An agent-based model of stock markets incorporating
momentum investors
J. R. Wei*, J. P. Huang*, and P. M. Hui**
* Department of Physics, Fudan University, Shanghai, China
** Department of Physics, The Chinese University of Hong Kong, Hong Kong, China
It has been widely accepted that there exist investors who adopt momentum strategies in real stock markets. Understanding the
momentum behavior is of both academic and practical importance. For this purpose, we propose and study a simple agent-based model of
trading incorporating momentum investors and random investors. The model is able to reproduce some of the stylized facts observed in
real markets. To illustrate how the model can be applied, we show that real market data can be used to constrain the model parameters,
which in turn provide information on the behavior of momentum investors in different markets.
I . Agent-based Model
Hyp.1: Random investors (Nr)
Hyp.2: Price change is decided by excess demand [2,3]
Sell
Market trend
Decision-making
Up
Buy
Hyp.3: Momentum investors (Nm):
Hyp.4: Action threshold λ (λ > 0) for momentum investors
Situation at time t-1
Action at time t
D[t-1]/σ > λ
Buy a unit of stock
D[t-1]/σ < -λ
Sell a unit of stock
D[t-1]/σ
<λ
Remain inactive
Table 1 How a momentum investor trade? σ=
III. Model’s application
II . Simulation & analysis
The model is used to reproduce the well-known stylized facts in real
market, such as fat-tail behavior(Fig.1), weak long-term correlation
and scaling behavior of kurtosis.
Fig.1 Left, simulated price series (Nr =100,
=3, λ =4); Right, PDF of returns.
Fig.2 Contours showing constant (left) kurtosis κ and (right) probability
Popp that two consecutive returns are of opposite signs in the α-λ space.
Nr .
Fig.3 Based on the monthly returns of
the S&P500 index between 1950 and
2011, we find κ=5.45 which gives a
constant-κ contour, while Popp=0.46
which gives a constant-Popp contour.
These two contours intersect at a point
corresponding to (α, λ) = (3.7, 2.5).
Stock market
USA
China
Hong Kong
Japan
3.7
4.2
3.8
3.8
2.5
2.7
2.6
2.9
Table 2 We have carried out similar
analysis on the China stock market,
the Hong Kong stock market and
the Japan stock market.
Our findings: (i)The similar values of λ indicate that the
momentum investors react to strong and significant volatility. (ii)
The value of α in the China market is higher than that in the
other three mature markets, suggesting that there is a better
opportunity for momentum strategies in the China market. This
is reasonable within the viewpoint of momentum behavior being
related to market inefficiency. As an emerging market, the China
market is less efficient than the other three mature markets, thus
providing more opportunities for momentum investors.
IV. Conclusions
In summary, we have proposed and studied an agent-based model of trading incorporating momentum investors,
which provides an alternative approach for studying the impacts of momentum investors on market behavior. The model gives simulated
time series of stock prices that carries some of the well-known stylized facts. Furthermore, we illustrated how real data sets could be used to
constrain the model parameters, which in turn provided information on the behavior of momentum investors in different markets.
References:
[1] J. R. Wei, J. P. Huang, and P. M. Hui, “An agent-based model of stock markets incorporating momentum investors”, Physica A 392, 2728-2735 (2013).
[2] R. Cont and J.P. Bouchaud, “Herd behavior and aggregate fluctuations in financial markets”, Macroeconomic Dynamics 4,170 (2000).
[3] J.D. Farmer, “Market force, ecology, and evolution”, Santa Fe Inst. Working Paper 98-12-117.