mental traders become more risk averse, then even in the no cost case, moving average traders can survive in the market and affect the price by their actions.
We set a equal to 4 and study the local dynamical behavior when varying the exponential moving average parameter µ. To observe a change in the dynamical behavior for the parameter µ we double the parameter λ to 14 basis points and we decrease the intensity of choice parameter β to 125. Figure 6.5a shows the bifurcation diagram with respect to µ, if µ is varied between 0.04 and 0.98. Figure 6.5b shows the corresponding largest LCE plot. Remember that by increasing the parameter µ the moving average follows the price series more closely and generates earlier a trading signal when the directional trend in prices changes direction. From the bifurcation diagram and the LCE plot it can be seen that the fundamental steady state becomes locally stable if the technical traders use a very fast moving average (µ>0.82), that is if the technical traders quickly change their trading position if the directional trend in prices changes direction. For lower values of µ the LCE plot is close to zero and thus the dynamical system exhibits quasi periodic behavior.
Price simulations
Figures 6.6a, b, c and d show, given the parameter values in section 6.6.2, the time series plots of the price, return, fraction of fundamental traders and trading volume. The price series plot shows that there is a slow movement away from the fundamental value and a quick movement back. In figure 6.6a price starts below the fundamental value of 1000 and slowly increases with a declining positive return, or stated differently, the price sequence is concave. As price is increasing further and further above the fundamental value of 1000, the fundamental traders go short a larger fraction of their wealth, causing volume to increase as can be seen in figure 6.6d. The fraction of fundamental traders starts below 0.50 and is slowly increasing until the point that stock returns become smaller than the risk-free interest rate. Then the moving average forecasting rule is not profitable anymore and the fraction of fundamental traders increases sharply until approximately 0.56. These fundamental traders cause the price to turn back in the direction of the fundamental value. This change in trend is picked up by the moving average traders and they reinforce the downtrend by holding also short positions in the risky asset. Because as well the fundamental traders as the moving average traders are expecting price to decline, price falls quickly back to the fundamental value in a convex way. However, because the moving average traders are doing better than the fundamental traders, the fraction of fundamental traders declines sharply. Thus, the fundamentalists change the direction of the trend, but the chartists push prices back to the fundamental value. Because a
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