1. X Workshop on Quantitative Finance Milan, 29th January 2009 THE IMPLICATIONS OF HERDING ON VOLATILITY. THE CASE OF THE SPANISH STOCK MARKET Natividad Blasco* Pilar Corredor # Sandra Ferreruela* * Dept. of Accounting and Finance. (University of Zaragoza) # Dept. of Business Management (Public University of Navarre)

2. X Workshop on Quantitative Finance Milan, 29th January 2009 1.- Introduction ACCURATE VOLATILITY MEASUREMENT is the basis of pricing models, investment and risk management strategies. If MARKET IS EFFICIENT prices instantaneously adjust to new information  Then volatility is only caused by the adjustment of stock prices to new information But…

3. X Workshop on Quantitative Finance Milan, 29th January 2009 1.- Introduction … THERE IS EVIDENCE of price adjustments that are due not to the arrival of new information but to market conditions or collective phenomena such as herding Herding is said to be present in a market when investors opt to imitate the trading decisions of those who they consider to be better informed, rather than acting upon their own beliefs and information.

4. X Workshop on Quantitative Finance Milan, 29th January 2009 1.- Introduction The link between investor behavior and market volatility was first noted by Friedman (1953): –Irrational investor destabilize prices, rational investors move prices towards their fundamentals. Hellwig (1980) and Wang (1993) –Volatility is driven by uninformed or liquidity trading Froot et al (1992), Avramov et al (2006) –Investors imitate each other and this drives volatility Following these authors we…

5. X Workshop on Quantitative Finance Milan, 29th January 2009 1.- Introduction …we set out to assess the effect of different levels of herding intensity on the degree of market volatility. This study contributes to provide an explanation for that portion of volatility not due to changes on fundamentals or other know effects. Results  could prove highly relevant in achieving a better understanding of market functioning and serve both academics and practitioners.

6. X Workshop on Quantitative Finance Milan, 29th January 2009 2.- Dataset Sample period: Jan 1st 1997 to Dec 31st 2003 Data supplied by Spanish Sociedad de Bolsas SA Intraday data include: date, exact time, stock code, price and volume traded of ALL TRADES Ibex-35 data include: composition of the index, volume traded and number of trades, daily opening, closing, maximum and minimun prices, 15-minute price data.

7. X Workshop on Quantitative Finance Milan, 29th January 2009 2.- Dataset Database provided by MEFF (the official Spanish futures and options market) including date of trade, underlying of the contract (Ibex-35), expiration date, exercise price and volatility at the close of trading.

8. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Herding intensity measure Measure proposed by Patterson and Sharma (2006) based on the information cascade models of Bikhchandani, Hirshleifer and Welch (1992). Major advantages: –Constructed from intraday data. –It considers the market as whole rather than only a few institutional investors.

9. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Herding intensity measure An information cascade will be observed when buyer initiated or seller initiated runs last longer than would be expected if no such cascade existed S can take three different values (Ha Hb Hc)

10. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Herding intensity measure On average herding intensity is significantly negative accross all types of run. Ha Ibex35Hb Ibex35Hc Ibex35 Mean-8.8152-8.7263-4.0399 Median-8.8950-8.7773-3.9789 St. Dev.2.12772.14991.3820 Minimum-14.3633-15.5900-8.9243 Maximum-1.0853-1.54330.2202

11. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Volatility measures Absolute return residuals are obtained from the following regression: Rit is the index return i on day t, four values: –AA from opening on day t to opening on day t+1, –AC from opening to closing on day t, –CC from closing on day t-1 to closing on day t, –CA from closing on day t to opening on day t+1

12. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Volatility measures Realized volatility. Andersen et al (2001): By summing up the squares of intraday returns calculated from high frequency data we obtain an accurate volatility estimator.

13. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Volatility measures Historic volatility. –Parkinson (1980) –and Garman and Klass (1980)

14. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Volatility measures Implied volatility. Result from the inversion of the Black Scholes option pricing model. Fleming(1998), Christensen and Prabhala (1998), Corredor and Santamaría (2001, 2004) show that implied volatility is a reliable predictor of future volatility. We focus on the implied volatility of short term ATM call options on the Ibex-35.

15. X Workshop on Quantitative Finance Milan, 29th January 2009 3.- Correlation |  AA ||  AC ||  CC ||  CA | ST ATM |  AA | 1.0000 |  AC | 0.27671.0000 |  CC | 0.58610.30701.0000 |  CA | 0.24520.69860.34851.0000 0.56420.53760.46780.40611.0000 0.67640.50210.80760.44920.87941.0000 0.41770.75360.37270.55520.81670.71141.0000 0.43130.52710.34790.40390.86380.72610.89621.0000 ST ATM0.31000.31070.31370.30430.53050.49970.44900.48471.0000

16. X Workshop on Quantitative Finance Milan, 29th January 2009 4.- Volatility and herding Having obtained the volatility measures the second stage is to purge them of the volume and day of the week effects documented in the literature. We run a series of regressions where the described volatility measures are made to depend on the Monday effect and a proxy for the volume (V, NT, ATS) and corrected for autocorrelation. We take the residuals of the regressions.

17. X Workshop on Quantitative Finance Milan, 29th January 2009 4.- Volatility and herding

18. X Workshop on Quantitative Finance Milan, 29th January 2009 4.- Volatility and herding Having obtained the “CLEAN” volatility series we determine the extent of the linear effect of herding on volatility on day t. We run linear regressions where the residuals of prior regressions depend on a constant and PS(2006) herding intensity measure.

19. X Workshop on Quantitative Finance Milan, 29th January 2009 4.- Volatility and herding Since there is no reason why the relationships between variables need to be exclusively linear, we test for possible non-linear causality between the different measures of volatility and the herding level. Using the procedure described in Hiemstra and Jones (1994), we find no evidence at all of non- linear causality in the results.

20. X Workshop on Quantitative Finance Milan, 29th January 2009 5.-Results -0.00000.0000-0.00010.0001 -0.0000 0.0000-0.0001 Implied -0.0006-0.0004-0.0006-0.0002-0.0000-0.0002-0.0003-0.0001-0.0003 -0.0008-0.0005-0.0007-0.0004-0.0001-0.0003-0.0005-0.0002-0.0003 -0.0008-0.0005-0.0006-0.0004-0.0001-0.0002-0.0005-0.0002-0.0003 -0.0005-0.0003-0.0005-0.00010.0000-0.0001-0.0002-0.0001-0.0002 -0.0012-0.0008 -0.0007-0.0003 -0.0008-0.0002-0.0004 |  CA | -0.0015-0.0008-0.0010-0.0014-0.0004-0.0005-0.0010-0.0004-0.0005 |  CC  -0.0013-0.0008-0.0009-0.0007-0.0003 -0.0008-0.0004 |  AC | -0.0010-0.0006-0.0007-0.0004-0.0001 -0.0006-0.0003 |  AA | HcHbHaHcHbHaHcHbHa 

21. X Workshop on Quantitative Finance Milan, 29th January 2009 5.- Results Overall, all three types of herding have a significantly negative effect on all the volatility measures except implied volatility. The results for the measures of historical and realized volatility are very similar, irrespective of which volume proxy is used, and also unanimous. –a higher level of herding (uninformed trading) leads to greater price changes (volatility) Herding affects current volatility but not expected volatility

22. X Workshop on Quantitative Finance Milan, 29th January 2009 Our results are partially consistent with prior literature. The short-term implied volatility provide new information that has not be presented in former studies. Our study contributes to the robustness and novelty of the herding literature through the number of volatility measures and types of volume considered and the explicit use of a measure of intraday herding. 5.- Results

23. X Workshop on Quantitative Finance Milan, 29th January 2009 6.-Conclusions This paper examines the way in which market volatility is affected by the presence of herding behavior. The results presented are consistent with prior literature: –the higher the observed level of herding intensity, the greater volatility we can expect to find. –This does not apply in the case of implied volatility

24. X Workshop on Quantitative Finance Milan, 29th January 2009 6.-Conclusions Herding affects current market volatility, but has no impact on expected future volatility The overall results of this paper may be useful for interpreting the concept of risk and for defining risk management strategies. The choice of a specific type of volatility measure may be relevant since estimates calculated with stock market data are “contaminated” by herding

25. X Workshop on Quantitative Finance Milan, 29th January 2009 Thanks