Nonlinear dynamics in stock market returns: an empirical study of
Taiwan stock market
Wu-Jen Chuang1
Wen-Chen Lo 2
1
Associated Professor, Graduate Institute of Money, Banking and Finance, Tamkang University,
Taiwan, R.O.C.
2
Instructor, Department of Information Management, St. John’s University, Taiwan, R.O.C
Graduate Institute of Management Science, Tamkang University, Taiwan, R.O.C
Abstract
Recent empirical research reports that nonlinear dynamics is present in asset returns
because of noise traders involved in the market. This study examines whether there
exits any nonlinear dynamics resulting from the irrational investing behaviors in
Taiwan stock market. We employ a smooth transition regime switching model to
capture the movements of Taiwan stock market returns. The nonlinear dynamics of
the stock market differ between large and small returns. Multiple thresholds of regime
transition exist due to positive and negative asset returns. The transition variable
causing the regime change reveals the influence of the irrational investing behaviors.
These results suggest that nonlinear dynamics exists in Taiwan stock market due to
the irrational investors’ beliefs.
Key words: Stock market returns, Behavioral finance
1. Introduction
Stock prices are believed to reflect sensitive to the relevant economic news. Based
upon the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT),
stock market returns can be predicted by many financial and macroeconomic
variables and investors can reward excess returns by taking systematic risks, but not
earn extra premium by bearing diversifiable risk1. In multifactor asset pricing models,
any variables that affects the future investment opportunity set or the level of
consumption (given wealth) could be a priced factor in equilibrium (Merton, 1973 ;
Breeden, 1979).
However, no satisfactory theory can argue that the relation between financial
market and macroeconomy is entirely in one direction (Chen, Roll and Ross, 1986). A
1
CAPM is proposed by William Sharpe (1964) and John Lintner (1965). The CAPM states that the
only systematic risk can be priced and that the expected return of a asset is equal to risk-free rate plus a
risk premium multiplied by the asset’s systematic risk. Ross (1976) develops the APT which implies
that there are multiple risk factors that need to be taken into account when calculating asset returns.
number of increasing empirical evidences challenge the EMH and APT. First,
theoretically investors are thought rationality under EMH. More and more results
show that investors are not rational all the time and that irrational investment behavior
has influences on the price formation of securities. Hence, investor psychology
provides an alternative view for the investors’ irrational decisions. For example, De
Long et al(1990) propose a model to show that investors’ irrational beliefs have
influences on price formation of assets. They point out that the irrational beliefs
would drive the stock prices further away from the fundamental values, so the
deviations of stock prices become more extreme. The process above causes another
source of risk, named as “noise trader risk”, assumed to be market-wide and having
influence on the stock market. Moreover, Lee, Jiang and Indro(2002) employ a
GARCH-M model to show that the conditional volatility and excess returns are
affected by investor sentiment.
Second, the EMH and APT are both linear models in asset returns. However, recent
studies emphasize the models which asset returns are characterized by non-linear
dynamics (Abhyanker, Copeland and Wong ,1997). Leung, Daouk and Chen (2000)
predict the international stock returns by neural network methods. Perez-Quiros and
Timmermann(2000) examine U.S. stock market by a Markov switching model and
McMillan (2001) employs the threshold model to predict U.S. stocks returns.
To sum up, inconsistent with market efficiency reflects irrational investor
behavior and APT does not imply that stock returns are a linear function of multiple
economic factors. Hence, this study try to examine whether there exits any nonlinear
dynamics resulting from the irrational investing behaviors in Taiwan stock market by
employing a smooth transition regime switching model to capture the movements of
Taiwan stock market returns.
2. Literatures Review
In capital market, only general economic variables have influence on the pricing
of stock market. Ross (1976) concludes that macroeconomic variables can affect the
real investment opportunities, firms’ cash flows, and the risk-adjusted discounted rates.
Hence macroeconomic variables can influence the stock prices. Many literatures have
documented that aggregate stock returns are related to economic factors. For example,
stock returns are negatively related to inflation and to money growth (Bodie,1976;
Fama,1981, Geske and Roll,1983; Pearce and Roley,1983,1985). Moreover, Chen,
Roll, and Ross (1986) report another five factors: the monthly growth rate of
Industrial Production, Expected Inflation, Unexpected Inflation, a bond Default Risk
Premium, and a Term Structure Spread. They conclude that industrial production and
risk premium are good risk factors and that inflation shows weaker evidence. Lamont
(2000) also concludes that the growth rates of Industrial Production, Consumption,
and Labor Income earn abnormal positive returns, but the CPI does not. Cutler,
Porterba, and Summers (1989) find that Industrial Production growth is significantly
positively correlated with real stock returns over the period 1926-1986, but not in the
1946-1985 subperiod, which overlaps the sample period (1958-1984) of Chen, Roll,
and Ross (1986).
Although, many literatures support that macroeconomic variables are priced
factors of stock returns. However, Cutler, Porterba, and Summers (1989) do not show
that Inflation, Money Supply, and long-term Interest Rates affect stock returns.
McQueen and Roley(1993) state that macro factors do not support significant
evidence with stock returns because the constant-coefficient models show poor
explanatory power. They suggest that a given announcement surprise may have
different implications at different points in the business cycle. Moreover, Ferson and
Harvey (1991) argue that such poor predictability on stock returns is not due to
market inefficient, but due to poor explanatory power of macroeconomic variables.
Many empirical studies find nonmacroeconomic factors can affect stocks returns
and also provide evidence to support irrational investor behavior. Basu (1977) shows
the price earning ratio (P/E) anomaly: stocks with extremely low P/E ratios earn
larger risk-adjusted returns than those with high P/E ratios. The anomaly can be
resulted from irrational investor behavior. Investors are excessively pessimistic about
stocks after a series of bad earnings. Once the future earnings turn out to be better, the
prices of stocks with extremely low P/E ratios adjust much more than those of stocks
with extremely high P/E ratios.
Moreover, Fama and French (1992) conclude that size and market to book ratios
do a good job explaining the cross-section of average stock returns. The high market
to book ratio also reflects that investors are overconfident about the future
profitability of companies with past good performance. Hence, the prices of
good-performance stocks go up and diverge away from the fundamental values.
Consequently, the stocks with high market to book ratios earn lower returns because
of investors’ overvaluation. To conclude, some noneconomic factors, such as the P/E
ratio, market to book ratio and dividend yield, can represent as irrational investor
behavior. And hence, we put them into the model to predict stock returns.
Furthermore, many increasing studies emphasize that financial market is
characterized by non-linear dynamics and non-linear models of stock returns can
capture investor’ irrational behavior. MaMillan (2001, 2003,2005) employ
smooth-transition threshold models to examine non-linear relationship of priced
factors and index returns, such as: UK, CAC, Nikki, DAX and so on. The
smooth-transaction model (Chan and Tong, 1986; Teräsvirta and Anderson,1992;
Granger and Teräsvirta, 1993; Teräsvirta, 1994) can capture two types of asymmetric
adjustment. First, the smooth-transition threshold model can capture investors’
different reactions during the bull and bear market. Shiller (2000) has shown that
the adjustment of investor sentiment is slow at the beginning of the market cycle.
When stock prices keep on rising, investor sentiment will be buoyed. However, when
the speculative bubble happens, the initial decline in stock prices discourages
investors. As investors reduce their holdings, stock prices decline further. If the
downward correction process continues, investors feel extremely pessimistic. Prices
are also declining until at a certain point where the downward correction stops. Hence,
the investors’ beliefs during the whole stock market cycle seem to be non-linear
relations with market returns. The smooth-transition threshold model is suitable to
estimate such non-linear relationship.
Secondly, the smooth-transition threshold model suggests different dynamics
exist different regimes. Such the model can capture more violate of investors’
behavior when stock returns are far away the intrinsic values and gradual movement
of investors’ beliefs when the returns show slow mean reversion.
To conclude, in order to examine whether irrational investors’ behavior has
impacts on stock returns, we employ the smooth-transition threshold model to capture
the non-linear relations.
3. The Model and Data
This study examines a potential non-linear relationship between Taiwan stock
market returns and economic variables by the smooth-transition threshold model.
Based upon the CAPM and APT, only undiversifiable risk factors can affect the price
formation of market returns. We choose some macroeconomics as section 2
mentioned to predict the market returns, such as the money growth, inflation, the
growth rate of industrial production, and the term structure spread. Moreover, we also
want to test the effects of irrational investor’ behavior on stock returns, so we add the
P/E ratio, market-to-book ratio and dividend yield as Busa(1977) and Fama and
French (1992) suggest. Furthermore, we find a proxy for investor sentiment. Lee and
Swaminathan (2000) show that investor expectations affect not only the return but
also the trading activity of the stock. They point out that past turnover can also be
used as a proxy for measuring the fluctuations in investor sentiment. Thus, the change
of trading volume can represent the movement in the investor sentiment.
The model is as follows:
P
Rt = a0+
 ai Z t 1 + (θ0+
i 1
P
  i Z t 1 )F (rt-d) +εt
i 1
(1)
Where Zt are the money growth, inflation, the growth rate of industrial production, the
term structure spread, P/E ratio, market-to-book ratio ,dividend yield and investor
sentiment index. Rt is stock market returns. F (rt-d) is the transition function.
4. Expected Results
First, we want to check which type of smooth-transition threshold models is
suitable for Taiwan stock market. LSTR? ESTR? QLSTR? Secondly, we expect
multiple thresholds of regime transition exist due to positive and negative asset
returns. Finally, we expect the transition variable causing the regime changes reveals
the influence of irrational investing behavior. More specifically, we expect the
investor sentiment index is the transition variable and we can suggest that nonlinear
dynamics exists in Taiwan stock market due to the irrational investors’ beliefs.
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