This chapter implements an imperfect evolutionary market under the integrated individual and social learning paradigm. The imperfect evolutionary market is studied from three aspects: absorption of new challenges and creation of new knowledge; roles of individual learning in terms of its intensity; and roles of social learning in terms of its popularity. This chapter has been disseminated via the following publications: Kendall and Yan (2004, 2006).
6.1 Modelling An Incomplete Environment
The problem of modelling an imperfect environment, i.e. an incomplete environment that constantly evolves, is essentially the problem of modelling an incomplete problem space. In our simulated stock market model, described in the last chapter, the problem space of artificial traders consists of 20 market indicators. The task for artificial traders is to discover successful trading models from these 20 indicators. During a 15-year trading period, the market maintains a static problem space of 20 market indicators. This is generally not true in real world markets, where novel financial techniques and models are continually being developed. What will happen when a new market index or financial tool is introduced to the market? When a new market index is introduced, it will be experimented with and analysed by investors and analysts from the financial
markets. These people who have used the index will then tell other investors in the market what they think about the index, possibly with suggestions on how to refine the use of the index in making financial decisions. Gradually the new market index will be accepted by most of the investors if it works well with the market. If we view the market as a perfect information system, there will be no space or opportunities for new techniques to be introduced. A perfect information system will refuse to react to new challenges from its environments. Note that in information economics, imperfect information is more related to asymmetric information. In our imperfect evolutionary system, imperfect information is more related to new challenges.
Therefore, we have changed the perfect problem space of 20 market indicators in the simulated stock market model to an incomplete problem space where new challenges are introduced to artificial traders at varying times. Instead of initialising the simulated market with 20 stock indicators, we initialise the market with 10 market indicators, i.e. IND1 to IND10 in Table 6.1 below.
Technical
Indicator Description
Technical
Indicator Description
IND1 10 days Moving Average (price) IND11 14 days Relative Strength Index IND2 20 days Moving Average (price) IND12 21 days Relative Strength Index IND3 50 days Moving Average (price) IND13 Stochastic Oscillators (K%) IND4 200 days Moving Average (price) IND14 Fast Stochastics (D%)
IND5 Closing Price (normalized) IND15 Slow Stochastics (slow D%)
IND6 Rate of Change (price) IND16 Primary Market Index Rate of Change
IND7 Oscillator (price) IND17 Relative performance to Primary Market Index
IND8 10 days bias (price) IND18 Secondary Market Index Rate of Change
IND9 20 days volume Rate of Change IND19 Relative performance to Secondary Market Index IND10 10 days Relative Strength Index IND20 Third Market Index Rate of Change
TABLE 6.1 Dynamic environmental variables for an incomplete problem space. All values are normalised in the range of [0, 1] before being used as input to the neural networks. For all stocks, the Secondary Market Index refers to DJ INDU AVERAGE. For stocks from HKEx, the Primary Market Index refers to Hang Seng Index; the Third Market Index refers to NIKKEI 225 index. For stocks from TSE, the Primary Market Index refers to NIKKEI 225 index; the Third Market Index refers to Hang Seng Index.
The other 10 indicators, i.e. IND11 to IND20, are gradually introduced into the simulated stock market as new indexes every two years. Artificial traders in the imperfect evolutionary market must react to the 10 new indicators when they appear in the market and learn how to use them. For experiments on imperfect evolutionary market, we use five stocks from the Hong Kong Stock Exchange and TOKYO Stock Exchange. Indicators IND16 to IND20 are based on three major market indexes, i.e. the Dow Jones Industrial Average, the Hang Seng Index, and the NIKKEI 225, respectively.
6.2 Integrated Individual Learning and Social Learning
The market model is changed slightly to reflect more realistic account on transactions and costs:
• Every trader is given an initial portfolio of 10,000 cash and 5000 shares of a stock. A more realistic scheme used for transactions is employed compared to the either sell or buy it all scheme used in the previous chapter (Kendall and Yan 2003, 2003a). For every transaction, the amount of buying or selling is indicated by the output from the neural network, δ, in percentages as shown in Table 6.2.
δ Mapped trading decision
δ > 0.5 Buy (COH*(δ-0.5)/0.5)
-0.5 ≤ δ ≤ 0.5 Hold
δ < -0.5 Sell (SOH*(δ+0.5)/0.5)
TABLE 6.2 Mapping the outputs (δ) from the artificial neural networks to trading decisions. δ is in the range of [-1,1]. COH stands for cash_on_hold that equals to the amount of cash the trader is holding currently. Formula, COH*(δ-0.5)/0.5, gives the amount of cash the trader will use to buy the share, e.g., when δ is 0.70, the trader will use 40% of his cash to buy shares. SOH stands for share_on_hold which equals to the amount of shares the trader is holding currently. Formula, SOH*(δ+0.5)/0.5, gives the amount of shares the trader will sell, e.g., when δ is -0.70, the trader will sell 40% of the shares he holds.