Explaining the statistical features of the Spanish Stock Market from the bottom-up. José A....

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

Explaining the statistical features of the Spanish Stock Market from the bottom-up.Artificial Economics 2006 Aalborg September 14-15

Outline

The InSiSoc-ASM ModelThe Ibex 35

Fundamental Investors: The Basic ModelPsychological InvestorsTechnical Investors

Conclusions

Introduction


IntroductionMainstream 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


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:


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


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.


The Basic ModelIn 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:

2dp,t,i

ft1t1tt,it,i

)r1(p)dp(Ex

where pt and dt are prices and dividends in t, E means expectations, λ is a measure of the risk aversion, and σ2 is the forecast variance.


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


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


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.


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

15BF5KT 10BF10KT 5BF15KT


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 Signalt

MA(h)

MA(l)

Sell Signal


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

15BF5TF 10BF10TF 5BF15TF


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.


ConclusionsOur 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.

Explaining the statistical features of the Spanish Stock Market from the bottom-up.

Thanks for your attendance.

José A. Pascual . [email protected]


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 periodE(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 0 0

Predictor 1 1 1 # # # No Match

Predictor 2 # 0 1 0 0 Match

101000110111000 +d ) = a(p+d)tE(p+d)t+1 = a(p+d)t+b

Explaining the statistical features of the Spanish Stock Market from the bottom-up. José A....

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