What are the reasons that cause stock price fluctuation? What factors determine the individual stock price? The relationship between stock prices and the fundamental factors has long been the subject of both theoretical and empirical research in financial economics. Studies by Cutler, Poterba, and Summers [1], have claimed that the variation in aggregate stock price can be attributed to various types of economic news.
A standard approach to examine stock price is the present-value model; this fundamental valuation formula implies the stock price is the expected present discount value of future dividend streams.
The present-value model was first used in the stock price determination by Chow [2].
It was based on the model that stated the price of a stock at the beginning of time t was the sum of the expected discounted values of all of its future dividends. In other words, the model of Chow [2] assumed that the logarithm of the price of a stock is a linear function of the expected current log dividend and the expected rate of growth of dividends. Since future dividends were uncertain, Chow proposed to summarize by the expected level dividends and expected growth rate under adaptive expectations. The fundamental valuation formula became nonlinear function of the four parameters.
Furthermore, the empirical research of the nonlinear present-value model was widely used in financial economics since 1958. Michael [3] first used nonlinear present-value model in labor migration and urban unemployment. Michael assumed that the percentage change in the urban labor force was governed by the differential between the discounted streams of expected urban and expected rural real income. Michael and Eduardo [4] used the model for the evaluation natural resource investment projects. The model suggested that the cash flow stream was then equal to the current value of the replicating portfolio. Hamilton and Flavin [5] used the nonlinear present-value model in
Government Deficits. The research investigated whether the historical data provided a basis for expecting a violation of the present-value borrowing constraint. The results provided the proposition that in order to be able to issue interest-bearing debt, the government must promise to balance its budget in expected present-value terms. Lloyd [6] used the nonlinear present-value model to discuss the land price. This paper presented the relationship between land prices and cash rents derived from an encompassing present value framework.
Patricia [7] focused on the estimation of future profitability as the fundamental determinant of firm value. The model indicated that book value and earnings have distinct roles. The price earnings ratio (P/E) was a function of expected changes in future profitability, and the price book ratio (P/B) was a function of the expected level of future profitability. The model predicted that P/B should correlate positively with future return on book value, and that P/E should correlate positively with growth in earnings. Liu [8] used a nonlinear present-value model that allows for a time-varying expected discount rate in conjunction with a VAR process to decompose real-estate risk.
The study indicated that cash-flow risk was found to result in a weaker mean reversion process for real estate relative to stocks. Geltner [9] provided an improved present-value model, taking account of the predictability of property returns, was described and found to track or the traditional present-value model with constant expected returns. Analysis in this paper suggested that most of the changes in commercial property market values have been due to changes in expected returns, rather than changes in expected future operating cash flows.
For stock price volatility, Yuhn [10] aimed to an alternative approach based on a cointegrating regression model for the present value relation. Different from the Campbell and Shiller [11], which demonstrated a linear cointegration between stock prices and dividends, this study lied in its distinction between linear and nonlinear
cointegration. The results indicated that a linear cointegration was not appropriate for investigating stock price volatility and a non-linear representation of cointegration was developed. Duffie and Singleton [12] developed a multi-factor econometric model of the term structure of interest-rate swap yields. The model showed that the fixed payment rate of a swap, assuming that the floating rate was London Interbank Offering Rate (LIBOR), can be expressed in terms of present values of net cash flows of the swap contract discounted by a default and liquidity-adjusted instantaneous short rate. In other words, there was an adjusted short rate process that allowed us to develop a term structure model for the swap market in the same way that models have been developed for government yield curves. Kallberg and Liu [13] applied the West and Campbell–Shiller tests of the dividend pricing relation to an index of real estate investment trusts (REITs). Similar to previous research, this research suggested that, for the REIT population, dividend pricing models cannot be rejected. The present-value model was poor predictors of true prices when tested on market indexes.
Talan [14] used the nonlinear present-value model on the current account of durables consumption. Different from the previous studies, assuming that all goods were traded and that aggregate consumption decisions can be closely approximated by a random walk process, Talan extended these models by explicitly introducing durables and nontrade goods into an intertemporal model of the current account. Since forecasts derived from standard intertemporal current account (ICA) models generally failed to match the volatility of actual current accounts, Gruber [15] offered a solution to the
‘‘excess volatility’’ problem of standard ICA models by incorporating consumption habits into the standard model. The model showed that significant habit formation implies increased current account volatility, as sluggishness was introduced into the consumption adjustment process that followed income shocks. According to Hall [16], which pointed out that because stock price predicted the future state of the economy, it
predicted consumption. Yoshihiro [17] used the present-value model on the current account and stock returns. The model assumed that consumption depended on permanent income, and the empirical finding indicated that a representative agent smoothes consumption based on stock market information.
Recent stock price movements had led to a re-examination of the present-value model.
Several studies of asset pricing have challenged the views that stock price were attributed to future dividend streams. Bansal and Lundblad [18] and Bansal and Yaron [19] argued that dividends may be potentially poor instruments because dividends were often manipulated or smoothed. Shiller [20] had shown evidence that stock returns were fluctuating too much to be explained by shocks to future cash flows or plausible variations in future discount rates, argued for other sources of movement in asset prices.
Shiller [21] also claimed a change in the volatility of either future cash flows or discount rates caused a change in the volatility of stock returns in present-value models.
In addition, Shiller showed the evidence that stock market volatility cannot be explained by movements in the rational expectation of future dividends and interest rates. Hence, we believe that more than one factor drives the dynamics of cash flows. Grossman and Shiller [22] argued the variability of stock prices can be attributed to information regarding discount factors (i.e., real interest rates), which were in turn related to current and future levels of economic activity. The capital asset pricing model (CAPM) of Sharp [23] implied that the expected return on a risky asset was estimated as the risk free rate plus an expected risk premium. The CAPM implied that the risk of the market portfolio was measured by the variance of its returns, so that the risk premium for the market portfolio increased with the variance of its returns. Further, Merton [24] gave an intertemporal CAPM model which implied a linear relationship between the equity premium and the market return variance.
The empirical validity of the hypothesis of rational expectations and adaptive expectations have been studied since the 1980s. According to Muth [25], under the rational expectations, we equate the subjective expectations in the minds of the economic agents with the mathematical expectations generated by the econometric model used by the econometrician. Based on Hicks [26], under the adaptive expectations, we interpret the subjective expectation in the minds of economic agents and not as a mathematical expectation given the information used by the econometrician.
Even though Lovell [27] has shown further evidence that the validity of the rational expectation hypothesis by applying it to the present-value model. Many studies have attempted to test the present-value model under the rational expectation hypothesis and have different results from Lovell [27]. The studies of Campbell and Shiller [11], Fama and French [28], Poterba and Summers [29] and West [30] have found that the rational expectation hypothesis may have some restrictions on the present-value model. These restrictions for the rational expectation hypothesis may suggest that the data was inconsistent with the models. In spite of the skepticism of empirical validity for the rational expectations, the hypothesis of rational expectation still have much interested in financial economics in 1980s.
According to results by Chow and Kwan [31], who used the rational expectations hypothesis and the adaptive expectations hypothesis to discuss the Hong Kong stock prices, the present-value model can explain panel data of prices of individual stock and aggregate time series data on Hong Kong stock price index under the adaptive expectations hypothesis. The result indicated that an argument supporting the rational expectations hypothesis for econometric models was followed from (1) the correctness of the model, and (2) the economic agents having at least as much information as the econometrician building the model. In addition, both Campbell and Shiller [11] and Chow [32] have shown strong statistical evidence that the model is not significant under
rational expectations. The problems arisen from applying the rational expectation hypothesis may be due to the fact that the general investors have no better model to estimate the expected variables. Based on Chow [32], which has provided the strong statistical evidence to support the present-value model under adaptive expectations, we assume the variables of this model, dividends, growth rate of dividends, nominal risk-free rates and risk premiums, following the adaptive expectations hypothesis.
In contrast to the models of Chow [2], we try to build a general model which includes the variables of dividends, growth rate of dividends, nominal risk-free rates, and risk premiums. We still assume the expected dividends grow at a constant rate g, but the restriction of a constant discount rate is removed. Our model implies that the logarithm stock price is a linear function of expected log dividends, expected log rate of growth, expected log nominal risk-free rates, and expected log risk premiums under the assumption of adaptive expectation. According to Merton [24] and [33], we consider a linear relationship between risk premiums and market return variances. To examine if the present-value model is suitable for different kinds of stocks with a new approach, we will be using the individual stock of market index as well as different kinds of industry data to construct the model in our researches. Data in our models is divided into two parts. First, we use individual stock of the stock market index in Taiwan, which including TWSE Taiwan 50 Index, TWSE Taiwan Mid-Cap 100 Index, and TWSE Taiwan Dividend+ Index. Secondly, we also use individual stock of the eight major sectors in Taiwan, which including Cement & Ceramics, Foods, Plastics & Chemicals, Textiles, Electric & Machinery, Construction, Finance and Paper sectors.
The aforementioned analyses focus on two purposes: First, we try to build a general nonlinear present-value model, which consider expected level of dividends, expected rate of growth and expected discount factors. Secondly, by using different kinds of stock data, we would like to know if the present-value model built under the assumption of
adaptive expectation can explain different industries’ stock price. The remainder of the article is organized as follows. Section 2 presents the theoretical framework of individual stock prices given by Chow [2]. We present the data and the estimation result in section 3. In section 4, we compare and discuss the estimation result from four models, which one is the best model to explain the stock prices. The last section provides the conclusion for this paper.