Market fraction hypothesis: A proposed test
Introduction
In the agent-based financial literature, the proportion of different types of trading strategies in a market can be referred to as the Market Fraction. A common observation in many agent-based financial models is that the market fraction of the trading strategy types that exist in a market keeps swinging (i.e., changing). In other words, if for instance we have two types of agents in the market (e.g., fundamentalists and chartists), it has been found that the fraction of these two types of strategies keeps changing over time. If, for example at time t 90% of the market participants adopt the fundamental strategy and 10% of them adopt the chartist strategy, these fractions change continuously over time; therefore, in a future time period, we could observe that the fundamentalists occupy only 10% of the agents, and the chartists the other 90%. This swinging feature has been observed in many agent-based financial models (Amilon, 2008, Boswijk et al., 2007, Brock and Hommes, 1998, Gilli and Winker, 2003, Kirman, 1991, Kirman, 1993, Lux, 1995, Lux, 1997, Lux, 1998, Winker and Gilli, 2001).
Based on these observations about the swinging of the market fraction, Chen (2008) and Chen, Chang, and Du (2012) suggested a new hypothesis, called the Market Fraction Hypothesis (MFH). The MFH states that there is a constant swinging among the fractions of the types of trading strategies that exist in a market. However, although the term ‘Market Fraction Hypothesis’ was introduced and used by Chen, it has never been formalized as a hypothesis. This thus motivates us to formalize the MFH, by presenting its main constituents. Formalizing the hypothesis is very important, because it allows us to suggest and formulate tests that will examine its plausibility.
Furthermore, as we mentioned, the swinging feature that the MFH describes has been observed in several agent-based models. However, all of the above models assume that the trading strategy types are static and pre-specified. By this we mean that these models endow their agents with a specific number of trading strategy types which they have to choose from. To the best of our knowledge, the MFH has not been empirically examined under a more dynamic environment in which strategies are not static and are not exogenously given. Therefore, in this paper we will present a new agent-based financial model which incorporates this more general setting and test it.
In addition, motivated by the fact that the observations about the swinging of the market fraction have so far only taken place under artificial frameworks (Chen et al., 2012), we test the MFH under empirical datasets. We run tests for 10 international markets and hence provide a general examination of the plausibility of the MFH. One goal of our empirical study is to use the MFH as a benchmark and examine how well it describes the empirical results which we observe from various markets. In particular, we are interested in knowing how this benchmark performs when we tune the key parameter, i.e., the number of types in the market. More details regarding tuning the number of trading strategies can be found in Section 7.
Therefore, the objectives of this paper can be summarized in the following way: (i) formalizing the MFH, (ii) suggesting a new agent-based financial model which does not assume pre-fixed types of trading strategies, (iii) suggesting a testing methodology for the MFH, and (iv) testing the hypothesis under empirical datasets.
The remainder of this paper is organized as follows. Section 2 formalizes the MFH by presenting its main constituents. Section 3 then presents a brief overview of the different types of agent-based financial models that exist in the literature, and also discusses their limitations. In order to address these limitations, we have created a new agent-based financial model, which is presented in Section 4. In addition, Section 4 presents the two techniques that our agent-based model uses, namely, Genetic Programming (GP) (Koza, 1992, Poli et al., 2008) and Self-Organizing Maps (SOM) (Kohonen, 1982). Furthermore, Section 5 presents the experimental designs. Section 6 addresses the methodology employed to test the MFH and explains the technical approaches needed to be taken to facilitate the testing of the MFH. Section 7 presents the test results. It first starts by presenting the results over a single run for a single dataset. Then it continues by presenting the summary results over 10 runs for this dataset and it finally presents summary results for all datasets. Section 8 concludes this paper and briefly discusses possible directions for further research.
Section snippets
The Market Fraction Hypothesis
Within a market there exist different types of trading strategies. The Market Fraction Hypothesis (MFH) says that the fraction among these types of strategies keeps changing (swinging) over time. The following two statements are the basic constituents of the MFH, and are based on a summary of the empirical development of the agent-based financial models, presented in Chen et al. (2012).
- 1.
In the short run, the fraction of different clusters of strategies keeps swinging over time, which implies a
Agent-based financial models
Agent-based financial models are models of financial markets, where artificial agents can trade with each other. According to Chen et al. (2012), these models can be divided into two basic designs: the N-type design, and the autonomous agent design. The rest of this section presents these two designs.
Model
In this section, we present our agent-based financial model. This model first allows the creation of novel, autonomous and heterogeneous agents by the use of GP. The reason for using GP is because the market is regarded as an evolutionary process; this is inspired by Andrew Lo's Adaptive Market Hypothesis (AMH) (Lo, 2004, Lo, 2005), where Lo argued that the principles of evolution (i.e., competition, adaptation, and natural selection) can be applied to financial interactions. Thus, agents can
Experimental designs
The experiments were conducted for a period of 17 years (1991–2007) and the data were taken from the daily closing prices of 10 international market indices. These 10 indices are the CAC 40 (France), DJIA (USA), FTSE 100 (UK), HSI (Hong Kong), NASDAQ (USA), NIKEI 225 (Japan), NYSE (USA), S&P 500 (USA), STI (Singapore) and the TAIEX (Taiwan). For each of these indices, we run each experiment 10 times. To make it easier for the reader, we will first present the testing methodology and results for
Testing methodology
After having presented the necessary tools and the experimental designs, we can now proceed to present the testing methodology. Our methodology consists of three parts: GP, SOM and the time-invariant SOM.
Let us start with GP. As we have already seen, we have used GP in order to generate and evolve trading strategies. However, there is a problem with comparing trading strategies from different periods. This happens because we cannot compare the fitness function of a trading strategy (GDT) from
Results
This section presents the results of our tests. We ran two tests, one per each Statement of the MFH (see Section 2). Therefore, Test 1 investigates the plausibility of Statement 1, and Test 2 investigates the plausibility of Statement 2. In the following sections, we present the results of these tests first for a single run of a single dataset, TAIEX, then for 10 runs of TAIEX, and finally, for 10 runs of all 10 indices.
Conclusion
To summarize, this paper has presented the Market Fraction Hypothesis (MFH), which states that the market fraction of the types of trading strategies that exist in a financial market changes over time. However, this hypothesis had never been formalized in the past. Our first contribution was thus to formalize the hypothesis. This then allowed us to suggest a testing methodology and test the statements of the hypothesis under 10 financial markets. The latter was very important, because until now
Acknowledgments
An early version of this paper was presented at the Econophysics Colloquium 2010, Academia Sinica, Taipei, Taiwan, November 4–7, 2010. The authors benefited significantly from the discussions with conference participants. This version has been substantially revised in light of two anonymous referees' very painstaking reviews, for which we are most grateful. The Taiwan NSC grant 98-2410-H-004-045-MY3 and EPSRC grant EP/P563361/01 are also gratefully acknowledged.
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