The Influence of Confidence and Social Networks on an Agent-Based Model of Stock Exchange

The aim of this paper is to investigate the influence of investors’ confidence in their portfolio holding with respect to their social group and of various social network topologies on the dynamics of an artificial stock exchange. An investor’s confidence depends on the growth rate of her wealth relative to her social group average wealth. If the investor’s confidence is low, the agent will change her asset allocation, otherwise she will maintain it. We consider three types of social networks: Barabási, small-world, and random.
It is noteworthy that the behavioral (confidence) variable plays a crucial role within the model, as it determines that the investor - whether fundamentalist, chartist or random – decides to change or not her investment strategy, once confidence changes according to the her wealth growth rate in comparison with the investor’s average wealth growth rate in her social network. The confidence is not very volatile, and enjoys a large interval of stability and, in addition, the investor only changes her strategy when her confidence value reaches below Cn, a neutral confidence index. In other words, the fundamentalist, chartist or random investor will change her strategy to a more profitable one whenever she has little confidence in her current investment strategy.
Many statistical properties of the real stock exchange data are recovered in our model: high excess kurtosis, skewness, volatility clustering, random walk prices, and stationary return rates. The incorporation of networks in conjunction with the behavioral variable sheds light on several properties that are little explored in this literature. For instance, the small-world network has the highest degree of homophily. As the investors can switch to more profitable strategies, we found that the fundamentalist strategy is prevalent only in the random network. In the other networks (Barabási and small-world), the best approach to make profitable investments is the chartist one, which is a surprising outcome, since the network models are compatible with the random walk hypothesis. We also investigated the cumulative distribution function of the absolute value of normalized returns. The exponent of the power law distribution is found close to 3, in agreement with empirical stylized facts. Also, the largest spread of social contagion occurs in the small-world network, an expected result since this network topology has the highest clustering. Finally, more unequal wealth distribution and a greater relative gain were found in the Barabási network, followed by the random network.