78) | (1.64) | (1.37) | (3.94) | (4.82) | (4.66) | |||||
\(Media\) | −0.0143*** | −0.0143** | −0.0140*** | −0.0135*** | −0.0135** | −0.0133*** | ||||||||
(−2.86) | (−2.16) | (−6.21) | (−2.73) | (−2.07) | (−5.88) | |||||||||
\(Manager\) | −0.0106*** | −0.0106** | −0.0101*** | −0.0101** | −0.0101** | −0.0096*** | ||||||||
(−2.70) | (−2.28) | (−5.71) | (−2.60) | (−2.18) | (−5.43) | |||||||||
\(Theme\) | 0.0285 | 0.0285*** | 0.0282** | 0.0295 | 0.0295*** | 0.0287** | ||||||||
(0.79) | (13.46) | (2.27) | (0.81) | (16.29) | (2.31) | |||||||||
\(wikiNumber\) | −0.0001 | −0.0001 | −0.0001** | −0.0001 | −0.0001 | −0.0001** | ||||||||
(−0.71) | (−0.44) | (−2.01) | (−0.98) | (−0.61) | (−2.59) | |||||||||
\({lnT}^{num}\) | 0.0042*** | 0.0042*** | 0.0040*** | 0.0016*** | 0.0026*** | 0.0016*** | 0.0026*** | 0.0042*** | 0.0042*** | 0.0040*** | 0.0016*** | 0.0026*** | 0.0016*** | 0.0026*** |
(12.84) | (11.01) | (27.02) | (8.15) | (14.15) | (7.92) | (14.11) | (12.81) | (10.98) | (26.85) | (8.15) | (14.22) | (7.91) | (14.14) | |
\(ETF\) | −0.0195*** | −0.0195*** | −0.0187*** | −0.0100*** | −0.0137*** | −0.0101*** | −0.0137*** | −0.0194*** | −0.0194*** | −0.0186*** | −0.0100*** | −0.0137*** | −0.0102*** | −0.0137*** |
(−24.19) | (−20.87) | (−46.33) | (−17.79) | (−28.69) | (−18.03) | (−28.59) | (−23.98) | (−20.68) | (−45.92) | (−17.81) | (−28.70) | (−18.05) | (−28.60) | |
\(ETP\) | −0.0040*** | −0.0040*** | −0.0027*** | −0.0091*** | −0.0083*** | −0.0074*** | −0.0065*** | −0.0040*** | −0.0040*** | −0.0026*** | −0.0091*** | −0.0082*** | −0.0074*** | −0.0064*** |
(−3.25) | (−2.98) | (−2.70) | (−8.36) | (−7.94) | (−6.74) | (−6.24) | (−3.24) | (−2.98) | (−2.65) | (−8.36) | (−7.89) | (−6.73) | (−6.19) | |
\(Derivative\) | −0.0332*** | −0.0332*** | −0.0330*** | −0.0192*** | −0.0250*** | −0.0180*** | −0.0243*** | −0.0336*** | −0.0336*** | −0.0333*** | −0.0192*** | −0.0250*** | −0.0180*** | −0.0244*** |
(−22.91) | (−21.38) | (−55.74) | (−23.41) | (−35.83) | (−22.00) | (−34.83) | (−22.80) | (−21.28) | (−56.31) | (−23.43) | (−35.95) | (−22.02) | (−34.95) | |
\(HWM\) | −0.0013*** | −0.0013 | −0.0023*** | 0.0012*** | 0.0002 | 0.0010** | −0.0002 | −0.0007 | −0.0007 | −0.0016*** | 0.0015*** | 0.0007** | 0.0014*** | 0.0003 |
(−0.98) | (−0.98) | (−5.29) | (3.37) | (0.69) | (2.54) | (−0.49) | (−0.50) | (−0.50) | (−3.81) | (4.32) | (2.01) | (3.51) | (0.85) | |
\(Age\) | 0.0001* | 0.0001 | −0.0001*** | 0.0002*** | 0.0001*** | −0.0000 | 0.0001** | 0.0001** | 0.0000*** | 0.0002*** | 0.0001*** | 0.0000 | ||
(1.79) | (1.63) | (−5.08) | (13.61) | (11.35) | (−0.27) | (2.58) | (2.33) | (−2.66) | (13.82) | (11.85) | (0.17) | |||
\({R}^{2}\) | 0.0294 | 0.0294 | 0.0353 | 0.3015 | 0.2104 | 0.3048 | 0.2140 | 0.0307 | 0.0307 | 0.0364 | 0.3015 | 0.2104 | 0.3048 | 0.2140 |
Panel B: Number nonlottery | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | 0.1484*** | 0.1484*** | 0.1487*** | 0.1484*** | 0.1521*** | 0.1512*** | 0.1504*** | 0.1409*** | 0.1409*** | 0.1407*** | 0.1492*** | 0.1468*** | 0.1511*** | 0.1449*** |
(29.40) | (26.96) | (85.83) | (91.84) | (71.94) | (101.74) | (68.18) | (27.82) | (25.26) | (80.27) | (88.57) | (68.01) | (96.51) | (64.58) | |
\(RR\) | 0.0377*** | 0.0377*** | 0.0375*** | 0.0064*** | 0.0178*** | 0.0064*** | 0.0177*** | 0.0405*** | 0.0405*** | 0.0406*** | 0.0061*** | 0.0196*** | 0.0063*** | 0.0197*** |
(30.25) | (27.89) | (68.35) | (12.05) | (32.72) | (12.05) | (32.64) | (30.97) | (27.97) | (73.01) | (10.72) | (34.67) | (11.12) | (34.90) | |
\({RR}^{2}\) | −0.0034*** | −0.0034*** | −0.0034*** | −0.0006*** | −0.0016*** | −0.0006*** | −0.0016*** | −0.0036*** | −0.0036*** | −0.0036*** | −0.0006*** | −0.0018*** | −0.0006*** | −0.0018*** |
(−30.14) | (−27.81) | (−70.96) | (−13.67) | (−34.36) | (−13.68) | (−34.36) | (−28.31) | (−25.94) | (−74.75) | (−12.15) | (−35.54) | (−12.46) | (−35.79) | |
\(Leverage\) | −0.0138*** | −0.0138*** | −0.0141*** | −0.0331*** | −0.0330*** | −0.0126*** | −0.0126*** | −0.0129*** | −0.0321*** | −0.0321*** | ||||
(−5.00) | (−4.45) | (−13.23) | (−22.94) | (−22.93) | (−4.59) | (−4.09) | (−12.12) | (−22.25) | (−22.25) | |||||
\(RealMoney\) | −0.0168*** | −0.0168*** | −0.0171*** | −0.0200*** | −0.0201*** | −0.0159*** | −0.0159*** | −0.0162*** | −0.0193*** | −0.0194*** | ||||
(−3.05) | (−2.86) | (−10.61) | (−7.30) | (−7.36) | (−2.90) | (−2.74) | (−10.05) | (−7.03) | (−7.09) | |||||
\(Investable\) | −0.0055** | −0.0055** | −0.0052*** | 0.0016 | 0.0011 | −0.0054** | −0.0054** | −0.0048*** | 0.0020 | 0.0017 | ||||
(−2.37) | (−2.12) | (−6.25) | (1.14) | (0.80) | (−2.33) | (−2.08) | (−5.77) | (1.41) | (1.17) | |||||
\(Closing\) | −0.0138 | −0.0138 | −0.0137** | −0.0210*** | −0.0205** | −0.0131 | −0.0131 | −0.0127** | −0.0204** | −0.0197** | ||||
(−0.91) | (−0.88) | (−2.27) | (−2.66) | (−2.60) | (−0.86) | (−0.84) | (−2.12) | (−2.58) | (−2.50) | |||||
\(Closed\) | −0.0109*** | −0.0109*** | −0.0100*** | −0.0069*** | −0.0075*** | −0.0112*** | −0.0112*** | −0.0097*** | −0.0067*** | −0.0070*** | ||||
(−3.30) | (−2.96) | (−7.65) | (−4.08) | (−4.31) | (−3.37) | (−3.02) | (−7.44) | (−3.95) | (−4.04) | |||||
\(Fee\) | −0.1543*** | −0.1543*** | −0.1521*** | −0.0694*** | −0.0683*** | −0.1537*** | −0.1537*** | −0.1508*** | −0.0675*** | −0.0663*** | ||||
(−10.73) | (−9.00) | (−29.75) | (−7.93) | (−7.83) | (−10.75) | (−9.01) | (−29.51) | (−7.72) | (−7.60) | |||||
\(Media\) | 0.0258 | 0.0258 | 0.0246*** | 0.0234 | 0.0234 | 0.0221*** | ||||||||
(1.62) | (1.49) | (5.46) | (1.50) | (1.37) | (4.90) | |||||||||
\(Manager\) | −0.0289** | −0.0289** | −0.0296*** | −0.0302*** | −0.0302** | −0.0310*** | ||||||||
(−2.52) | (−2.23) | (−8.40) | (−2.63) | (−2.37) | (−8.83) | |||||||||
\(Theme\) | −0.0433 | −0.0433*** | −0.0434* | −0.0476 | −0.0476*** | −0.0464* | ||||||||
(−1.13) | (−11.11) | (−1.75) | (−1.23) | (−11.06) | (−1.88) | |||||||||
\(wikiNumber\) | −0.0013*** | −0.0013*** | −0.0013*** | −0.0013*** | −0.0013*** | −0.0013*** | ||||||||
(−7.19) | (−5.19) | (−19.22) | (−6.91) | (−4.99) | (−18.42) | |||||||||
\({lnT}^{num}\) | 0.0210*** | 0.0210*** | 0.0209*** | 0.0204*** | 0.0243*** | 0.0205*** | 0.0243*** | 0.0211*** | 0.0211*** | 0.0210*** | 0.0204*** | 0.0242*** | 0.0206*** | 0.0243*** |
(26.29) | (21.71) | (70.19) | (54.60) | (68.41) | (54.99) | (68.63) | (26.81) | (22.08) | (70.49) | (54.66) | (68.31) | (55.03) | (68.54) | |
\(ETF\) | −0.1090*** | −0.1090*** | −0.1090*** | −0.0528*** | −0.0879*** | −0.0535*** | −0.0885*** | −0.1093*** | −0.1093*** | −0.1092*** | −0.0528*** | −0.0878*** | −0.0534*** | −0.0885*** |
(−43.09) | (−35.16) | (−135.08) | (−49.77) | (−93.64) | (−50.46) | (−94.28) | (−42.83) | (−35.09) | (−135.11) | (−49.70) | (−93.57) | (−50.40) | (−94.20) | |
\(ETP\) | −0.0326*** | −0.0326*** | −0.0337*** | −0.0254*** | −0.0333*** | −0.0263*** | −0.0345*** | −0.0332*** | −0.0332*** | −0.0343*** | −0.0255*** | −0.0337*** | −0.0264*** | −0.0349*** |
(−10.44) | (−8.96) | (−17.15) | (−12.33) | (−16.32) | (−12.77) | (−16.89) | (−10.54) | (−9.07) | (−17.46) | (−12.40) | (−16.55) | (−12.84) | (−17.09) | |
\(Derivative\) | −0.1456*** | −0.1456*** | −0.1464*** | −0.0836*** | −0.1197*** | −0.0835*** | −0.1198*** | −0.1449*** | −0.1449*** | −0.1457*** | −0.0838*** | −0.1197*** | −0.0837*** | −0.1198*** |
(−46.99) | (−39.37) | (−123.87) | (−54.17) | (−87.70) | (−54.23) | (−87.66) | (−46.70) | (−39.17) | (−123.41) | (−54.31) | (−87.73) | (−54.36) | (−87.68) | |
\(HWM\) | 0.0038 | 0.0038 | 0.0068*** | −0.0025*** | −0.0002 | −0.0018** | 0.0013* | 0.0029 | 0.0029 | 0.0058*** | −0.0028*** | −0.0008 | −0.0022*** | 0.0005 |
(1.51) | (1.50) | (7.95) | (−3.83) | (−0.24) | (−2.40) | (1.66) | (1.09) | (1.08) | (6.87) | (−4.37) | (−1.21) | (−2.99) | (0.64) | |
\(Age\) | 0.0001 | 0.0001 | 0.0000 | 0.0002*** | 0.0002*** | 0.0003*** | 0.0000 | 0.0000 | −0.0001*** | 0.0001*** | 0.0002*** | 0.0002*** | ||
(0.79) | (0.71) | (0.30) | (6.69) | (8.07) | (5.72) | (−0.36) | (−0.33) | (−3.86) | (6.15) | (6.89) | (4.69) | |||
\({R}^{2}\) | 0.1871 | 0.1871 | 0.1918 | 0.4770 | 0.3616 | 0.4808 | 0.3655 | 0.1885 | 0.1885 | 0.1933 | 0.4769 | 0.3617 | 0.4807 | 0.3657 |
Panel C: Volume lottery | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | 0.0603*** | 0.0603*** | 0.0642*** | 0.0411*** | 0.0457*** | 0.0435*** | 0.0487*** | 0.0650*** | 0.0650*** | 0.0682*** | 0.0426*** | 0.0483*** | 0.0449*** | 0.0511*** |
(17.07) | (15.52) | (53.82) | (27.85) | (31.06) | (30.73) | (31.74) | (18.56) | (16.75) | (57.42) | (28.73) | (32.73) | (31.56) | (33.24) | |
\(RR\) | −0.0098*** | −0.0098*** | −0.0095*** | −0.0008*** | −0.0032*** | −0.0008*** | −0.0032*** | −0.0116*** | −0.0116*** | −0.0112*** | −0.0014*** | −0.0042*** | −0.0014*** | −0.0041*** |
(−13.40) | (−12.30) | (−34.94) | (−2.82) | (−11.66) | (−2.86) | (−11.52) | (−14.56) | (−13.17) | (−40.40) | (−4.58) | (−14.63) | (−4.56) | (−14.37) | |
\({RR}^{2}\) | 0.0009*** | 0.0009*** | 0.0009*** | 0.0001*** | 0.0003*** | 0.0001*** | 0.0003*** | 0.0010*** | 0.0010*** | 0.0010*** | 0.0001*** | 0.0004*** | 0.0001*** | 0.0004*** |
(14.20) | (13.05) | (37.58) | (4.21) | (13.26) | (4.26) | (13.20) | (15.04) | (13.71) | (41.99) | (5.42) | (15.32) | (5.43) | (15.16) | |
\(Leverage\) | 0.0020* | 0.0020 | 0.0023*** | −0.0017** | −0.0019** | 0.0015 | 0.0015 | 0.0019*** | −0.0020*** | −0.0021*** | ||||
(1.73) | (1.65) | (4.38) | (−2.38) | (−2.55) | (1.36) | (1.28) | (3.60) | (−2.79) | (−2.92) | |||||
\(RealMoney\) | 0.0077*** | 0.0077*** | 0.0076*** | 0.0054*** | 0.0056*** | 0.0075*** | 0.0075*** | 0.0073*** | 0.0052*** | 0.0053*** | ||||
(3.25) | (2.86) | (9.50) | (3.87) | (4.00) | (3.15) | (2.78) | (9.13) | (3.72) | (3.84) | |||||
\(Investable\) | −0.0017* | −0.0017 | −0.0002 | 0.0004 | 0.0015** | −0.0017* | −0.0017 | −0.0004 | 0.0003 | 0.0014* | ||||
(−1.81) | (−1.57) | (−0.57) | (0.61) | (2.06) | (−1.88) | (−1.64) | (−0.94) | (0.46) | (1.87) | |||||
\(Closing\) | −0.0100* | −0.0100* | −0.0098*** | −0.0105*** | −0.0095** | −0.0103* | −0.0103* | −0.0103*** | −0.0107*** | −0.0098** | ||||
(−1.86) | (−1.79) | (−3.28) | (−2.61) | (−2.38) | (−1.95) | (−1.87) | (−3.43) | (−2.66) | (−2.44) | |||||
\(Closed\) | −0.0061*** | −0.0061*** | −0.0034*** | −0.0023*** | −0.0007 | −0.0061*** | −0.0061*** | −0.0035*** | −0.0024*** | −0.0009 | ||||
(−5.24) | (−4.63) | (−5.27) | (−2.74) | (−0.83) | (−5.19) | (−4.59) | (−5.47) | (−2.83) | (−0.97) | |||||
\(Fee\) | 0.0116** | 0.0116* | 0.0129*** | 0.0225*** | 0.0219*** | 0.0107* | 0.0107 | 0.0121*** | 0.0219*** | 0.0213*** | ||||
(2.03) | (1.71) | (5.07) | (5.06) | (4.93) | (1.89) | (1.60) | (4.74) | (4.92) | (4.79) | |||||
\(Media\) | −0.0135*** | −0.0135** | −0.0133*** | −0.0128*** | −0.0128** | −0.0126*** | ||||||||
(−3.28) | (−2.47) | (−5.94) | (−3.14) | (−2.37) | (−5.61) | |||||||||
\(Manager\) | −0.0102*** | −0.0102** | −0.0094*** | −0.0097** | −0.0097** | −0.0089*** | ||||||||
(−2.71) | (−2.34) | (−5.40) | (−2.60) | (−2.23) | (−5.12) | |||||||||
\(Theme\) | 0.0391 | 0.0391*** | 0.0389*** | 0.0401 | 0.0401*** | 0.0394*** | ||||||||
(1.08) | (18.82) | (3.16) | (1.11) | (23.49) | (3.21) | |||||||||
\(wikiNumber\) | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | ||||||||
(0.33) | (0.21) | (0.60) | (0.06) | (0.04) | (0.00) | |||||||||
\({lnT}^{vol}\) | −0.0002 | −0.0002 | −0.0005*** | −0.0007*** | −0.0006*** | −0.0008*** | −0.0007*** | −0.0001 | −0.0001 | −0.0005*** | −0.0007*** | −0.0006*** | −0.0008*** | −0.0007*** |
(−0.86) | (−0.72) | (−5.55) | (−5.91) | (−6.07) | (−6.13) | (−6.88) | (−0.82) | (−0.68) | (−5.30) | (−5.87) | (−5.78) | (−6.11) | (−6.61) | |
\(ETF\) | −0.0189*** | −0.0189*** | −0.0179*** | −0.0105*** | −0.0137*** | −0.0106*** | −0.0136*** | −0.0188*** | −0.0188*** | −0.0178*** | −0.0105*** | −0.0137*** | −0.0106*** | −0.0136*** |
(−24.71) | (−21.44) | (−44.96) | (−18.76) | (−28.78) | (−18.95) | (−28.45) | (−24.32) | (−21.14) | (−44.62) | (−18.78) | (−28.81) | (−18.97) | (−28.48) | |
\(ETP\) | −0.0024** | −0.0024* | −0.0011 | −0.0076*** | −0.0066*** | −0.0061*** | −0.0050*** | −0.0024** | −0.0024* | −0.0011 | −0.0076*** | −0.0065*** | −0.0061*** | −0.0049*** |
(−2.16) | (−1.95) | (−1.16) | (−7.01) | (−6.37) | (−5.58) | (−4.80) | (−2.16) | (−1.95) | (−1.13) | (−7.00) | (−6.33) | (−5.57) | (−4.76) | |
\(Derivative\) | −0.0278*** | −0.0278*** | −0.0276*** | −0.0166*** | −0.0212*** | −0.0156*** | −0.0206*** | −0.0282*** | −0.0282*** | −0.0280*** | −0.0166*** | −0.0213*** | −0.0156*** | −0.0207*** |
(−21.03) | (−19.57) | (−48.08) | (−20.48) | (−30.93) | (−19.22) | (−29.99) | (−21.10) | (−19.61) | (−48.71) | (−20.50) | (−31.09) | (−19.25) | (−30.15) | |
\(HWM\) | −0.0008 | −0.0008 | −0.0017*** | 0.0015*** | 0.0007** | 0.0014*** | 0.0003 | −0.0001 | −0.0001 | −0.0010** | 0.0018*** | 0.0012*** | 0.0018*** | 0.0008** |
(−0.63) | (−0.63) | (−3.92) | (4.34) | (1.99) | (3.36) | (0.70) | (−0.09) | (−0.09) | (−2.34) | (5.38) | (3.36) | (4.42) | (2.08) | |
\(Age\) | 0.0000 | 0.0000 | −0.0001*** | 0.0001*** | 0.0001*** | −0.0001*** | 0.0000 | 0.0000 | −0.0001*** | 0.0001*** | 0.0001*** | −0.0001** | ||
(0.12) | (0.11) | (−10.27) | (8.92) | (6.14) | (−2.92) | (0.89) | (0.81) | (−7.79) | (9.18) | (6.72) | (−2.40) | |||
\({R}^{2}\) | 0.0266 | 0.0266 | 0.0320 | 0.2873 | 0.1996 | 0.2900 | 0.2026 | 0.0279 | 0.0279 | 0.0330 | 0.2872 | 0.1996 | 0.2900 | 0.2027 |
Panel D: Volume nonlottery | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | 0.1240*** | 0.1240*** | 0.1239*** | 0.0922*** | 0.1016*** | 0.0935*** | 0.0933*** | 0.1183*** | 0.1183*** | 0.1184*** | 0.0937*** | 0.0984*** | 0.0942*** | 0.0901*** |
(18.68) | (16.44) | (49.64) | (31.43) | (33.57) | (33.31) | (29.57) | (18.56) | (16.11) | (47.68) | (31.85) | (32.42) | (33.35) | (28.56) | |
\(RR\) | 0.0390*** | 0.0390*** | 0.0388*** | 0.0075*** | 0.0188*** | 0.0075*** | 0.0187*** | 0.0415*** | 0.0415*** | 0.0415*** | 0.0069*** | 0.0203*** | 0.0071*** | 0.0203*** |
(30.01) | (27.47) | (67.90) | (13.43) | (33.10) | (13.42) | (32.97) | (31.11) | (27.81) | (71.75) | (11.58) | (34.31) | (11.99) | (34.43) | |
\({RR}^{2}\) | −0.0035*** | −0.0035*** | −0.0035*** | −0.0007*** | −0.0017*** | −0.0007*** | −0.0017*** | −0.0037*** | −0.0037*** | −0.0037*** | −0.0007*** | −0.0018*** | −0.0007*** | −0.0018*** |
(−30.37) | (−27.70) | (−70.49) | (−15.11) | (−34.78) | (−15.10) | (−34.73) | (−28.75) | (−26.00) | (−73.54) | (−13.08) | (−35.23) | (−13.40) | (−35.37) | |
\(Leverage\) | −0.0114*** | −0.0114*** | −0.0116*** | −0.0322*** | −0.0316*** | −0.0103*** | −0.0103*** | −0.0105*** | −0.0313*** | −0.0307*** | ||||
(−4.11) | (−3.62) | (−10.55) | (−21.39) | (−21.01) | (−3.72) | (−3.28) | (−9.51) | (−20.75) | (−20.39) | |||||
\(RealMoney\) | −0.0041 | −0.0041 | −0.0045*** | −0.0076*** | −0.0082*** | −0.0030 | −0.0030 | −0.0035** | −0.0068** | −0.0073** | ||||
(−0.76) | (−0.71) | (−2.68) | (−2.67) | (−2.87) | (−0.56) | (−0.53) | (−2.08) | (−2.38) | (−2.56) | |||||
\(Investable\) | 0.0031 | 0.0031 | 0.0029*** | 0.0097*** | 0.0076*** | 0.0032 | 0.0032 | 0.0034*** | 0.0101*** | 0.0082*** | ||||
(1.31) | (1.16) | (3.36) | (6.61) | (5.11) | (1.38) | (1.23) | (3.93) | (6.89) | (5.50) | |||||
\(Closing\) | −0.0124 | −0.0124 | −0.0124** | −0.0138* | −0.0158* | −0.0115 | −0.0115 | −0.0112* | −0.0132 | −0.0149* | ||||
(−0.87) | (−0.81) | (−1.97) | (−1.68) | (−1.91) | (−0.81) | (−0.76) | (−1.79) | (−1.60) | (−1.81) | |||||
\(Closed\) | −0.0058* | −0.0058 | −0.0058*** | −0.0028 | −0.0064*** | −0.0061* | −0.0061 | −0.0055*** | −0.0026 | −0.0059*** | ||||
(−1.74) | (−1.55) | (−4.29) | (−1.57) | (−3.51) | (−1.81) | (−1.62) | (−4.05) | (−1.46) | (−3.26) | |||||
\(Fee\) | −0.1697*** | −0.1697*** | −0.1689*** | −0.0775*** | −0.0770*** | −0.1691*** | −0.1691*** | −0.1674*** | −0.0757*** | −0.0750*** | ||||
(−11.52) | (−9.51) | (−31.65) | (−8.49) | (−8.45) | (−11.53) | (−9.51) | (−31.37) | (−8.28) | (−8.23) | |||||
\(Media\) | 0.0297** | 0.0297** | 0.0287*** | 0.0274** | 0.0274* | 0.0261*** | ||||||||
(2.14) | (2.09) | (6.12) | (2.01) | (1.94) | (5.59) | |||||||||
\(Manager\) | −0.0459*** | −0.0459*** | −0.0463*** | −0.0472*** | −0.0472*** | −0.0477*** | ||||||||
(−4.00) | (−3.75) | (−12.67) | (−4.10) | (−3.89) | (−13.06) | |||||||||
\(Theme\) | −0.0690* | −0.0690*** | −0.0695*** | −0.0735** | −0.0735*** | −0.0727*** | ||||||||
(−1.90) | (−15.50) | (−2.70) | (−2.03) | (−14.80) | (−2.83) | |||||||||
\(wikiNumber\) | −0.0012*** | −0.0012*** | −0.0012*** | −0.0011*** | −0.0011*** | −0.0011*** | ||||||||
(−6.37) | (−4.62) | (−16.46) | (−6.08) | (−4.40) | (−15.62) | |||||||||
\({lnT}^{vol}\) | 0.0060*** | 0.0060*** | 0.0060*** | 0.0099*** | 0.0096*** | 0.0100*** | 0.0098*** | 0.0059*** | 0.0059*** | 0.0058*** | 0.0099*** | 0.0094*** | 0.0100*** | 0.0097*** |
(13.84) | (11.65) | (33.62) | (39.32) | (43.65) | (39.78) | (44.57) | (13.65) | (11.45) | (32.80) | (39.18) | (42.91) | (39.61) | (43.79) | |
\(ETF\) | −0.1118*** | −0.1118*** | −0.1123*** | −0.0582*** | −0.0922*** | −0.0588*** | −0.0934*** | −0.1121*** | −0.1121*** | −0.1123*** | −0.0581*** | −0.0920*** | −0.0587*** | −0.0932*** |
(−41.90) | (−33.84) | (−134.55) | (−52.31) | (−94.22) | (−52.94) | (−95.26) | (−41.46) | (−33.67) | (−134.35) | (−52.20) | (−94.03) | (−52.83) | (−95.05) | |
\(ETP\) | −0.0228*** | −0.0228*** | −0.0236*** | −0.0217*** | −0.0263*** | −0.0226*** | −0.0277*** | −0.0234*** | −0.0234*** | −0.0242*** | −0.0218*** | −0.0267*** | −0.0227*** | −0.0281*** |
(−6.55) | (−5.56) | (−11.61) | (−10.04) | (−12.36) | (−10.43) | (−13.02) | (−6.68) | (−5.68) | (−11.90) | (−10.10) | (−12.56) | (−10.49) | (−13.20) | |
\(Derivative\) | −0.1320*** | −0.1320*** | −0.1324*** | −0.0727*** | −0.1066*** | −0.0726*** | −0.1062*** | −0.1312*** | −0.1312*** | −0.1316*** | −0.0729*** | −0.1066*** | −0.0728*** | −0.1062*** |
(−42.45) | (−34.97) | (−110.05) | (−45.18) | (−75.62) | (−45.16) | (−75.32) | (−41.99) | (−34.66) | (−109.46) | (−45.31) | (−75.60) | (−45.27) | (−75.29) | |
\(HWM\) | 0.0043* | 0.0043* | 0.0071*** | −0.0018*** | 0.0010 | −0.0014* | 0.0022*** | 0.0035 | 0.0035 | 0.0063*** | −0.0021*** | 0.0003 | −0.0018** | 0.0014* |
(1.68) | (1.67) | (8.04) | (−2.64) | (1.34) | (−1.74) | (2.65) | (1.31) | (1.31) | (7.21) | (−3.12) | (0.46) | (−2.27) | (1.73) | |
\(Age\) | 0.0001* | 0.0001 | 0.0001*** | 0.0001*** | 0.0002*** | 0.0005*** | 0.0000 | 0.0000 | 0.0000 | 0.0001*** | 0.0001*** | 0.0005*** | ||
(1.66) | (1.50) | (3.98) | (4.98) | (6.72) | (10.58) | (0.42) | (0.38) | (−0.21) | (4.38) | (5.45) | (9.46) | |||
\({R}^{2}\) | 0.1732 | 0.1732 | 0.1775 | 0.4540 | 0.3433 | 0.4576 | 0.3472 | 0.1743 | 0.1743 | 0.1788 | 0.4539 | 0.3433 | 0.4574 | 0.3472 |
The results suggest a highly significant quadratic relation between the traded share of lottery-like stocks and past wikifolio performance. The regression coefficients relating to the employed wikifolio performance measures are significant throughout all conducted analyses. The considered coefficients remain statistically significant when computing standard errors simultaneously clustered by month and wikifolio, as well as when computing standard errors simultaneously clustered by month and trader (Petersen 2009). Moreover, all models including fixed effects yield statistically significant coefficients corresponding to the relative performance variables.
The signs of the respective coefficients—negative sign of the past performance measure and positive sign for the squared term—suggest a U-shaped relationship, i.e. signal providers increase the traded share of lottery-like stocks when exhibiting relatively good or relatively bad performance. These results are not particularly surprising. Schneider and Oehler (2021) report a similar pattern for traded currency pairs which exhibit extreme past daily returns.
The dummy variable indicating whether a signal provider has invested his own money in the corresponding wikifolio certificate (\({RealMoney}_{i}\)) is significantly positive in all regression specifications, i.e. signal providers with an investment in their own wikifolio are more likely to trade a higher share of lotteries. The dummy variables indicating whether an ETF (\({ETF}_{i,t}\)), ETP (\({ETP}_{i,t}\)) or derivative (\({Derivative}_{i,t}\)) is traded within wikifolio \(i\) in month \(t\) are significantly negative in all conducted regressions. Signal providers trading ETFs, ETPs, or Derivatives may, on average, be less likely to trade stocks due to their pursued trading strategy focusing on non-stock instruments. Furthermore, signal providers trading derivatives do not depend on stocks when intending to trade assets with lottery-like payoffs. Although not significant in all models, the regression analyses yield positive coefficients relating to the variable depicting the level of a wikifolio’s performance fee (\({Fee}_{i}\)). As described in Sect. 3.4, performance fees are determined by signal providers when creating the wikifolio. In this context, the following applies: The higher the performance fee, the better the prospect of high compensation. Signal providers with self-selected high performance fees might have a stronger focus on receiving a certain level of benefits from the wikifolio platform, and thus try to substantially exceed previous high watermarks by trading lottery-like stocks more frequently.
4.3 Transactions nonlottery-like stocks
To gain further insights, we assess if relative peer performance has a significant impact on the share of traded nonlottery stocks (Kumar 2009).25 Therefore, we set the relative monthly number/volume of nonlottery-like stocks traded (\({RTNL}_{i,t}^{num}\)/\({RTNL}_{i,t}^{vol}\)) as the according dependent variable:\({TNL}_{i,t}^{num}\)/\({TNL}_{i,t}^{vol}\) denote the monthly number/volume of traded nonlottery-like stocks. As before, all wikifolio-month observations with no conducted transaction are excluded. The corresponding dependent variables are transformed for the constituent regression analyses by adding the constant \(1\) and then applying the natural logarithm:
$${{RTNL_{i,t}^{num} = \frac{{TNL_{i,t}^{num} }}{{T_{i,t}^{num} }}} \mathord{\left/ {\vphantom {{RTNL_{i,t}^{num} = \frac{{TNL_{i,t}^{num} }}{{T_{i,t}^{num} }}} {RTNL_{i,t}^{vol} = \frac{{TNL_{i,t}^{vol} }}{{T_{i,t}^{vol} }},}}} \right. \kern-\nulldelimiterspace} {RTNL_{i,t}^{vol} = \frac{{TNL_{i,t}^{vol} }}{{T_{i,t}^{vol} }},}}$$
(10)
$${{lnRTNL_{i,t}^{num} = ln\left( {1 + RTNL_{i,t}^{num} } \right)} \mathord{\left/ {\vphantom {{lnRTNL_{i,t}^{num} = ln\left( {1 + RTNL_{i,t}^{num} } \right)} {lnRTNL_{i,t}^{vol} = ln\left( {1 + RTNL_{i,t}^{vol} } \right).}}} \right. \kern-\nulldelimiterspace} {lnRTNL_{i,t}^{vol} = ln\left( {1 + RTNL_{i,t}^{vol} } \right).}}$$
(11)
As in the previous analyses, we set relative past wikifolio performance (\({RR}_{i,t-1}/ {R\overline{R} }_{i,t-6}^{t-1}\)) as relevant independent variable. The previously depicted panel regression is applied. Results of the regression analysis are reported in Table 4 (Panel B and Panel D).
Our results indicate an inverse U-shaped quadratic relationship, i.e. signal providers administering wikifolios with more moderate peer performance are more likely to trade nonlottery-like stocks. The coefficients corresponding to relative past performance are highly significant within all model specifications.
4.4 Net lottery flow
In order to gain a deeper understanding of the relationship between relative past performance and the traded share of lottery-like stocks, we create two further dependent variables respectively reflecting the share of lottery-like stock purchases (\({RIL}_{i,t}^{num}/{RIL}_{i,t}^{vol}\)) and the share of lottery-like stock sales (\({RSL}_{i,t}^{num}/{RSL}_{i,t}^{vol}\)):\({I}_{i,t}^{num}/{I}_{i,t}^{vol}\) denote the number/volume of purchase transactions conducted within wikifolio \(i\) in month \(t\); accordingly, \({S}_{i,t}^{num}/{S}_{i,t}^{vol}\) denote the number/volume of sale transactions. \({IL}_{i,t}^{num}/{IL}_{i,t}^{vol}\) reflects the number/volume of lottery-like stock purchases; \({SL}_{i,t}^{num}/{SL}_{i,t}^{vol}\) depicts the number/volume of lottery-like stock sales. As before, we transform the respective dependent variables for the constituent regression analyses by adding the constant \(1\) and then applying the natural logarithm:
$${{RIL_{i,t}^{num} = \frac{{IL_{i,t}^{num} }}{{I_{i,t}^{num} }}} \mathord{\left/ {\vphantom {{RIL_{i,t}^{num} = \frac{{IL_{i,t}^{num} }}{{I_{i,t}^{num} }}} {RIL_{i,t}^{vol} = \frac{{IL_{i,t}^{vol} }}{{I_{i,t}^{vol} }},}}} \right. \kern-\nulldelimiterspace} {RIL_{i,t}^{vol} = \frac{{IL_{i,t}^{vol} }}{{I_{i,t}^{vol} }},}}$$
(12)
$${{RSL_{i,t}^{num} = \frac{{SL_{i,t}^{num} }}{{S_{i,t}^{num} }}} \mathord{\left/ {\vphantom {{RSL_{i,t}^{num} = \frac{{SL_{i,t}^{num} }}{{S_{i,t}^{num} }}} {RSL_{i,t}^{vol} = \frac{{SL_{i,t}^{vol} }}{{S_{i,t}^{vol} }}.}}} \right. \kern-\nulldelimiterspace} {RSL_{i,t}^{vol} = \frac{{SL_{i,t}^{vol} }}{{S_{i,t}^{vol} }}.}}$$
(13)
$${{lnRIL_{i,t}^{num} = ln\left( {1 + RIL_{i,t}^{num} } \right)} \mathord{\left/ {\vphantom {{lnRIL_{i,t}^{num} = ln\left( {1 + RIL_{i,t}^{num} } \right)} {lnRIL_{i,t}^{vol} = ln\left( {1 + RIL_{i,t}^{vol} } \right),}}} \right. \kern-\nulldelimiterspace} {lnRIL_{i,t}^{vol} = ln\left( {1 + RIL_{i,t}^{vol} } \right),}}$$
(14)
$${{lnRSL_{i,t}^{num} = ln\left( {1 + RSL_{i,t}^{num} } \right)} \mathord{\left/ {\vphantom {{lnRSL_{i,t}^{num} = ln\left( {1 + RSL_{i,t}^{num} } \right)} {lnRSL_{i,t}^{vol} = ln\left( {1 + RSL_{i,t}^{vol} } \right).}}} \right. \kern-\nulldelimiterspace} {lnRSL_{i,t}^{vol} = ln\left( {1 + RSL_{i,t}^{vol} } \right).}}$$
(15)
The obtained results are roughly similar to those of the previous model where the relative share of traded lottery-like stocks is set as dependent variable. Hence, the effect regarding the traded share of lotteries cannot clearly be attributed to purchases or sales.
The results obtained through the previous analyses do not allow us to make a statement about the net exposure towards risk. Addressing this issue—trying to obtain an indication regarding the relation between the net exposure towards risk induced by lottery-like stocks and relative past performance—we assess the cumulative net investment into lottery-like stocks. In this context, we compute the net lottery flow (\({LF}_{i,t=1}^{num,t}/{LF}_{i,t=1}^{vol,t}\)) as the difference between the cumulative number/volume of lottery-like stock purchases and the cumulative number/volume of lottery-like stock sales from the creation of wikifolio \(i\) to month \(t\):
$$LF_{i,t = 1}^{num,~t} = \mathop \sum \limits_{t = 1}^t LI_{i,t}^{num} - \mathop \sum \limits_{t = 1}^t LS_{i,t}^{num}/LF_{i,t = 1}^{vol,t} = {\text{ln}}\left( {\mathop \sum \limits_{t = 1}^t LI_{i,t}^{vol}} \right) - {\text{ln}}\left( {\mathop \sum \limits_{t = 1}^t LS_{i,t}^{vol}} \right)$$
(16)
The initial panel regression is applied where we focus on relative past wikifolio performance (\({RR}_{i, t-1}/{R\overline{R} }_{i,t-6}^{t-1}\)) as the primarily relevant independent variable. All variables are displayed and described in Appendix Table 11. The results of the regression analysis are reported in Table 5.
Table 5
Net flow lottery-like stocks
Panel A: Number net lottery flow | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | -4.5640*** | -4.5640*** | -4.2017*** | 1.0087*** | -1.5981*** | 3.3079*** | −0.5286*** | -4.0821*** | -4.0821*** | -3.7665*** | 1.2987*** | -1.2855*** | 3.5761*** | −0.2279 |
(−4.35) | (−3.20) | (−26.90) | (10.04) | (−8.61) | (37.89) | (−2.67) | (−3.94) | (−2.86) | (−23.85) | (12.59) | (−6.86) | (39.76) | (−1.14) | |
\(RR\) | −0.1035*** | −0.1035*** | −0.0938*** | −0.0387*** | −0.0637*** | −0.0381*** | −0.0621*** | −0.1930*** | −0.1930*** | −0.1797*** | −0.0965*** | −0.1254*** | −0.0944*** | −0.1238*** |
(−3.11) | (−2.76) | (−6.27) | (−4.51) | (−5.44) | (−4.40) | (−5.24) | (−3.16) | (−2.90) | (−12.02) | (−10.23) | (−10.12) | (−9.91) | (−9.89) | |
\(Leverage\) | 0.5396 | 0.5396 | 0.5359*** | -1.6622*** | -1.7998*** | 0.5243 | 0.5243 | 0.5230*** | -1.6725*** | -1.8090*** | ||||
(1.27) | (1.17) | (4.17) | (−11.09) | (−11.99) | (1.23) | (1.14) | (4.07) | (−11.16) | (−12.06) | |||||
\(RealMoney\) | 0.0872 | 0.0872 | 0.0636 | 4.5005*** | 4.5585*** | 0.1850 | 0.1850 | 0.1530 | 4.5623*** | 4.6184*** | ||||
(0.05) | (0.04) | (0.33) | (15.74) | (15.96) | (0.10) | (0.09) | (0.78) | (15.96) | (16.16) | |||||
\(Investable\) | 0.0020 | 0.0020 | 0.3219*** | 1.5727*** | 2.0198*** | 0.0180 | 0.0180 | 0.3354*** | 1.5921*** | 2.0391*** | ||||
(0.01) | (0.00) | (3.17) | (10.65) | (13.49) | (0.05) | (0.04) | (3.30) | (10.79) | (13.62) | |||||
\(Closing\) | -2.9027** | -2.9027* | -2.8246*** | 0.8062 | 1.4067* | -2.7708* | -2.7708* | -2.7028*** | 0.7995 | 1.3995* | ||||
(−2.04) | (−1.86) | (−3.86) | (0.98) | (1.71) | (−1.95) | (−1.78) | (−3.70) | (0.97) | (1.70) | |||||
\(Closed\) | -2.1418*** | -2.1418*** | -1.5415*** | −0.0237 | 0.7035*** | -2.1782*** | -2.1782*** | -1.5769*** | −0.0641 | 0.6660*** | ||||
(−3.38) | (−2.74) | (−9.70) | (−0.13) | (3.86) | (−3.43) | (−2.78) | (−9.93) | (−0.36) | (3.66) | |||||
\(Fee\) | −0.1397 | −0.1397 | 0.2659 | 2.0995** | 2.0850** | −0.2781 | −0.2781 | 0.1422 | 2.0198** | 2.0115** | ||||
(−0.04) | (−0.03) | (0.43) | (2.30) | (2.29) | (−0.08) | (−0.06) | (0.23) | (2.22) | (2.21) | |||||
\(Media\) | -3.7821 | -3.7821 | -3.8566*** | -3.7576 | -3.7576 | -3.8354*** | ||||||||
(−1.14) | (−0.97) | (−7.05) | (−1.13) | (−0.97) | (−7.01) | |||||||||
\(Manager\) | -1.2542** | -1.2542* | -1.3173*** | -1.2691** | -1.2691* | -1.3330*** | ||||||||
(−2.29) | (−1.66) | (−3.09) | (−2.31) | (−1.70) | (−3.12) | |||||||||
\(Theme\) | -3.3909*** | -3.3909** | -2.8959 | -3.1293*** | -3.1293** | -2.6392 | ||||||||
(−3.31) | (−2.53) | (−0.96) | (−3.09) | (−2.37) | (−0.88) | |||||||||
\(wikiNumber\) | 0.1952*** | 0.1952** | 0.1913*** | 0.1957*** | 0.1957** | 0.1918*** | ||||||||
(3.27) | (2.18) | (23.10) | (3.28) | (2.19) | (23.16) | |||||||||
\({lnT}^{num}\) | 2.7015*** | 2.7015*** | 2.6709*** | 0.0557* | 0.9408*** | 0.0421 | 0.9427*** | 2.7113*** | 2.7113*** | 2.6796*** | 0.0689** | 0.9562*** | 0.0543* | 0.9571*** |
(6.55) | (5.37) | (73.88) | (1.83) | (25.45) | (1.38) | (25.45) | (6.56) | (5.38) | (74.12) | (2.26) | (25.84) | (1.78) | (25.82) | |
\(ETF\) | 0.0637 | 0.0637 | 0.2838*** | −0.0195 | −0.3403*** | −0.0637 | −0.2671*** | −0.0087 | −0.0087 | 0.2156** | −0.0241 | −0.3627*** | −0.0677 | −0.2886*** |
(0.14) | (0.11) | (2.91) | (−0.23) | (−3.48) | (−0.74) | (−2.72) | (−0.02) | (−0.02) | (2.20) | (−0.28) | (−3.71) | (−0.78) | (−2.94) | |
\(ETP\) | 0.2359 | 0.2359 | 0.3975 | -1.7177*** | -1.4457*** | -1.4610*** | -1.1645*** | 0.1999 | 0.1999 | 0.3622 | -1.7183*** | -1.4541*** | -1.4625*** | -1.1741*** |
(0.34) | (0.28) | (1.67) | (−10.25) | (−6.80) | (−8.69) | (−5.46) | (0.29) | (0.24) | (1.52) | (−10.26) | (−6.84) | (−8.70) | (−5.51) | |
\(Derivative\) | -2.6168*** | -2.6168*** | -2.7520*** | 0.1732 | −0.4819*** | 0.2515** | −0.5855*** | -2.6339*** | -2.6339*** | -2.7684*** | 0.1787 | −0.4815*** | 0.2561*** | −0.5862*** |
(−4.76) | (−3.98) | (−19.29) | (1.38) | (−3.39) | (2.00) | (−4.11) | (−4.77) | (−3.98) | (−19.41) | (1.42) | (−3.39) | (2.04) | (−4.11) | |
\(HWM\) | −0.8213*** | −0.8213*** | −0.8903*** | −0.1092** | −0.2143*** | −0.0546 | −0.1771* | −0.6806*** | −0.6806*** | −0.7112*** | −0.0553 | −0.1484** | 0.0185 | −0.0847 |
(−3.48) | (−3.52) | (−8.65) | (−2.05) | (−2.97) | (−0.88) | (−2.13) | (−2.80) | (−2.81) | (−6.94) | (−1.05) | (−2.08) | (0.30) | (−1.03) | |
\(Age\) | 0.0954*** | 0.0954*** | 0.0648*** | 0.1136*** | 0.1167*** | 0.0475*** | 0.0952*** | 0.0952*** | 0.0649*** | 0.1133*** | 0.1164*** | 0.0473*** | ||
(5.69) | (4.77) | (21.48) | (59.67) | (46.88) | (9.61) | (5.70) | (4.78) | (21.53) | (59.50) | (46.78) | (9.57) | |||
\({R}^{2}\) | 0.0315 | 0.0315 | 0.0336 | 0.7206 | 0.4384 | 0.7212 | 0.4394 | 0.0319 | 0.0319 | 0.0340 | 0.7207 | 0.4385 | 0.7213 | 0.4395 |
Panel B: Volume net lottery flow | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14) | |
\(\alpha\) | 1.8221*** | 1.8221*** | 1.9495*** | 1.2794*** | 1.3006*** | 1.0103*** | 1.3396*** | 1.8243*** | 1.8243*** | 1.9494*** | 1.2857*** | 1.3022*** | 1.0162*** | 1.3414*** |
(17.73) | (16.62) | (60.12) | (42.09) | (34.13) | (34.84) | (33.36) | (18.11) | (16.92) | (60.36) | (42.29) | (34.22) | (35.07) | (33.44) | |
\(RR\) | −0.0008 | −0.0008 | −0.0014 | −0.0043*** | −0.0032** | −0.0052*** | −0.0040** | −0.0014 | −0.0014 | −0.0014 | −0.0065*** | −0.0040** | −0.0075*** | −0.0049*** |
(−0.27) | (−0.27) | (−0.71) | (−3.44) | (−2.00) | (−4.08) | (−2.42) | (−0.38) | (−0.37) | (−0.73) | (−4.72) | (−2.34) | (−5.39) | (−2.84) | |
\(Leverage\) | 0.0035 | 0.0035 | −0.0012 | −0.0897*** | −0.0916*** | 0.0034 | 0.0034 | −0.0013 | −0.0899*** | −0.0919*** | ||||
(0.06) | (0.06) | (−0.07) | (−4.31) | (−4.40) | (0.06) | (0.06) | (−0.07) | (−4.32) | (−4.41) | |||||
\(RealMoney\) | 0.3413*** | 0.3413*** | 0.3430*** | 0.1216*** | 0.1247*** | 0.3421*** | 0.3421*** | 0.3436*** | 0.1235*** | 0.1270*** | ||||
(3.17) | (3.02) | (13.38) | (3.07) | (3.15) | (3.18) | (3.03) | (13.40) | (3.12) | (3.21) | |||||
\(Investable\) | −0.1800*** | −0.1800*** | −0.1448*** | −0.1307*** | −0.1214*** | −0.1799*** | −0.1799*** | −0.1447*** | −0.1300*** | −0.1206*** | ||||
(−3.72) | (−3.63) | (−10.99) | (−6.42) | (−5.87) | (−3.72) | (−3.63) | (−10.98) | (−6.39) | (−5.83) | |||||
\(Closing\) | −0.0103 | −0.0103 | −0.0036 | −0.1979* | −0.1844 | −0.0094 | −0.0094 | −0.0028 | −0.1979* | −0.1846 | ||||
(−0.02) | (−0.02) | (−0.04) | (−1.73) | (−1.61) | (−0.02) | (−0.02) | (−0.03) | (−1.73) | (−1.61) | |||||
\(Closed\) | −0.2579*** | −0.2579*** | −0.1831*** | −0.1824*** | −0.1583*** | −0.2581*** | −0.2581*** | −0.1833*** | −0.1833*** | −0.1595*** | ||||
(−4.13) | (−4.03) | (−8.80) | (−7.46) | (−6.27) | (−4.13) | (−4.02) | (−8.81) | (−7.50) | (−6.31) | |||||
\(Fee\) | −0.5521* | −0.5521* | −0.4264*** | 0.5731*** | 0.5845*** | −0.5533* | −0.5533* | −0.4273*** | 0.5706*** | 0.5816*** | ||||
(−1.86) | (−1.67) | (−5.23) | (4.53) | (4.62) | (−1.86) | (−1.68) | (−5.24) | (4.51) | (4.60) | |||||
\(Media\) | 0.0993 | 0.0993 | 0.0897 | 0.0995 | 0.0995 | 0.0898 | ||||||||
(0.38) | (0.57) | (1.25) | (0.38) | (0.57) | (1.25) | |||||||||
\(Manager\) | 0.2937 | 0.2937 | 0.2825*** | 0.2934 | 0.2934 | 0.2823*** | ||||||||
(1.15) | (1.01) | (5.05) | (1.15) | (1.01) | (5.04) | |||||||||
\(Theme\) | 0.9473 | 0.9473*** | 0.9733** | 0.9491 | 0.9491*** | 0.9753** | ||||||||
(1.06) | (15.67) | (2.47) | (1.06) | (15.84) | (2.47) | |||||||||
\(wikiNumber\) | −0.0084** | −0.0084** | −0.0085*** | −0.0084** | −0.0084** | −0.0085*** | ||||||||
(−2.59) | (−2.31) | (−7.88) | (−2.59) | (−2.31) | (−7.88) | |||||||||
\({lnT}^{vol}\) | −0.0328*** | −0.0328*** | −0.0436*** | −0.0223*** | −0.0116*** | −0.0218*** | −0.0128*** | −0.0327*** | −0.0327*** | −0.0435*** | −0.0217*** | −0.0113*** | −0.0210*** | −0.0123*** |
(−3.93) | (−3.64) | (−16.04) | (−7.90) | (−3.83) | (−7.69) | (−4.18) | (−3.90) | (−3.62) | (−15.98) | (−7.64) | (−3.70) | (−7.40) | (−4.03) | |
\(ETF\) | −0.3721*** | −0.3721*** | −0.3276*** | −0.0093 | −0.1568*** | −0.0057 | −0.1493*** | −0.3727*** | −0.3727*** | −0.3280*** | −0.0097 | −0.1574*** | −0.0061 | −0.1502*** |
(−10.88) | (−10.06) | (−25.70) | (−0.74) | (−11.57) | (−0.45) | (−10.97) | (−10.95) | (−10.12) | (−25.66) | (−0.77) | (−11.62) | (−0.49) | (−11.03) | |
\(ETP\) | −0.0132 | −0.0132 | −0.0257 | 0.0183 | 0.0191 | 0.0050 | 0.0088 | −0.0134 | −0.0134 | −0.0259 | 0.0183 | 0.0189 | 0.0049 | 0.0085 |
(−0.25) | (−0.24) | (−0.83) | (0.75) | (0.65) | (0.20) | (0.30) | (−0.25) | (−0.24) | (−0.83) | (0.75) | (0.64) | (0.20) | (0.29) | |
\(Derivative\) | −0.3610*** | −0.3610*** | −0.3841*** | −0.0459** | −0.2650*** | −0.0431** | −0.2685*** | −0.3611*** | −0.3611*** | −0.3842*** | −0.0454** | −0.2649*** | −0.0426** | −0.2684*** |
(−7.50) | (−7.19) | (−20.94) | (−2.52) | (−13.60) | (−2.37) | (−13.74) | (−7.51) | (−7.20) | (−20.94) | (−2.50) | (−13.59) | (−2.34) | (−13.73) | |
\(HWM\) | 0.0714*** | 0.0714*** | 0.0984*** | 0.0600*** | 0.0669*** | 0.0756*** | 0.0820*** | 0.0723*** | 0.0723*** | 0.0984*** | 0.0608*** | 0.0669*** | 0.0767*** | 0.0824*** |
(3.40) | (3.36) | (7.28) | (7.73) | (6.70) | (8.36) | (7.09) | (3.42) | (3.38) | (7.32) | (7.92) | (6.77) | (8.60) | (7.20) | |
\(Age\) | −0.0157*** | −0.0157*** | −0.0193*** | −0.0128*** | −0.0125*** | −0.0144*** | −0.0157*** | −0.0157*** | −0.0193*** | −0.0128*** | −0.0125*** | −0.0144*** | ||
(−12.99) | (−12.26) | (−47.56) | (−45.91) | (−36.00) | (−20.79) | (−12.99) | (−12.27) | (−47.56) | (−46.00) | (−36.03) | (−20.79) | |||
\({R}^{2}\) | 0.0178 | 0.0178 | 0.0202 | 0.6452 | 0.3601 | 0.6456 | 0.3606 | 0.0178 | 0.0178 | 0.0202 | 0.6452 | 0.3601 | 0.6457 | 0.3606 |
Our results indicate a negative linear relationship between the net lottery flow and relative past wikifolio performance. When the net lottery flow variable is based on volume (\({LF}_{i,t=1}^{vol,T}\)), the performance measure is not statistically significant in all regression specifications. However, when wikifolio-level fixed effects are included, the performance measure is statistically significant at the per mill level. The obtained results suggest that signal providers increase the net position of lottery-like stocks when underperforming their peers.
4.5 Evaluation of main empirical results
To sum up, our results indicate a quadratic relationship between the primarily examined independent variable, relative past wikifolio performance, and the traded share of lottery-like stocks: Signal providers exhibiting relatively bad past performance and signal providers exhibiting relatively good past performance seem to trade a higher share of lottery-like stocks as defined by Kumar (2009).
The observed results might be explained by several well-documented behavioral phenomena as well as peculiarities of the social trading platform and the established signal provider compensation scheme.
Regarding signal providers at the lower end of the performance spectrum, i.e. signal providers administering underperforming wikifolios, there are several factors which may induce lottery trading. Underperforming wikifolios are unlikely to generate—or maintain—a desirable base of signal followers. Accounting for their limited monetary downside risk (see Sects. 3.1 and 3.4), signal providers corresponding to wikifolios at the lower end of the relative performance spectrum have little to lose. Due to their specific return characteristics, i.e. high idiosyncratic volatility and positive idiosyncratic skewness (Kumar 2009), lottery-like stocks may be particularly appealing to signal providers looking to improve the positioning of an underperforming wikifolio.
Hoping for an exceptionally high positive return, previously underperforming signal providers may include lottery-like stocks more frequently into their corresponding wikifolios. In turn, when included lottery-like stocks fail to deliver the desired return, signal providers may shortly thereafter replace the corresponding assets.
With regard to signal providers operating wikifolios at the upper end of the peer performance range, overconfidence might be a suitable explanation for the observed results. Barber and Odean (2001), Broihanne et al. (2014), De Long et al. (1991), and Odean (1999) document a positive relation between overconfidence and risk taking. When their overconfidence is increased due to good relative past performance (Gervais and Odean 2001; Odean 1999; Statman et al. 2006), signal providers might be drawn to assets exhibiting more risk and thus increase the proportion of traded lottery-like stocks. Furthermore, overconfident traders overestimate the precision of their information (Benos 1998; Daniel et al. 1998; Odean 1998; 1999), and thus may severely overestimate their ability to make profits by timing the market. When believing to have precise or superior information, signal providers may increase trading with regard to stocks where major (positive) price movements are more likely, i.e. stocks exhibiting high idiosyncratic volatility and high idiosyncratic skewness—lottery characteristics (Kumar 2009).
The obtained results indicate an inverted U-shape quadratic relationship between relative past performance and the traded share of nonlottery-like stocks. Hence, signal providers administering wikifolios with more moderate peer performance are more likely to trade low idiosyncratic volatility and low idiosyncratic skewness stocks. Signal providers located somewhere in the middle of the relative performance spectrum may pursue an investment strategy focusing on feasible long-term returns—instead of speculating on potential (short-term) extreme returns. Thus, those signal providers may be more prone to invest in stocks exhibiting low levels of (idiosyncratic) volatility and (idiosyncratic) skewness.
Addressing the net exposure towards risk induced by lottery-like stocks, we report a negative linear relation between net lottery flow and the applied relative performance variables. In addition to trading lottery-like stocks more frequently, our results indicate that signal providers administering underperforming wikifolios increase their net exposure towards lottery-like stocks. Even though signal provider compensation is not directly linked to a corresponding administered wikifolio’s ranking, the platform’s compensation scheme (see Sect. 3.4) indirectly imposes tournament incentives as signal providers must achieve a position reasonably suited for generating attention from signal followers.26 Regarding the lower end of the relative performance spectrum, our results are in line with Kirchler et al. (2018), who provide evidence that tournament incentives increase risk-taking among underperforming traders.
Allowing signal providers to simultaneously operate more than one account, a feature common to social trading platforms27, may further help to explain why underperforming signal providers exhibit an increased preference for lottery-like stocks. The wikifolio platform enables signal providers to operate up to eight wikifolios at the same time with no or limited exposure to their generated returns.28 As unsuccessful wikifolios may be closed—and potentially replaced—at any time, signal providers incur very limited costs when abandoning unsuccessful projects. Hence, signal providers with underperforming wikifolios may be particularly inclined to employ lottery-like characteristics—speculating on the unlikely but possible event of an extreme positive return—in an attempt to turn around a fruitless portfolio.
In brief, our results suggest that peer performance in social trading is a significant factor with regard to signal provider gambling behavior. Attaining a position at the upper or at the lower end of the performance spectrum may induce signal providers to trade lottery-like stocks more frequently. Furthermore, signal providers operating wikifolios which have previously underperformed increase their net exposure towards lottery-like stocks, exposing their followers to lottery-like return characteristics.
Although our results are consistent, we can’t exclude the existence of an omitted variable. We acknowledge the possibility that the regression analyses may be subject to omitted variable bias (Clarke 2005).
5 Robustness
5.1 Alternative definition for lottery-like stocks
First, in order to test the robustness of our results, we select a definition of lottery-like stocks that differs from Kumar’s (2009) classification. A relatively simple and more intuitive definition is introduced by Bali et al. (2011) who define stocks with extreme past daily returns as lottery-like assets. Stocks are sorted into decile portfolios based on the constituent maximum daily return over the past month. Stocks in the highest decile portfolio (\(Max\)), i.e. stocks exhibiting the highest constituent daily return over the previous month, are categorized as lottery-like. As a variation, decile portfolios are formed based on the average comprising the five highest returns of the previous month. Accordingly, stocks in the highest decile portfolio (\(Max5\)), i.e. stocks exhibiting the highest average regarding the five highest daily returns over the previous month, are categorized as lottery-like.
Signal providers on the wikifolio platform are mostly individual investors. Assuming limited cognitive processing capabilities and, in this context, limited investor attention (Barber and Odean 2008; Kahneman 1973; Odean 1999), signal providers may select lottery-like assets solely based on maximum past returns. Kumar (2009) argues that investors are searching for cheap bets and thus should tend towards low-priced stocks. Consequently, Kumar (2009) employs stock price as one of the defining criteria for lottery-like stocks. However, since signal provider portfolios on the wikifolio platform are purely virtual, i.e. signal providers simply chose their starting capital when creating a wikifolio, the price criterion might not be as relevant.
5.2 Alternative benchmarks for lottery-like stocks
Second, we test the robustness of our results by categorizing lottery-like stocks with regard to a different benchmark. As described in Sect. 3.3, signal providers can choose from a broad investment universe, including stocks, funds, ETFs, investment certificates, and leverage products. Available assets are selected by the wikifolio platform. Hence, within the previous analyses, we might define certain stocks as lottery-like which would not be categorized as such when a comprehensive country-specific stock index was employed as benchmark and vice versa. Based on the number and volume of transactions by issuing country (see Appendix Table 8), we select ten comprehensive country-specific stock indices.29 The employed indices are displayed in Appendix Table 10. We identify lottery-like stocks within each index by applying the Kumar (2009) method.30 Subsequently, the information if a stock is identified as lottery-like during a respective month is merged to the transaction dataset.
Sorting stocks with regard to comprehensive national stock indices leads to results which are very similar to those described in the previous sections.
5.3 Idiosyncratic skewness computation
In our main experiment, we define lottery-like stocks according to Kumar (2009). Therefore, idiosyncratic skewness is computed following Harvey and Siddique (2000). Idiosyncratic skewness computed according to Harvey and Siddique (2000) is under debate for not being a robust measured variable (Hou et al. 2020). Therefore, in addition, we measure idiosyncratic skewness according to Boyer et al. (2010): Skewness of regression residuals obtained from applying the Fama and French (1993) three-factor model. As before, we characterize lottery-like stocks as stocks with below median price, above median idiosyncratic volatility (\(IVol\)) and above median idiosyncratic skewness (\(ISkew3F\)).
We conduct our main experiment with idiosyncratic skewness calculated according to Boyer et al. (2010). The obtained results are not fundamentally different than those previously reported. The U-shaped quadratic relationship between the traded share of lottery-like stocks and relative past wikifolio performance is still consistently significant. Likewise, the inverse U-shaped quadratic relationship between nonlottery-like stocks and relative past wikifolio remains its significance. Finally, as before, we report a negative linear relationship between the net lottery flow and relative past wikifolio performance. When the dependent variable is based on volume, the coefficient of the variable reflecting relative performance is not statistically significant in all of the applied regression specifications. Yet, in each specification where wikifolio or trader fixed-effects are included, the coefficient is statistically significant at the per mill level.
Results from the robustness checks are not included in the paper but available upon request.
6 Conclusion
Social trading is a financial innovation which facilitates the interaction of various private investors. With regard to signal provider trading behavior, social trading platforms enable visibility and traceability. Employing the published information, platform users can copy one or several signal providers, i.e. delegate their investment decisions, and thereby become signal followers (Doering et al. 2015; Oehler et al. 2016).
Previous studies on social trading assess the performance of participants (Dorfleitner et al. 2018; Oehler et al. 2016), as well as certain behavioral phenomena like the disposition effect (Gemayel and Preda 2018a; Glaser and Risius 2018; Pelster and Hofmann 2018), herding (Gemayel and Preda 2018b), attention from peers (Pelster and Breitmayer 2019), and the establishment of trust (Wohlgemuth et al. 2016).
Social trading involves severe asymmetries regarding the distribution of economic consequences between signal providers and signal followers and thus creates a unique environment for (private) traders. When an administered portfolio performs well, the corresponding signal provider is remunerated via performance fees. Furthermore, portfolios with good past performance are placed at the top of the platforms’ selection lists and thus generate attention—the increased attention leading to higher inflows and, in consequence, a continued eligibility for remuneration (Röder and Walter 2019). On the other hand, a failing portfolio barely bears any consequences for the corresponding signal provider. In the context of social trading, Doering and Jonen (2018) argue that signal providers face convex incentives—similar to managers of hedge funds and mutual funds (Carpenter 2000)—and thus increase risk when nearing their high watermark.
We argue that the asymmetries and incentives created by social trading may induce signal providers to buy stocks exhibiting a lottery-like return structure (Kumar 2009). Analyzing a comprehensive dataset from a popular social trading platform, we provide empirical evidence that signal providers tend to increase the traded relative share of lottery-like stocks when occupying a position at one of the ends of the relative performance spectrum. Furthermore, in line with research on tournament incentives (Kirchler et al. 2018), we provide evidence that signal providers increase the net lottery flow subsequent to underperforming their peers, indicating an increased net exposure towards risk induced by lottery-like stocks.
As signal provider behavior bears severe and asymmetric consequences for signal followers, our results yield valuable implications for (potential) investors as well as the operators of social trading platforms.
Declarations
Conflict of interest
None.
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