Uncertainty, Fear and Herding Behavior: Evidence from Size-Ranked Portfolios

Abstract

This study is aimed at testing the relationship between investors’ uncertainty reflected by market sentiment and herding behavior phenomenon. Using data for 1990–2019 for size-ranked portfolios, the evidence documented here indicates that herding is strongly related to market sentiment as captured by the CBOE’s Volatility Index, the VIX. The results indicate that the VIX, which is also recognized as the fear index, has a substantial impact on herding across all groups and subgroups of size-ranked portfolios. Overall, the effect of VIX exists in most of the quantiles of the cross-sectional absolute deviation distribution. In this context, the scale and magnitude of the fear index impact rises toward the highest parts of the herding distribution. We also show that herding behavior is more pronounced when the market is overwhelmed by sentiment. The findings have several practical implications for investment professionals such as portfolio managers, investment officers, analysts, and other market participants. They also provide academic insights for researchers dealing with market efficiency and investors’ behavior.

Keywords:

• Investor sentiment
• Herding
• Size ranked portfolios
• Market efficiency
• Behavioral finance
• Uncertainty

Notes

1 http://www.cboe.com/. The VIX is computed as follows: ${\mathrm{\sigma }}^2=\frac{2}{T}\sum _i\frac{{\Delta K}_i}{K_i^2}{e}^{RT}Q\left(K_i\right)-\frac{1}{T}{\left[\frac{F}{K_0}-1\right]}^2$ where the VIX= σ × 100 is calculated by using the formula on two consecutive months of option data. T denotes time to expiration. F is the forward index level desired from the index’s option prices. K₀ is the first strike below the forward index level, F. K_i is the strike price of the i-th out-of-the-money option—a call if K_i > K₀; a put if K_i < K₀; both a put and a call if K_i = K₀. ΔK is the interval between strike prices. R represents the risk-free interest rate to expiration, and Q(Ki) is the midpoint of the bid-ask spread for each option with strike Ki.

2 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

3 According to Fama and French (1993), the size-ranked portfolios are constructed at the end of each June using the June market equity and NYSE breakpoints. The portfolios for July of year t to June of t + 1 include all stocks in the NYSE, AMEX, and NASDAQ for which market equity data for June of t are available. The returns data about size-ranked portfolios are available on a daily, monthly and annual basis.

4 In this context, we present the results of testing for serial correlation in the squared-return series using the Ljung and Box (1978) test. Following previous works in finance, we use the Q-statistic of Ljung–Box QLBk for lags k = 5 and k = 10 to control for near and far-lag serial correlations. According to the reported values of QLBk in Table 4, the null hypothesis of no serial correlation is not rejected at the 5% level for roughly all of the tested periods. These results indicate that the residual series do not exhibit conditional heteroscedasticity and that the GARCH(1,1) specification applied is an appropriate one.

5 Note that according to Bohl, Branger, and Trede (2017), such findings actually do point to herding because the true value for no herding by the null hypothesis is a positive${\gamma }_2$ value. Recently, Demirer, Leggio, and Lien (2019) also embraced this interpretation of the presence of herding if there is a negative ${\gamma }_2$ coefficient, regardless of its significance.

6 See for example, among others, the works of Chiang et al. (2013), Gębka and Wohar (2013), Babalos, and Stavroyiannis (2015), Fang, Shen, and Lee (2017), Stavroyiannis and Babalos (2017), Chong, Liu, and Zhu (2017), Bouri, Gupta, and Roubaud (2019), Stavroyiannis and Babalos (2019a, 2019b), and Babalos, and Stavroyiannis (2015).

7 We would like to thank an anonymous referee for this valuable suggestion.

8 Complete information about the values of the coefficients and the results of the estimation of the asymmetric model are available upon request.