Asset Pricing Under Endogenous Expectations in an Artificial Stock Market

Abstract

We propose a theory of asset pricing based on heterogeneous agents who continually adapt their expectations to the market that these expectations aggregatively create. And we explore the implications of this theory computationally using our Santa Fe artificial stock market.Asset markets, we argue, have a recursive nature in that agents' expectations are formed on the basis of their anticipations of other agents' expectations, which precludes expectations being formed by deductive means. Instead traders continually hypothesize-continually explore-expectational models, buy or sell on the basis of those that perform best, and confirm or discard these according to their performance.Thus individual beliefs or expectations become endogenous to the market, and constantly compete within an ecology of others' beliefs or expectations. The ecology of beliefs co-evolves over time.Computer experiments with this endogenous-expectations market explain one of the more striking puzzles in finance: that market traders often believe in such concepts as technical trading, "market psychology, " and bandwagon effects, while academic theorists believe in market efficiency and a lack of speculative opportunities. Both views, we show, are correct, but within different regimes. Within a regime where investors explore alternative expectational models at a low rate, the market settles into the rationalexpectations equilibrium of the efficient-market literature. Within a regime where the rate of exploration of alternative expectations is higher, the market self-organizes into a complex pattern. It acquires a rich psychology, technical trading emerges, temporary bubbles and crashes occur, and asset prices and trading volume show statistical features-in particular, GARCH behavior-characteristic of actual market data.

Genetic Programming in Statistical Arbitrage

“…Instead of using a fixed block size, it varies probabilistically according to a geometric distribution. 2 Thus, sampling with replacement is performed from the holdings, and statistics are gathered from 500 bootstrap runs. The 99% upper confidence limits are 16.1% and 17.7% for the single and dual tree method, respectively.…”

“…In order to make some general inferences, we consider an aggregation or bagging of the evolved trading strategies in the following. 5 Table 1 contains the test 2 With the probability parameter p = 0.01, blocks with an expected length of 100 samples are generated. 3 For the interested reader, the benchmark of an equally weighted portfolio of the banking stocks in excess of the risk free rate obtains an annualized return of 4.47% and has a Sharpe Ratio of 0.35 in the out-of-sample period.…”

“…This leads to an "infinite regress in subjectivity", where no agent irrespective of reasoning powers, can form expectations by deductive means, thus perfect rationality is not well-defined. Instead, investors are forced to hypothesize expectational models, where the only means of verification is to observe the models' performance in practice [2]. In such a world it is indeed sensible to develop expectational models beyond traditional equilibrium analysis which we seek to accomplish using genetic programming (GP).…”

Co-evolutionary Agent Self-Organization for City Traffic Congestion Modeling

“…Holland [14] proposed the use of learning classifier systems to represent the agents for an artificial stock market [2], which started the research on agentbased computational economics (ACE), e.g. [14,2].…”

Agent Based Model of Livestock Movements

“…The ABM approach is grounded in complex systems science and can be used to model non-linear systems such as those found in social and biological systems. For example, ABM techniques have been used in the development of models for the study of financial markets [1, 2,11].…”