3.2. Trader Types and Structure
There were 5000 traders in the model. To examine the impact of financial literacy changes on different traders, we classified all individual accounts into five categories based on account-level transaction data: (1) Retail: less than RMB 100,000; (2) Sinvestor: between RMB 100,000 and 500,000; (3) Minvestor: between RMB 500,000 and 5 million; (4) Linvestor: between RMB 5 million and 10 million; and (5) XLinvestor: larger than RMB 10 million. We also included institution accounts as a separate group, which included mutual funds, insurance companies, security firms, and pension funds (the investor structure data of Shanghai main-board (SHM Market) and Technology Innovation Board (STAR Market) were drawn from the 2019 Shanghai Stock Exchange Statistics. The investor structure data of Shenzhen main-board (SZM Market) and Second-board (SB Market) were derived from the
2019 Investor Structure and Behavior Analysis Report of Shenzhen Stock Exchange). The specific number and wealth distribution of the five categories of investors can be found in
Section 4.1, where the parameters of the model are set.
Next, we defined the portfolio wealth for each agent. Upon entering the market initially, traders received an allocation of both stock and cash. The initial stock position
for agent
was:
where
was the position of each trader equally allocated to stock
, and
followed a uniform distribution between 0.01 and 0.99.
The assumed initial cash position
for agent
was:
where
was the initial price of stock
. The optimal composition of the agent’s portfolio was determined in the usual way by trading-off expected return against expected risk. However, the agents were not allowed to engage in short selling. Specifically, when the total wealth of a trader was negative, we considered the trader to be bankrupt. At this time, a new trader would enter the market to ensure the normal operation of the agent-based model (Based on simulation data, during normal market operations, the percentage of such traders was minimal, and the augmented wealth of investors had an insignificant impact on the market. In the event of a market crash, the proportion of new traders would expand. However, the primary market driver did not lie in augmenting traders' wealth, thereby resulting in a negligible impact on the model.)
3.3. Traders Financial Literacy and Price Expectations
Financial literacy is a complex factor encompassing the information processing ability mentioned, along with various other socioeconomic or psychological abilities. It is challenging to articulate this comprehensively in both empirical and experimental research. Fortunately, in an agent-based model, we can measure an individual’s level of financial literacy by their precise control over the outcome of a particular event. For instance, in the case of negative news, investors with high financial literacy are more likely to quickly acquire information, synthesize various factors such as market sentiment, socioeconomic conditions, and personal considerations, and efficiently draw conclusions about the decline in stock prices. They can also make more accurate predictions about the extent of the decline. On the other hand, investors with low financial literacy may acquire information more slowly and arrive at conclusions with greater deviations. The process from the appearance of information to drawing conclusions involves a series of “black box” operations, including information acquisition and internal cognitive processes, which are not observable. However, in an agent-based model, we can infer from the results: investors with high financial literacy will exhibit differences in the speed and accuracy of their reactions to market information, compared with those with low financial literacy.
In accordance with Chiarella et al. (2017) [
22], the demand for the risky asset by each trader was assumed to comprise three components: a fundamentalist component, a chartist component, and a noise-induced component. However, rather than simply using statistical data as parameters, we incorporated each investor’s financial literacy to reflect the proportions of their investment behavior attributable to fundamentalist, chartist and noise-induced components. Furthermore, the fundamental value of stocks in the market was not transparent or fixed, but rather varied among individuals and changed with time and various events. The level of financial literacy reflects investors’ abilities to obtain information and process events, thereby affecting their estimation of the fundamental value of stocks and their sensitivity to changes in fundamental value.
At any time,
, a trader was chosen to enter the market. The chosen agent,
, formed an expectation about the stock return,
, where
represents the agent’s time horizon. Agents utilized a blend of fundamental value and chartist rules to shape expectations regarding stock returns, resulting in:
where the quantities
and
represent the weights given to the chartist and fundamentalist components, respectively. For normalization purposes, we assumed that
= 1.
We assumed that
and
where
is the financial literacy of agent
, and
represents the conversion strength of investor financial literacy. Barber and Odean (2000) [
23] indicated that investors with a high level of financial literacy are more inclined to make investment decisions by thoroughly analyzing fundamental factors such as a company’s financial statements and industry prospects. They are also more likely to opt for long-term stock holdings rather than frequent trading. The study also indicated that 20% of trades are noise trading and are hazardous. Therefore, the
was set as 80% in our model. Equation (3) also means that if an investor is completely lacking in financial literacy, i.e.,
(which will not happen in most cases), they will be completely unable to access useful financial news or events, or obtain price information from such news or events. Therefore, they would have no choice but to be a pure momentum-based trader, relying solely on the historical price trend to make their stock price predictions with a maximum proportion of noise-induced component of 0.2. In another extreme case, i.e., when
, the investor would have full information of the market and would be able to immediately perceive the fundamental changes in the value of a stock and accurately determine its value. In this case, the trader would still have speculative motives (
), which means they would also engage in momentum trading and profit from price fluctuations.
also indicates that the higher the financial literacy of agent
,
, the smaller the proportion of chartist components the agent will have, while there is a diminishing marginal benefit to improving financial literacy. The variable
, featuring a zero mean and variance
to agent’s expectations, signifies the noisy beliefs of investors.
indicates the anticipated future trend of the chartist component derived from observations of spot returns over the last
time steps. In other words,
where
is the short-term average price of stock
, and
is the long-term average price of stock
.
represents the trader’s predicted return on stock
j based on fundamental beliefs, that is,
where
is the price of stock
at time
. The variable
represents the time scale over which the fundamentalist component calculates the mean reversion of the price to the fundamental.
is the fundamental value of stock
predicted by agent
, that is,
where
is the real fundamental value of stock
at time
. Equation (6) means that the higher the financial literacy, the less the agents will be influenced by historical price trends, and their predictions will be closer to the real fundamental value of stocks.
It is common to assume that the time horizon of an agent depends on its characteristics. Fundamentalist strategies are typically given much greater weight by long term institutional investors who have longer time horizons, whilst day traders have shorter time horizons and give more weight to chartist rules. Hence, we chose the time horizon
of each agent according to:
We assumed that each trader arrived to the market according to a Poisson process with parameter and traded continuously.
The future price,
, expected at time
by agent
was given by:
3.4. Order Submission Rules
Traders trade only when their expected order profit from trading is high enough to offset the transaction cost. In a dynamic equilibrium model of an order driven market with asymmetric information, Foucault et al. (2016) [
24] showed that informed traders submit both market orders and limit orders, depending on whether their information advantage is above or below a cutoff value. Gil-Bazo and Ruiz-Verdú (2009) [
25] introduced similar order submission rules, being that traders submit market orders when the price deviations from their forecasting fundamental value are large, and limit orders when the deviations are small. Depending on traders’ forecasting and order book states, traders submit either limit or market orders. We introduced similar order submission rules. When trader
arrived in the market at time
, within the time period
, they assessed their expected price
against the current best bid
and best ask
factoring in the transaction cost
, where
was the midpoint of the optimal bid and ask quotes. Depending on the current order book, following Sornette and Zhou (2006) [
26], we considered four scenarios that aligned with the characteristics of the order book in the Chinese A-share market, summarized in
Table 1. In the first scenario, where there was at least one ask and one bid in the current limit order book, the trader placed a market order to buy if their expected price
was above the sum of the best ask
and the transaction cost
, i.e.,
. Conversely, if their expected price
was below the best bid
minus the transaction cost
, i.e.,
, they placed a market order to sell. In case of
, the trader submitted a limit buy order. For
, they submitted a limit sell order, depending on whether their expected price
was above or below the current
. The rules for order submission in the other three cases were defined in a similar manner.