Does herding affect volatility? Implications for the Spanish stock market

Abstract

According to rational expectation models, uninformed or liquidity trading make market price volatility rise. This paper sets out to analyse the impact of herding, which may be interpreted as one of the components of uninformed trading, on the volatility of the Spanish stock market. Herding is examined at the intraday level, considered the most reliable sampling frequency for detecting this type of investor behavior, and measured using the Patterson and Sharma (Working Paper, University of Michigan–Dearborn, 2006) herding intensity measure. Different volatility measures (historical, realized and implied) are employed. The results confirm that herding has a direct linear impact on volatility for all of the volatility measures considered, although the corresponding intensity is not always the same. In fact, herding variables seem to be useful in volatility forecasting and therefore in decision making when volatility is considered a key factor.

Keywords:

• Herding
• Capital markets
• Behavioral finance
• Volatility

Acknowledgements

The authors are grateful to the anonymous referees and editors for their helpful comments and suggestions with respect to the first version of our paper. NB and SF wish to acknowledge the financial support of the Spanish Ministry of Education and Science (SEJ2006-14809-C03-03/ECON), the Spanish Ministry of Science and Innovation (ECO2009-12819-C03-02), ERDF funds, the Caja de Ahorros de la Inmaculada (Europe XXI Programme) and the Government of Aragon. PC is grateful for the financial support of the Spanish Ministry of Education and Science (SEJ2006-14809-C03-01), the Spanish Ministry of Science and Innovation (ECO2009-12819-C03-01), ERDF funds and the Government of Navarra.

Notes

† For further information on the relationship between uninformed investors and volatility, see also Black (1976), De Long et al (1990) and Campbell and Kyle (1993).

† We use in this paper those implied volatilities offered by the MEFF. However, we previously computed the implied volatilities for the period 1997–1998 by numerical simulation inverting the Black–Scholes model. We carried out the analysis with these data and the results do not change significantly when compared with those obtained using the implied volatilities available from the MEFF.

‡ Under the null hypothesis that stock prices follow a random walk reacting quickly and completely to the arrival of new information and if there is no discernible pattern in the information arrival process, then the probability assignable to each type of price sequence should be the same. However, given that stock markets may reflect other tendencies or phenomena than herd behaviour that may influence such probability, as shown by the results of Blasco et al. (2010a), we have selected a sample of stocks that do not present any evidence of herd effects and we have calculated the probability of upwards/downwards and zero-tick price sequences. In the Spanish market, upwards and downwards sequences occur with a 30% probability for each. Zero-tick sequences occur over our time horizon with a 40% probability. In this paper we use the case of p_i  = 1/3, given that the significance and the conclusions do not change significantly because of the high herding intensity (the use of the alternative probabilities only implies a 10% reduction in the absolute value of the H statistics).

† A trade is classed as a buy if the price is higher (an up-tick) than the most recent previous trade, and as a sell if the price is lower (a down-tick) than the most recent previous trade. If the price is the same as the most recent previous trade, the trade is classed as a zero-tick.

‡ There are different means to identify a transaction as a buy or a sell. Finucane (2000) demonstrates how this method yields similar results to others. This, together with the unavailability of a database that included the bid–ask spread, led us to opt for the tick test to categorise trades.

§ In order to see whether there is any link between the herding statistic and the return dispersion measures suggested in the literature, we calculate the correlation coefficients between variations in the H values and the corresponding variations in the cross-sectional standard deviation proposed by Christie and Huang (1995). We find a positive correlation, as expected, of 12%. We also observe that upwards or downwards variations of these measures agree in around 60% of cases.

¶ A preliminary analysis of the complete Spanish stock market produced evidence that, although the financial assets not included in the Ibex35 showed negative H values, no significant values of the herding measure could be found. That is why only those assets belonging to the index are considered in this paper.

† The t-statistic for the null hypothesis of no mean difference between small and large capitalization stocks is 90.28 for H_a , 89.49 for H_b and 69.12 for H_c . This lends weight to the idea that firm size may influence the herd behaviour of agents.

‡ Blasco et al. (2009) offer further details for the characterization of the herding effect in all stocks in the Spanish market.

† The authors additionally carry out an additional test for detecting ‘leader brokers’ in the Spanish market with the aim of empirically corroborating the arguments in favour of the presence of herd behaviour. They find a small number of brokers who very often initiate the transaction sequences either as buyers or sellers, the rest of the brokers being considered as followers.

† For further information on realized volatility, see French et al. (1987), Schwert (1989) and Ferland and Lalancette (2006).

‡ Bandi and Russell (2008) obtain optimal intervals for the calculation of realized volatility and show errors for 5-minute intervals to be approximately equal to those of the optimal interval, where the 5-minute interval is the one used to calculate realized volatility in the majority of empirical studies. We were forced by the lack of superior data to use 15-minute intervals to calculate this measure of volatility. Nevertheless, Andersen et al. (2000) showed in an experiment that volatilities start to stabilize at 30-minute intervals. Our results can therefore be considered free of significant error, thanks to the data frequency used.

§Nevertheless, we made some previous tests using values of n = 5, 50, 250 and running a rolling procedure. The results were still significant although the coefficients rapidly decrease when n increases.

† Nevertheless, despite the observed differences across the three volume measures considered, if we focus on the adjusted R ², we find no major differences between V, NT and ATS within each volatility measure.

† There are some exceptions; certain types of herding do not impact significantly on volatility captured by ∣ε _AA|, σ _R-AC, σ _R-AA and σ _GK.

†Data have been extracted from the data base SABI (Sistema de Análisis y Balances Ibéricos) and BankScope and refer to the significant ownership information that was notified to the Spanish stock market national commission (CNMV) in 2003. Prior data are not available. The CNMV is aimed at supervising and inspecting the Spanish stock markets and the activities of all the participants in the market.

‡ Nonetheless they are available from the authors upon request.

§ The linear and nonlinear analysis has been repeated adding to the volatility model the leverage effect (throughout the asset's returns). The results are similar to those presented here and are available from the authors upon request.