A multi-factor model of heterogeneous traders in a dynamic stock market

Abstract

This study develops an agent-based computational stock market model in which each trader’s buying and selling decisions are endogenously determined by multiple factors: namely, firm profitability, past stock price movement, and imitation of other traders. Each trader can switch from being a buyer to a seller, and vice versa, depending on market conditions. Simulation findings imply liquidity in the stock market decreases as more traders try to behave in a similar way to other traders. Stock return volatility is increasing in memory length when the information set of a trader includes only the fundamental of stock. On the other hand, when all traders consider only the past stock price movement, stock prices undergo boom and bust cycles with the occasional no-trade states. Furthermore, when traders consider three factors equally, the stock return is characterized by more pronounced fat-tail property and lower volatility.

Keywords:

• heterogeneous trader
• memory length
• asset pricing
• agent-based stock market

AMS Subject Classifications:

• G11
• G12
• G17

Public Interest Statement

This paper builds an agent-based computational stock market model to examine how simple behavioral trading rules by agents affect the asset price dynamics. In the model, the information set of a trader includes firm profitability, past stock price movement, and investment decisions by neighboring traders. Stock market dynamics are quite different depending on what factors are employed. When all traders attempt to mimic each other, the no-trade state quickly emerges. We also find the stock return volatility varies by the memory length of a trader, the extent of use of historical stock market data. It is also shown the fat-tail property in the stock return distribution is more pronounced when traders consider three factors equally. Interestingly, when all traders only respond the past stock return, stock prices are characterized by the boom and bust cycle.

Notes

Current affiliation: Macroeconomics and Finance Research Team, Financial Supervisory Service, Address: 38 Yeoui-Daero, Youngdeungpo-Gu, Seoul, Korea.

1 The prototype of agent-based artificial stock market can be found in Arthur et al. (1997). For studies on adaptive behavior based on genetic algorithms in asset market context, see Arifovic (1996), Chen and Yeh (2001), Kluger and McBride (2011), and Arthur, LeBaron and Palmer (1999). Endogenous switching between different forecasting rules are considered in numerous models, such as Brock and Hommes (1998), Lux and Marchesi (2005), and Chiarella and He (2002).

2 The idea of network effects dates back to Keynes ’s (1936) beauty contest metaphor for stock market investment. The modeling approach adopted here does not exactly coincide with the concept of Keynes’s beauty contest. This study rather focuses on the mimicking behavior of traders, while the beauty contest emphasizes the importance of higher order belief among market participants

3 This type of modeling approach is similarly implemented in Thurner, Farmer and Geanakoplos (2009).

4 We regard knowing the fundamental price of a stock share as being incompatible with the imperfect knowledge of the actual data generating process that determines firm’s fundamental value.

5 Analyses on the indirect mimetic behavior of traders in the context of computational stock markets are found in Lux (1998) and Iori (2002). Iori (2002) develops a multi-agent stock market model under which trading decision depends on communication between traders and idiosyncratic shocks. She identifies that the imitating behavior and trading frictions are key elements of volatility clustering. Compared to Iori (2002), Lux (1998) develops a model in which mimetic behavior is implemented in a less direct sense. In this model, conversion between optimistic chartist and pessimistic chartist is stochastically executed through a global variable, i.e. an opinion index.

6 Note that all of the trader subsequent actions are conditional on this information set. The notation for an information set of a trader i will be suppressed in the following sections for notational simplicity.

7 For the extensive survey of network analyses in economic contexts, see Jackson (2008). For a brief introduction to the Small-World Network, see Watts and Strogatz (1998). For application to bilateral trading, see Wilhite (2001).

8 In other words, the coordination among agents is made only through global variables.

9 As shown in Figure , the final desired stock holding will be determined in a subsequent step.

10 As in the financial literature, the stock return is defined to exclude dividend payments. This is usually done since dividend payments are irregular. For modeling purposes, this is to capture a pure price movement impact on the demand of a trader.

11 A price increase in a risky asset leaves additional room for capital buffers, which leads to more purchases of a risky asset. For more details, see Shin (2010).

12 Although trading frictions are not explicitly modeled in this study, the introduction of a tolerance level implicitly brings a similar effect of having trading frictions prevalent in the market.

13 We checked that the presence of heterogeneity in the threshold level is a key source of market liquidity. Even when the only structural differences among traders are their tolerance levels, we observed that exchanges among traders occur.

14 For the definition of $h_i$, see Section 2.4.

15 http://www.econ.yale.edu/shiller/data.htm. Data from 1950:1-2012:12 are used.

16 A heterogeneous memory length is a very critical aspect of the asset market dynamics. For simplicity, this study does not consider heterogeneous memory length or evolutionary learning algorithms. This topic would deserve a separate future study. For interested readers , refer to LeBaron (2001a, b, 2012), and Mitra (2005).

17 Note all traders are characterized by the same specification of weights on factors for each case. Refer to Table 3.

18 As in the dividend trader case, we observed that the heterogeneity in the tolerance level solely could generate stock exchanges among traders. And it should be noted that initial conditions are identical across different cases except trading styles.

19 In a run with the dividend being zero during all periods, we found that the upward trend vanishes, and the market collapses to the no-trading state after a few periods of active exchanges.

20 The no-trade states are marked by the discontinuous portion in the figure.

21 This pricing rule is arbitrary, and the market dynamics will depend on the specific pricing rule in no-trade states. The simple pricing rule adopted in this study prevents a complete explosion or a bust in stock prices during relatively short periods in case of the stock market with technical traders

22 The no-trade state poses delicate issues which have rarely been dealt within the earlier computational stock market models. The existing asset pricing models systemically exclude the occurrence of no-trade states since it is assumed that there is always a fixed number of stock shares supplied.

23 Herd behavior may arise from either cognitive biases (e.g. availability bias) or rational responses to uncertainty. Herd behavior can easily occur because, in a highly connected society, a peer group often provides a channel for easily accessible and recallable information on which people can rely. On the other hand, the latter case is related to the notion of information cascade in which an agent follows previous actions made by other agents, ignoring his private signal (i.e. Banerjee (1992), Bikhchandani, Hirshleifer, & Welch (1992)).

24 In this simulation, the real wealth refers to individual trader’s cash balance after each trading period.

25 Note that $Avg{M}_t^r={\sum }_i^{100}{M}_{\mathit{it}}^r/100$ where $M_{\mathit{it}}^r$ is individual trader i’s real wealth in period t for the rth run.

26 $Avg{M}_t={\sum }_r^{N_r}Avg{M}_t^r/N_r$ where $N_r$ is the number of simulation runs.

27 In this context, LeBaron (2001a) delivers a counterargument against Friedman’s natural selection hypothesis by reminding us that the population of the market itself is dynamically changing. He raises the question of “who is rational” in “what sense“: “In Friedman’s world, rational traders have started off rational world. So the small infusion of irrational traders doesn’t alter the whole picture of the market. But if we start the market off in another way such as market dominated by short-memory traders, the story would be reversed."

28 The full information set consists of three distinct elements: dividend as a measure for firm profitability, past stock return movements, and imitation of neighborhood traders, all of which are shown to be important in many empirical studies. See Section 2.4 for references for the studies which shows the significance of these factors.

29 See Section 2.4 for the exact definitions of trading types.

Additional information

Funding

The author received no direct funding for this research.

Notes on contributors

Dong-Jin Pyo

Dong-Jin Pyo is a financial economist at the Financial Supervisory Service. His research interests include agent-based computational modeling of financial markets, the interactions between financial sector and the macroeconomy, and the application of big data analytics to financial markets.