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Empirical Economics

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29-01-2019

Investor sentiment, investor crowded-trade behavior, and limited arbitrage in the cross section of stock returns

Authors: Liyun Zhou, Chunpeng Yang

Published in: Empirical Economics | Issue 1/2020

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Abstract

We examine the interaction effects of investor sentiment, investor crowded-trade behavior, and limited arbitrage on the cross section of stock returns. This paper presents strong evidence to reveal that investor crowded-trade behavior will increase stock prices greatly (little) among stocks with positive (negative) investor sentiment; and investor sentiment will increase (not increase) stock prices among stocks with extreme seller-initiated (buyer-initiated) crowded-trade behavior. Furthermore, this paper finds that the benchmark-adjusted returns are positive among stocks with relatively positive investor sentiment and buyer-initiated crowded-trade behavior, and negative among stocks with relatively negative investor sentiment and seller-initiated crowded-trade behavior. Finally, this paper demonstrates that limited arbitrage plays more roles on stocks with pessimistic sentiment and seller-initiated crowded-trade behavior. Taken together, this paper confirms the combined effects of investor sentiment and investor crowded-trade behavior on the cross section of stock returns, and further explores the moderating effect of limited arbitrage.

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Lutz (2016) finds that the relationship between sentiment and stock returns is relatively weak during trough-to-peak episodes (sentiment expansions). Li (2015) reveals that investor sentiment leads to not only much larger fluctuations of stock prices but also much longer duration in the stock market downturn than in the stock market expansion. Akhtar et al. (2012) find that a negative market effect occurs upon the release of bad sentiment news, and there is no market reaction for the good news. Hence, the asymmetric effect of investor sentiment shows that the relation between investor sentiment and stock return is relatively weak during sentiment contractions.

Thanks for the referee’s suggestion! This paper refers to the formula (\( {\text{MOM}}_{i,j,t} = \prod\nolimits_{j = 1}^{J} {(1 + R_{i,t - j} ) - 1} \)) provided by Grundy and Martin (2001) as the proxy for the momentum factor, where \( R_{i,t - j} \) represents firm-level stock returns of the \( i \)-th firm at the \( i - j \)-th day and \( j \) are 1, 5, and 22 days, respectively. The meaning of \( {\text{Mom}}_{i,j,t} \) represents the lagged cumulative \( j \) days' returns of the \( i \)-th firm from \( i - j \)-th to \( i - 1 \)-th days. After measuring the momentum factor of sorted stock portfolios \( {\text{Mom}}_{{{\text{p}},j,t}} \), we employ the following equation to test the roles of crowded-trade behavior on stock prices: \( R_{{{\text{p}},t}} - R_{{{\text{f}},t}} = \alpha + \beta_{\text{Rmrf}}\, {\text{Rmrf}}_{t} + \beta_{\text{Smb}} \,{\text{Smb}}_{t} + \beta_{\text{Hml}}\,{\text{Hml}}_{t} + \beta_{\text{Mom}} \,{\text{Mom}}_{{{\text{p}},j,t}} + \beta_{c} \Delta C_{{{\text{p}},t}} + \varepsilon_{{{\text{p}},t}} \), where \( {\text{Mom}}_{{{\text{p}},j,t}} \) represents the average-weighted value of the momentum factors of individual stocks in the in the portfolio \( p \) at day \( t \).

Here, we employ the following equation to test the roles of investor sentiment on stock prices: \( R_{{{\text{p}},t}} - R_{{{\text{f}},t}} = \alpha + \beta_{\text{Rmrf}}\, {\text{Rmrf}}_{t} + \beta_{\text{Smb}} \,{\text{Smb}}_{t} + \beta_{\text{Hml}}\,{\text{Hml}}_{t} + \beta_{\text{Mom}} \,{\text{Mom}}_{{{\text{p}},j,t}} + \beta_{s} \Delta S_{{{\text{p}},t}} + \varepsilon_{{{\text{p}},t}} . \), where \( {\text{Mom}}_{{{\text{p}},j,t}} \) represents the average-weighted value of the momentum factors of individual stocks in the in the portfolio \( p \) at day \( t \).

Specifically, Stambaugh et al. (2015) address the idiosyncratic volatility effect in underpriced versus overpriced stocks by reporting the alphas for the three-factor model of Fama and French (1993), the five-factor model of Fama and French (2015), the four-factor mispricing-factor model on 25 value-weighted portfolios formed by mispricing measure and idiosyncratic volatility. We also employ the same way to address the roles of individual stock investor sentiment and individual stock crowded-trade behavior.

Thanks for the referee’s helpful advices.

Here, we run the regression \( R_{{{\text{p}},t}} - R_{{{\text{f}},t}} = \alpha + \beta_{\text{Rmrf}}\, {\text{Rmrf}}_{t} { + }\beta_{\text{Smb}} \,{\text{Smb}}_{t} { + } \beta_{\text{Hml}}\,{\text{Hml}}_{t} { + } \beta_{c} \Delta C_{{{\text{p}},t}} { + } \beta_{\text{ill}}\, {\text{ill}}_{{{\text{p}},t}} + \varepsilon_{{{\text{p}},t}} \), where \( {\text{ill}}_{{{\text{p}},t}} \) is the price impact of portfolio \( p \) at day \( t \).

Here, we run the regression \( R_{{{\text{p}},t}} - R_{{{\text{f}},t}} = \alpha + \beta_{\text{Rmrf}}\, {\text{Rmrf}}_{t} + \beta_{\text{Smb}} \,{\text{Smb}}_{t} + \beta_{\text{Hml}}\,{\text{Hml}}_{t} + \beta_{s} \Delta S_{p,t} + \beta_{\text{ill}} \Delta {\text{ill}}_{{{\text{p}},t}} + \varepsilon_{{{\text{p}},t}} \), where \( {\text{ill}}_{{{\text{p}},t}} \) is the price impact of portfolio \( p \) at day \( t \).

Here, we run the regression \( R_{i,t} - R_{{{\text{f}},t}} = \alpha + \beta_{\text{Rmrf}}\, {\text{Rmrf}}_{t} + \beta_{\text{Smb}} \,{\text{Smb}}_{t} + \beta_{\text{Hml}}\,{\text{Hml}}_{t} + \beta_{\text{ill}} \Delta {\text{ill}}_{{{\text{p}},t}} + \varepsilon_{i,t} \), where \( {\text{ill}}_{p,t} \) is the price impact of portfolio \( p \) at day \( t \).

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Title: Investor sentiment, investor crowded-trade behavior, and limited arbitrage in the cross section of stock returns
Authors: Liyun Zhou
Chunpeng Yang
Publication date: 29-01-2019
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 1/2020
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-019-01630-7

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