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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Economic Dynamics and Control, Volume 31, Issue 6, June 2007, Pages 1910–1937
We study the relationship between liquidity and prices in an artificial financial market where portfolio traders with limited resources interact through a continuous, electronic open book. We depart from the standard asset pricing framework in two ways. First, we assume that investors have incomplete information about the distribution of returns. Second, we model the portfolio choice problem using prospect-type preferences. We model the utility function in terms of deviations of the portfolio growth rate from a specified target growth rate, and we assume that investors are more sensitive to downside movements. We show that the parameters defining the learning process affect the price dynamics through their impact on the variability of the market liquidity.
In the last years, there has been an increasing adoption of automated systems to trade financial securities (see Domowitz and Steil, 1999 for a taxonomy of automated systems). In these settings trading occurs through an electronic order book without involving financial intermediaries. Automated systems offer advantages in terms of operating and trading costs, but they depend on public limit orders for the provision of liquidity. The time variation in liquidity can affect the evolution of prices, and complex dynamics can arise between measures of market trading activity and measures of market volatility. This topic has been addressed by Domowitz in a series of papers analyzing the market behavior of real electronic markets (e.g., Coppejans et al., 2001, Domowitz and El-Gamal, 1999 and Domowitz and Wang, 2002). In this paper, we simulate an artificial electronic market where optimizing portfolio traders with imperfect information adjust their positions over time on the basis of the new public information becoming available. The present work extends the model developed in Consiglio et al. (2005) introducing endogenous target individual portfolio holdings. In our previous paper we analyzed the impact on price changes of the trading mechanism by modeling an economy populated by agents homogeneous in terms of trading strategies. Each agent traded to reach an exogenously assigned target portfolio. We showed that the institutional setting of a double-auction market may by itself generate non-normal univariate marginal distributions of assets’ returns and temporal patterns resembling those observed in real markets (such as serial dependence in volatility and in trading volume). Moreover, we analyzed the role played by the order-type submission strategy specifying a setting where agents selected the type of order to submit using the information revealed by the state of the book. We showed that the state of the book provides an implicit coordination device inducing agents to supply liquidity when the market needs it. In this paper we introduce a scenario optimization model to determine endogenously individual portfolio allocations. That is, agents are not anymore noise traders whose trading is driven by exogenous liquidity shocks. On the contrary, here we assign cognitive abilities to the agents. Each agent, given the joint distribution of asset returns, his initial endowment, and a target wealth growth rate to reach within his investment horizon, will select the portfolio that maximizes his objective function, and, over time, will trade to reach his optimal portfolio. The main ingredients of the model are the objective function used by the agents to select the optimal portfolio, the assumption of incomplete information, and the design of the trading mechanism. We depart from the full rationality hypothesis assigning to the investors prospect-type preferences. That is, we define the investors objective function in terms of financial wealth fluctuations (Kahneman and Tversky, 1979). Additionally, we assume that agents do not know the stochastic process driving the fundamentals and they must learn recursively the unknown data generating process. We operationalize the idea of structural uncertainty allowing agents to hold arbitrary priors about the univariate marginal distribution of returns, and we make agents update correctly those distributions using past realized returns. We assume that agents share a constant common view of the assets’ association structure, and that they correctly apply a copula function to generate the joint distribution of returns to be used to determine the optimal portfolio allocations. The copula-approach allows to study separately the impact of a learning process about each single component of the multivariate distribution of returns (the univariate marginals and the association structure). This separability is particularly useful considering that in real financial markets the assets’ association structure typically appears much less volatile in the short run than the marginal distributions of returns. In this paper, we assign to the agents a relatively short investment horizon (not longer than one year), and, therefore, we restrict the learning process to the univariate marginals assuming that the assets’ dependence structure does not change and it is known by the agents. The paper is related to the recent literature trying to highlight the economic mechanisms generating typical asset-pricing anomalies such as the heavy tails of the unconditional distribution of returns, the predictability of returns, the excess volatility, and the phenomenon of volatility clustering (see Barberis, 2000, Barberis et al., 2001, Benartzi and Thaler, 1995, Bossaerts, 1999, Brennan and Xia, 2001, Guidolin and Timmermann, 2007, Lewellen and Shanken, 2002, Timmermann, 1993 and Xia, 2001. Pagan (1996) provides a survey of the empirical evidence on financial markets). The theoretical work trying to explain financial market anomalies can be divided into two different strands. On one hand, we have papers relaxing the assumption of individual rationality either through the belief-formation process or through the decision-making process. Alternatively, a growing number of papers has been focusing on exploring the consequences of relaxing the assumption of consistent (or correct) beliefs while maintaining the assumption of individual rationality. In both cases the dynamics of asset prices have been studied assuming one representative agent and/or a financial market where one single risky asset is exchanged. In this paper, we overcome both these limitations building an artificial financial market populated by heterogeneous investors who can trade several risky assets (see Hommes, 2005 for a recent survey on heterogeneous agent models). We combine the two strands of literature designing a market where agents’ heterogeneity depends on the assumption of incomplete information, and, at the same time, investors’ preferences are, more realistically, defined over financial gains and losses rather than over final absolute wealth positions. Among all the non-expected utility theories, prospect theory has been very successful at capturing the experimental results. The theory is purely descriptive and does not have normative content. Thus, theoretically, there is no correct way to combine prospect-type preferences with learning. Any ad hoc specification for the learning process can be used. We have chosen to avoid any additional element of irrationality defining an efficient learning process based on bayesian updating. The third layer of the model is the continuous double-auction trading mechanism. In this setting agents enter the market sequentially and transactions occur when two agents can match their request at a given price. Therefore, whenever an agent cannot find a matching order, or the size of the matching order is lower than the required quantity, the agent will be rationed. Rationing may have important consequences in terms of price dynamics. Prices may not adjust to fully incorporate information/shocks as expressed by the trading requests, and, therefore, they may tend to be stickier and to generate returns more concentrated around the mean. In addition, rationing may increase the probability of having sequences of traders on the same side of the market, and that in turn may imply a higher frequency of extreme price movements with respect to the average price change (see Consiglio et al., 2005; Li Calzi and Pellizzari, 2003). In this paper we focus the attention on the interactions between market liquidity and the volatility of price changes and we try to understand how those interactions are affected by the learning process. We show that the automated auction market system with learning agents generates irregular price series characterized by sharp increases and decreases (looking like bubbles and crashes). We provide evidence supporting the hypothesis that the irregularities of the price process are related to the variability of market liquidity, interpreted in terms of the ability of the system to sustain sufficient contra-side order activity. Moreover, we provide evidence supporting the hypothesis that the parameters characterizing the learning process affect significantly the evolution of market liquidity. The paper is structured as follows. Section 2 describes the market structure. Section 3 introduces the assumptions we make in terms of agents’ behavior. Section 4 presents the calibration used for our simulations and discusses the results obtained. Section 5 concludes.
نتیجه گیری انگلیسی
In this paper we have analyzed the interactions between the volatility of price changes and market liquidity using the data generated simulating an artificial electronic market populated by portfolio traders learning over time. Agents do not have structural knowledge about the economy. In particular, they do not know the joint distribution of assets’ returns, but they try to learn it using public observable market data. We assume that, starting from their priors, the investors use efficiently the available information to form their posteriors. Agents follow a common trading strategy, that is they trade to rebalance their portfolio. Agents’ preferences are defined over fluctuations in the value of the portfolio of risky assets. Agents interact through a continuous double-auction market system. In the model there is no exogenous stochastic process driving the fundamentals. Thus, the volatility of price changes is endogenously determined by the functioning of the market system: the agents’actions (that depend on their beliefs), and the rules governing the interactions between the agents’ actions. In this framework, the issue is not to study what agents get to learn, but to understand how the endogenous component of market volatility is affected by the interaction between the process through which the distribution of agents’ beliefs changes over time and the market mechanism. We have run different simulations changing the parameters governing the learning process to understand if and how those parameters may affect the volatility of price changes. We have found that the parameters defining the learning process, such as the frequency of updating and the returns’ association structure assumed by the agents, affect significantly the interrelationships among price changes, trading activity, and market liquidity. In particular, we have shown that the variable measuring the level of unbalance in the length of the queues is fundamental to explain the jumps in the volatility of price changes. The unbalances between the two sides of the book affect not only the mean but also the dispersion of the distribution of the per-transaction volatility. The parameters governing the learning process affect the intensity of the relation between the per-transaction volatility and the variables measuring the trading activity and the unbalances between the two sides of the book.