1. Explaining the statistical features of the Spanish Stock Market from the bottom-up. José A. Pascual, Javier Pajares, and Adolfo López. InSiSoc Group. Valladolid University. E. T. S. Ingenieros Industriales, Valladolid

2. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Outline The InSiSoc-ASM Model The Ibex 35 Fundamental Investors: The Basic Model Psychological Investors Technical Investors Conclusions Introduction

3. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Introduction Mainstream finance is grounded on strong hypothesis: –rationality of investors –markets are efficient –investors are able to form rational expectations Elegant models have been built under this framework: CAPM. APT.... Real markets exhibit some “stylized facts”, which are difficult to explain under this framework:  excess volatility,  non-normality of returns,  excess kurtosis,  volatility clusters,  unit roots, etc. Relax the strong hypothesis about the rationality and take into account : psychology, emotions, risk aversion. Etc. Intractable with traditional mathematical models; we need a bottom-up, approach

4. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The Ibex-35 We compute the statistical properties of the prices and returns series of the Ibex-35 the most relevant index in the Spanish market, as instance of real market:

5. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Autocorrelation function of returns Autocorrelations of squared returns The Ibex-35  prices and returns are far away of normality  excess kurtosis in return series (fat tails)  excess variance in price series (excess volatility)  prices series are I(1), present a unit root and the return series not  absence of autocorrelations in returns  aut. of squ. ret. remains positive significant after many periods

6. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The InSiSoc- ASM Model We have development a model grounded on the artificial stock market by LeBaron et al. (1999), (SFASM). In ISS-ASM as well as SFASM, a single risky stock is traded and it is also possible to borrow or lend money at the risk free interest rate. The amount of dividends paid by the risky stock follows an order one auto- regressive model. Prices emerge endogenously as a consequence of bids and offers.

7. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The Basic Model In a first step, we study a market populated only with BFagents who reproduce the SF-ASM results. BFAgents. Process all the relevant information and form expectations about the future price and dividend. The demand of shares for agent i at t (LeBaron (op.cit.)), is computed as: where p t and d t are prices and dividends in t, E means expectations, λ is a measure of the risk aversion, and σ 2 is the forecast variance.

8. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Autocorrelation of squared returns. Autocorrelation of returns. The Basic Model The returns’ autocorrelations are close to zero, but the squared autocorrelations are also not significant after the first low lags. Excess kurtosis of return is 0.43, very lower than the real markets. The volatility is higher in the case of the Ibex than in our market. The prices series don’t have unit roots

9. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The Basic Model For many simulations the results are quite similar. –Our market is more efficient (in the financial sense). –The “rational market” populated with BFagents has an output which is closer to the theoretical models proposed in the financial literature. –Real markets exhibits some “anomalies”. Where is the difference?, How can we model a market closer to real stock exchanges?. HETEROGENEITY AND IRRATIONALITY

10. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Psychological investors KTAgents. Psychological agents. Similar to the BF but λ can take two values: the higher one when agent´s actual wealth is lower than the average that she/he enjoyed during the previous 10 periods and the lower one otherwise. If agent´s actual wealth is higher than the average, he thinks that is richer, and a successful trader, and his risk is reduced.

11. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Psychological investors When the proportion of KT investors increases: –the kurtosis and the difference between the variance of market prices and the theoretical one also increase –the number of significant lags for the autocorrelations of squared returns increase significantly (volatility clustering) –but prices series don’t have unit roots Autocorrelation of squared returns 15BF5KT10BF10KT5BF15KT

12. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The role of technical trading TFAgents. Technical Agents. Take decisions using technical rules. Compute MA with different periods and the use the crosses between them as trading signals. t MA(h) MA(l) Buy Signal t MA(h) MA(l) Sell Signal

13. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The role of technical trading When the proportion of TF investors increases: –the prices and the excess volatility are much higher. –excess kurtosis increases, –the number of significant lags of squared autocorrelations increases but only slightly –The prices series are I(1) with a unit root. Autocorrelation of squared returns 15BF5TF10BF10TF5BF15TF

14. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Conclusions We have built an ASM populated with different kinds of agents. We have studied the statistical features of the index Ibex-35 to use it as patterns. Markets only with BFagents are more similar to the “ideal market” than to real markets. Markets with psychological and technical traders become more “real” in terms of excess kurtosis, excess volatility, significant autocorrelations of squared returns.

15. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 Conclusions Our results are preliminary and a lot of research has to be done in order to find financial explanations of our results We also have to improve the model to include more realistic agents: a wider range of behaviours patterns as described by Kahneman and Tversky for the psychological investors, more technical rules, etc.. Anyway, we conclude that agent based modelling is a powerful tool to understand some issue concerning the evolution of financial markets.

16. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Thanks for your attendance. José A. Pascual. pascual@eis.uva.es

17. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Thanks for your attendance. José A. Pascual. pascual@eis.uva.es

18. Explaining the statistical features of the Spanish Stock Market from the bottom-up. Artificial Economics 2006 Aalborg September 14-15 The Basic Model Each BF, BF2 or KT have a set of PREDICTORS Condition Part Prediction Part Lineal forecast of Price + dividend for the next period E(p (1###00110#11#0#) (a,b) A predictor is active if match with the state of the world t+1 +d)+b World State 1 0 1 00 Predictor 1 1 1 # ##No Match Predictor 2 # 0 1 00Match 101000110111000 +d) = a(p+d) t E(p+d) t+1 = a(p+d) t +b