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Journal of Economic Interaction and Coordination

Erschienen in:

08.03.2017 | Regular Article

Revisiting the issue of survivability and market efficiency with the Santa Fe Artificial Stock Market

verfasst von: Chueh-Yung Tsao, Ya-Chi Huang

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 3/2018

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Abstract

The relevance of risk preference and forecasting accuracy for investor survival has recently been the focus of a series of theoretical and simulation studies. At one extreme, it has been proven that risk preference can be entirely irrelevant (Sandroni in Econometrica 68:1303–1341, 2000; Blume and Easley in Econometrica 74(4):929–966, 2006). However, the agent-based computational approach indicates that risk preference matters and can be more relevant for survivability than forecasting accuracy (Chen and Huang in Advances in natural computation, Springer, Berlin, 2005; J Econ Behav Organ 67(3):702–717, 2008; Huang in J Econ Interact Coord, 2015). Chen and Huang (Inf Sci 177(5):1222–1229, 2007, 2008) further explained that it is the saving behavior of traders that determines their survivability. However, institutional investors do not have to consider saving decisions that are the most influential investors in modern financial markets. Additionally, traders in the above series of theoretical and simulation studies have learned to forecast the stochastic process that determines which asset will pay dividends, not the market prices and dividends. To relate the research on survivability to issues with respect to the efficient markets hypothesis, it is better to endow agents with the ability to forecast market prices and dividends. With the Santa Fe Artificial Stock Market, where traders do not have to consider saving decisions and can learn to forecast both asset prices and dividends, we revisit the issue of survivability and market efficiency. We find that the main finding of Chen and Huang (2008) that risk preference is much more relevant for survivability than forecasting accuracy still holds for a wide range of market conditions but can fail when the baseline dividend becomes very small. Moreover, the advantage of traders who are less averse to risk is revealed in the market where saving decisions are not taken into account. Finally, Huang’s (2015) argument regarding the degree of market inefficiency is confirmed.

Vorheriger Artikel Artificial stock markets with different maturity levels: simulation of information asymmetry and herd behavior using agent-based and network models

Nächster Artikel The creative response and the endogenous dynamics of pecuniary knowledge externalities: an agent based simulation model

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Chen and Huang (2005) find that traders with RRA coefficients close to 0 suffer from extremely unstable saving behavior, which causes their wealth to evaporate. Chen and Huang (2007) indicate that agents with higher RRAs will end up with greater wealth shares, which results from their higher saving rates. Chen and Huang (2008) find that, among their seven types of agents, the log-utility agents with a constant RRA of one exhibited the most stable saving behavior, and hence, they ultimately dominated the market.

The description of the SFASM can also be found in Arthur et al. (1997), Ehrentreich (2003, 2006), Huang and Tsao (2017), Joshi et al. (2000), LeBaron et al. (1999), and LeBaron (2002, 2006).

The formation of agent i’s expectations at time $t,E_{i,t} ({p_{t+1} +d_{t+1}})$ and $\hat{{\sigma }}_{i,t,p+d}^2 $, will be specified in Sect. 2.2, and the former will be a function of $p_t $ when agent i’s desired holding $X_{i,t} $ is passed to the specialist. $X_{i,t} $ of Eq. (3) is therefore also a function of $p_t $.

Excess demand or supply within 0.1 is allowed by the price-clearing mechanism.

Agent i’s wealth is updated as $W_{i,t} =X_{i,t-1} \left( {p_t +d_t} \right) +\left( {W_{i,t-1} -p_{t-1} \cdot X_{i,t-1}} \right) \left( {1+r} \right) $.

The weighted average of the squared forecast error of agent i’s predictor j activated at time $t-1$, $v_{t,i,j}^2 $, is calculated as $v_{t,i,j}^2 =(1-\frac{1}{\theta })v_{t-1,i,j}^2 +\frac{1}{\theta }\left[ {\left( {p_t +d_t} \right) -E_{i,t-1} \left( {p_t +d_t} \right) } \right] ^{2}$.

Bits 11 and 12 are two useless bits in the form of an always on bit and an always off bit. These are intended to be zero information bits. They were compared with the others by the researchers who built the SFASM to assess if the number of rules using the real information was larger than that using the useless information.

Therefore, a rule’s fitness is negatively related to its weighted average of squared forecast error and the number of non-ignored bits. This penalizing rule specificity is to ensure that each bit is actually serving a useful purpose in terms of a forecasting rule. Moreover, to calculate the fitness of initial rules, a dividend history of 500 periods before formal trading is generated following Eq. (1), and an associated history of fundamental prices is generated.

It is operated by drawing a value s from the uniform distribution U(0,1). If $\hbox {s}<0.9$, a new predictor is generated by mutation and by crossover otherwise.

With probability 0.03, each bit in the string undergoes the following changes. $0 \rightarrow $ # with probability 2/3. $1 \rightarrow $ # with probability 2/3. # $\rightarrow 0$ with probability 1/3. Other changes are as expected, i.e., $0\rightarrow 1$ with probability 1/3. On average, this preserves the “specificity”, or fraction, of #’s of a rule (LeBaron et al. 1999).

More details can be found in Appendix A of Arthur et al. (1997).

LeBaron et al. (1999) solve for a homogeneous linear REE by conjecturing a linear function mapping the current state into a price

$$\begin{aligned} p_t =fd_t+e. \end{aligned}$$

The authors find that $f=\frac{\rho }{1+r-\rho }, e=\frac{\bar{{d}}\left( {f+1} \right) \left( {1-\rho } \right) -\lambda \sigma _{p+d}^2}{r} $. According to the parameter values in Table 2, $f=6.3333$ and $e=16.688$.

The explanations can be found in Huang and Tsao (2017).

The average correlation coefficient over all the runs between the lifetime-averaged forecasting error and the final wealth is −0.013, for which the absolute value is also much smaller than that of the average correlation coefficient between the ARA coefficient and the final wealth.

We also compute the average holding shares for 10 types of agents with different ARA. For each single run, we take an average of holding shares in all periods for each agent. Then, the lifetime average holding share for each agent is further averaged over three agents of each type to obtain 10 amounts of average holding shares for 10 types of agents with different ARA. The average holding shares over all runs, each of which is obtained by further averaging over the entire 50 simulation runs, of agents with ARA coefficients 0.01, 0.3, 0.7, 1.0, 1.3, 1.7, 2.0, 2.3, 2.7 and 3.0 are 8.93229, 0.44321, 0.21670, 0.14870, 0.10626, 0.04116, 0.03459, 0.02949, 0.02485, and 0.02275, respectively. This result clearly indicates that agents with lower ARA hold more shares on average.

Additionally, refer to Eq. (3) and Footnote 5.

From Eq. (3) and Footnote 5, more risk-averse agents seem to be able to gain advantages if the risk-free interest rate is large enough. However, it is not very likely to observe interest rates higher than 10%. Therefore, we stress that in a “normal” interest rate range, the previous result that risk preference is much more relevant for survivability than forecasting accuracy holds.

We find that the average standard deviation of asset prices over all runs from the original experiment is 5.98, which is higher than that from the control experiment, 4.20. Violent price fluctuations in the original experiment may also hurt the efficiency of the market.

On one hand, many studies, such as De Long et al. (1990), have proposed that the expected returns of those who are courageous in investing are higher. On the other hand, many papers, such as Chen and Huang (2007) and Brandouy et al. (2012), have suggested that traders with higher RRA coefficients will end up with more wealth.

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Titel: Revisiting the issue of survivability and market efficiency with the Santa Fe Artificial Stock Market
verfasst von: Chueh-Yung Tsao
Ya-Chi Huang
Publikationsdatum: 08.03.2017
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Economic Interaction and Coordination / Ausgabe 3/2018
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-017-0192-5

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