Essays On The Specification Testing For Dynamic Asset Pricing Models

Yun, Jaeho. 2009. Essays On The Specification Testing For Dynamic Asset Pricing Models. Doctoral Dissertation, Cornell University.

This dissertation consists of three essays on the subjects of specification testing on dynamic asset pricing models. In the first essay (with Yongmiao Hong), "A Simulation Test for ContinuousTime Models", we propose a simulation method to implement Hong and Li's (2005) s transition density-based test for continuous-time models. The idea is to simulate a sequence of dynamic probability integral transforms, which is the key ingredient of Hong and Li's (2005) test. The proposed procedure is generally applicable s whether or not the transition density of a continuous-time model has a closed form and is simple and computationally inexpensive. A Monte Carlo study shows that the proposed simulation test has very similar sizes and powers to the original Hong and Li's (2005) test. Furthermore, the performance of the simulation test s is robust to the choice of the number of simulation iterations and the number of discretization steps between adjacent observations. In the second essay (with Yongmiao Hong), "A Specification Test for Stock Return Models", we propose a simulation-based specification testing method applicable to stochastic volatility models, based on Hong and Li (2005) and Johannes et al. (2008). We approximate a dynamic probability integral transform in Hong and Li's s (2005) density forecasting test, via the particle filters proposed by Johannes et al. (2008). With the proposed testing method, we conduct a comprehensive empirical study on some popular stock return models, such as the GARCH and stochastic volatility models, using the S&P 500 index returns. Our empirical analysis shows that all models are misspecified in terms of density forecast. Among models considered, however, the stochastic volatility models perform relatively well in both in- and out-of-sample. We also find that modeling the leverage effect provides a substantial improvement in the log stochastic volatility models. Our value-at-risk performance analysis results also support stochastic volatility models rather than GARCH models. In the third essay (with Yongmiao Hong), "Option Pricing and Density Forecast Performances of the Affine Jump Diffusion Models: the Role of Time-Varying Jump Risk Premia", we investigate out-of-sample option pricing and density forecast performances for the a¢ ne jump diffusion (AJD) models, using the S&P 500 stock index and the associated option contracts. In particular, we examine the role of time-varying jump risk premia in the AJD specifications. For comparison purposes, nonlinear asymmetric GARCH models are also considered. To evaluate density forecasting performances, we extend Hong and Li's (2005) specification s testing method to be applicable to the famous AJD class of models, whether or not model-implied spot volatilities are available. For either case, we develop (i) the Fourier inversion of the closed-form conditional characteristic function and (ii) the Monte Carlo integration based on the particle filters proposed by Johannes et al. (2008). Our empirical analysis shows strong evidence in favor of time-varying jump risk premia in pricing cross-sectional options over time. However, for density forecasting performances, we could not find an AJD specification that successfully reconcile the dynamics implied by both time-series and options data.

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Essays in Empirical Asset Pricing: Liquidity, Idiosyncratic risk, and the Conditional Risk-Return Relation

Dissertation

zur Erlangung des Grades eines Doktors

der Wirtschafts- und Gesellschaftswissenschaften

durch die

Rechts- und Staatswissenschaftliche Fakultät

der Rheinischen Friedrich-Wilhelms-Universität

Bonn

vorgelegt von

Stefan Koch

aus Bottrop

Bonn 2010

Introduction

What kinds of risk do systematically drive stock returns? This question has prompted vast amounts of research and is still one of the main challenges in finance. It has not only been of interest in the finance literature, but it also concerns investors across the globe. In general, investors aim at avoiding risky stocks but are keen on earning high returns. But which stocks are considered to be risky? Does a premium exist for risky stocks? High returns and low risk - do these two goals conflict with each other? The following dissertation addresses these questions empirically. Studying the German and the US stock market, we investigate the risk-return relationship and evaluate which kind of stocks yield a significant risk premium.

The first model that gave an answer to these questions was the Capital Asset Pricing Model (CAPM). The model was developed by Sharpe (1964), Lintner (1965), and Mossin (1966) in the 1960s and set the foundation for modern asset pricing theory. Its central implication is that every asset’s expected return is a linear increasing function of its market risk or market beta. According to the CAPM, the market excess return is the only systematic risk factor and the market beta, the slope of an asset return on the market excess return, embodies the systematic risk of the asset. Early empirical evidence such as that of Black et al. (1972) and Fama and MacBeth (1973) finds support for the model. However, during the 1980s and 1990s it turned out that market risk is not the only systematic risk. The so-called anomaly literature provides a large amount of evidence that the CAPM does not hold empirically and that other variables also influence stock prices. Banz (1981) documents that small firms have on average higher market risk adjusted returns than large firms in the US. This anomaly is entitled as the size effect.

Further, Rosenberg et al. (1985) and Fama and French (1992) show that stocks with a high book-to-market equity ratio outperform stocks with a low one, which is the so-called book-to-market effect. The CAPM fails to explain the size and book-to-market effect. Fama and French (1993) show that portfolios constructed to mimic risk factors related to size and book-to-market equity add substantially to the variation in stock returns explained by the market factor. For this reason, they argue in favor of a three-factor model. Besides the inclusion of the market excess return as in the CAPM, the Fama-French three-factor model considers the size and book-to-market factor. The size factor is the return of a portfolio of small firms minus the return of a portfolio of big firms. The book-to-market factor is the difference between the return of a portfolio of high book-to-market equity stocks minus the return of a portfolio of low book-to-market equity stocks. Fama and French (1993, 1995) suggest that the size and book-to-market factor mimic combinations of two underlying risk factors or state variables of special hedging concern for investors. Furthermore, Fama and French (1995) argue that the book-to-market beta is a proxy for relative distress. Firms with persistently low earnings have low book-to-market equity and negative slopes on the book-to-market factor. Fama and French (1996) find that the three-factor model absorbs most of the anomalies that have plagued the CAPM. Since its inception, the Fama-French three-factor model has been the standard empirical asset pricing model in the finance literature. For this reason, it is used as a standard of comparison throughout this dissertation.

This dissertation pursues two main goals. The first goal is to examine the relation between risk and return and to develop an appropriate test procedure to evaluate whether significant risk premia prevail. Early tests of the risk-return relation by Lintner1 and Black et al. (1972) use a cross-sectional approach regressing mean returns for each asset on beta estimates. Fama and MacBeth (1973) introduce an alternative for estimating the risk-return relation. Instead of taking sample average returns, they regress asset returns on beta estimates for each month of the sample period. The sample mean of the slope coefficient represents the risk premium. Since its inception, the Fama-MacBeth test has been one of the standard econometric methodologies in the empirical asset pricing literature. In the first chapter of my dissertation, we question the Fama-MacBeth test and evaluate the risk-return relation by applying a conditional approach to the Fama-French model. Subsequently, we develop a procedure to test if the risk is also priced according to the conditional approach. This procedure is compared to the Fama-MacBeth test.

Second, we investigate whether other risk factors, which cannot be captured by the Fama-French factors, also influence stock returns. Although the Fama-French factors are well-established in the literature, there is some evidence that the Fama-French factors cannot explain all asset pricing effects. Jegadeesh and Titman (1993) discover that past winners earn higher returns than past losers, the so-called momentum effect. Fama and French (1996) and Grundy and Martin (2001) find that the momentum effect cannot be captured by the Fama-French factors. As a result of this anomaly, many papers also consider the momentum factor and use a four-factor model. The momentum factor has been first proposed by Carhart (1997) and is the return of a portfolio of past winners minus the return of a portfolio of past losers. There are plenty of other asset pricing variables and risk factors that have been endorsed to be helpful in explaining stock returns in the literature. For example, Chen et al. (1986) propound macroeconomic risk factors as, e.g., interest rates, inflation, and industrial production. Cochrane (1996) suggests a production factor, Jagannathan and Wang (1996) a factor for human capital, Harvey and Siddique (2000) a coskewness factor, Gervais et al. (2001) a trading volume factor, Lamont et al. (2001) a financial constraint factor, Ang et al. (2001) a downside correlation factor, Easley et al. (2002) a measure for information risk, Vassalou and Xing (2004) a measure for default risk, and Ang et al. (2006a) downside beta. This dissertation evaluates the impact of illiquidity (chapter II) and idiosyncratic risk (chapter III) on stock returns. Liquidity measures the ability to trade large quantities quickly at low costs with little price impact. Idiosyncratic or unsystematic risk is the company or industry specific risk that is uncorrelated to the systematic risk. The final goal of chapters II and III is to test whether illiquidity and idiosyncratic risk yield significant risk premia.

Chapter I.2 The first chapter challenges the widely used Fama-MacBeth test. Ac- cording to asset pricing theory, in expectation there is a positive reward for taking risks. Investors are assumed to be risk averse and demand a compensation for holding risky assets. For this reason, riskier assets should yield higher expected returns. For instance, the expected market excess return, the difference between the market return and the risk-free rate, should be positive. To be in line with theory, empirical tests should find a positive relation between risk and expected returns. However, empirical tests are based on realized returns instead of expectations and realized returns are frequently negative. During periods of negative returns, the risk-return relation should be reversed, which is neglected by the standard Fama-MacBeth procedure. In order to take this into account, we make use of a conditional approach differentiating between periods with positive risk factor realizations and negative ones to test the risk-return relation. The conditional approach follows Pettengill et al. (1995). In contrast to the existent literature, we apply the conditional approach to the Fama-French three-factor model. We condition not only on the sign of the market return, but on that of each of the three factors, and test if the book-to-market and size betas retain their explanatory power once the conditional nature of the relation between betas and return is taken into account. As predicted by theory, our results yield strong support for a positive risk-return relation when risk factor realizations are positive and a negative one when risk factor realizations are negative.

However, at this stage results are not comparable to the Fama-MacBeth test as the Fama-MacBeth approach tests if beta risk is priced. Thus, as a further contribution to the literature, we derive a test based on the conditional approach to evaluate if beta risks are priced making the two tests comparable. This test extends the approach by Freeman and Guermat (2006) to multi-factor models. Our results provide evidence that the FG test produces very similar results as the standard Fama-MacBeth test. This finding does not only hold for empirical data from the US stock market, but it is confirmed through simulations based on different return distributions. Therefore, the results of the first chapter justify the application of the Fama-MacBeth test in the next chapters of this dissertation.

In addition, our results stress the importance of the selection of test portfolios in empirical asset pricing. We detect that estimates for risk premia strongly rely on the choice of test portfolios. Results in chapters II and III confirm this finding, emphasizing the lack of robustness of asset pricing models to alternative portfolio formation.

The following two chapters study the German stock market. Although empirical asset pricing is an extensive research field, there are only a few studies dealing with the German stock market. This is mainly due to the fact that a comprehensive set of accounting data and numbers of shares outstanding is not electronically available back to the 1970s, which makes the construction of a long time-series for the book-to-market and size factors impossible. The empirical analyses of chapters II and III are based on a unique data set covering about 1000 German firms. We make use of hand collected data on the number of shares outstanding as well as accounting data from the Hoppenstedt Aktienführer allowing us to construct the size and book-to-market factor for Germany. Daily prices and trading volume are obtained from Deutsche Kapitalmarktdatenbank in Karlsruhe. The sample period runs from January 1974 to December 2006.

Chapter II.3 Numerous episodes of financial market distress have underscored the importance of the smooth functioning of markets for the stability of the financial system. These episodes have been characterized by sudden and drastic reductions in market liquidity, which have led, amongst others, to disorderly adjustments in asset prices and a sharp increase in the costs of executing transactions. For instance, in October 1987, stock markets around the world crashed. Especially, on October 19, denoted as the Black Monday, the S&P 500 plummeted by over 20% creating the greatest loss Wall Street had ever suffered on a single day. Insufficient liquidity had a significant effect on the size of the price drop. Even recent events underline the importance of liquidity in stock markets. The subprime crisis was mainly triggered by the sharp fall in housing prices in the United States. From 2007 to 2009 the crisis rapidly developed and spread into a global economic shock, causing uncertainty across financial institutions. Liquidity dried up, resulting in a number of bank failures, large reductions in the market value of equities and declines in various stock market indices.

These extreme events illustrate that a lack of liquidity in financial markets can cause a decline in asset prices. However, liquidity is not only a concept that is related to the whole market, so-called aggregate market-wide liquidity risk. It can also aim at the risk resulting from a single investment, individual stock liquidity risk. When investors face tight liquidity positions, they may be forced to convert assets into cash. This is relatively more costly and more difficult when liquidity is lower. In order to reduce costs and to avoid the risk that arises from the difficulty of buying or selling an asset, investors should prefer liquid assets. In turn, this implies that investors buying illiquid assets should be compensated by higher expected returns. In the second chapter of this dissertation, we address the question whether illiquidity is a priced risk.

Unfortunately, estimating illiquidity is not straightforward as there is hardly a single measure that captures all of its aspects. Illiquidity is a multi-dimensional concept consisting of four dimensions: trading quantity, trading speed, trading costs, and price impact. In this study, we cover all of them. Our measure for trading quantity is turnover following Datar et al. (1998). Trading speed is measured by the number of days with zero trading volume as suggested by Liu (2006). Trading costs are approximated by the limited dependent variable model as proposed by Lesmond et al. (1999) and price impact by the Amihud (2002) measure.

Although there is evidence for the US market, e.g., Amihud and Mendelson (1986), Pastor and Stambaugh (2003), Acharya and Pedersen (2005), and Liu (2006) that illiquidity is a priced risk, other papers like Mazouz et al. (2009) show that the existence of a liquidity premium outside the US seems to be unclear and requires further analysis. Instead of concentrating on one liquidity measure and one econometric approach as often done so in the literature, this chapter covers all dimensions of liquidity and applies a multitude  of different methodologies. Our results reveal that an illiquidity effect prevails. There exists a positive relation between stock returns and illiquidity. Further, we discover a significant risk premium on illiquidity independent of the measure chosen. Yet, the illiquidity premium is not consistent as it strongly relies on the selection of test portfolios. Furthermore, we analyze the link between the size of the firm and the illiquidity of the corresponding stock. Although the two concepts are correlated, we draw the conclusion that the two measures are no substitutes for each other.

Chapter III.4 The third chapter deals with a widely accepted measure of risk, volatility, the standard deviation of returns per time unit. Volatility is often used to identify how risky an investment is or as a measure of the security’s stability. In classical finance theory it is assumed that investors are risk averse and, hence, dislike high volatility. Therefore, they require a compensation for holding volatile stocks. Not only most of the empirical and theoretical asset pricing literature predicts a positive relationship between volatility and expected returns, but also many practitioners believe in the trade-off between volatility and expected returns. They share the view that high volatility must be connived in order to earn higher expected returns.

Volatility consists of two components: systematic and idiosyncratic risk. The largest component is idiosyncratic risk, which represents over 80% of the total volatility on average for single stocks. The last chapter of this dissertation investigates whether idiosyncratic volatility is a priced risk. Our results provide evidence that low idiosyncratic volatility stocks outperform high idiosyncratic volatility stocks. Further, our empirical findings do not support the positive relation between total volatility and expected returns, but show that the trade-off is negative.

Although this finding is in line with papers like Ang et al. (2006b, 2009), it stands in sharp contrast to most of the empirical and theoretical finance literature. Theoretical studies like Merton (1987), Jones and Rhodes-Kropf (2003), and Malkiel and Xu (2006) predict that investors demand a premium for holding stocks with high idiosyncratic risk. A large number of empirical papers confirm this prediction on the US market. Malkiel and Xu (2006), Spiegel and Wang (2005), and Fu (2009) provide unambiguous evidence that portfolios with higher idiosyncratic volatility earn higher average returns. In contrast to estimating idiosyncratic volatility based on daily data over the last month as done by Ang et al. (2006b, 2009), they obtain estimates for idiosyncratic risk based on monthly data. Studying the US market, Huang et al. (2010) find that the negative relation between idiosyncratic risk and returns is driven by monthly stock return reversals and, thus, disappears after controlling for past returns. Bali and Cakici (2008) detect that the negative relation vanishes for equally-weighted portfolios on the US market. In contrast to the existent literature, we construct an idiosyncratic risk factor and explicitly estimate the risk premium on the German stock market controlling for the market, size, book-to-market, and momentum factors. The results reflect the existence of a negative premium for idiosyncratic risk. The estimated factor risk premium is 10% per year after controlling for the other factors. Idiosyncratic risk is negatively significant in almost all specifications not only for the Fama-MacBeth test, but also for the GMM procedure, different test portfolios, different subperiods, and individual returns.

Motivated by the US evidence, we use equally-weighted portfolios and also control for short-term reversal. However, low idiosyncratic risk stocks still outperform high idiosyncratic risk stocks. Given these counterintuitive results, we undertake a multiplicity of new robustness checks. First of all, we evaluate the existence of a monotonic relation between expected returns and idiosyncratic risk applying the Monotonic Relation test proposed by Patton and Timmermann (2010). Further, we differentiate between upside and downside idiosyncratic volatility, apply an (E)GARCH approach, use Dimson Betas as well as different market models to estimate idiosyncratic volatility. We also change the data frequency and use monthly data. However, the puzzle still prevails.

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Behavioral Heterogeneity in Stock Prices

H. Peter Boswijk

Cars H. Hommes

Sebastiano Manzan

CeNDEF, University of Amsterdam, the Netherlands

Abstract

We estimate a dynamic asset pricing model characterized by heterogeneous boundedly rational agents. The fundamental value of the risky asset is publicly available to all agents, but they have different beliefs about the persistence of deviations of stock prices from the fundamental benchmark. An evolutionary selection mechanism based on relative past profits governs the dynamics of the fractions and switching of agents between different beliefs or forecasting strategies. A strategy attracts more agents if it performed relatively well in the recent past compared to other strategies. We estimate the model to annual US stock price data from 1871 until 2003. The estimation results support the existence of two expectation regimes. One regime can be characterized as a fundamentalists regime, because agents believe in mean reversion of stock prices toward the benchmark fundamental value. The second regime can be characterized as a chartist, trend following regime because agents expect the deviations from the fundamental to trend. The fractions of agents using the fundamentalists and trend following forecasting rules show substantial time variation and switching between predictors. The model offers an explanation for the recent stock prices run-up. Before the 90s the trend following regime was active only occasionally. However, in the late 90s the trend following regime persisted and created an extraordinary deviation of stock prices from the fundamentals. Recently, the activation of the mean reversion regime has contributed to drive stock prices back towards their fundamental valuation.

Introduction

Historical evidence indicates that stock prices fluctuate heavily compared to indicators of fundamental value. For example, the price to earnings ratio of the S&P500 was around 5 at the beginning of the 20s, but more than 25 about nine years later to fall back to about 5 again by 1933. In 1995 the price/earnings ratio of the S&P500 was close to 20, went up to more than 40 at the beginning of 2000 and then quickly declined again to about 20 by the end of 2003. Why do prices fluctuate so much compared to economic fundamentals?

 This question has been heavily debated in financial economics. At the beginning of the 80s, Shiller (1981) and LeRoy and Porter (1981) claimed that the stock market exhibits excess volatility, that is, stock price fluctuations are significantly larger than movements in underlying economic fundamentals. The debate evolved in two directions. On the one hand, supporters of rational expectations and market efficiency proposed modifications and extensions of the standard theory. In contrast, another part of the literature focused on providing further empirical evidence against the efficiency of stock prices and behavioral models to explain these phenomena. The debate has recently been revived by the extraordinary surge of stock prices in the late 90s. The internet sector was the main driving force behind the unprecedented increase in market valuations. Ofek and Richardson (2002, 2003) estimated that in 1999 the average price-earnings ratio for internet stocks was more than 600.

A recent overview of rational explanations based on economic fundamentals for the increase in stock prices in the late 90s is e.g. given by Heaton and Lucas (1999). They offer three reasons for the decrease of the equity premium, i.e. the difference between expected returns on the market portfolio of risky stocks and riskless bonds. A first reason is the observed increase of households’ participation in the stock market. This implies spreading of equity risk among a larger population, which could explain a decrease of the risk premium required by investors. Secondly, there is evidence that investors hold more diversified portfolios compared to the past. In the 70s a large majority of investors concentrated their equity holdings on one or two stocks. More recently households have invested a large proportion of their wealth in mutual funds achieving a much better diversification of risk. Both facts justify a decrease of the required risk premium by investors. Although the wider participation seems unlikely to play an important role in the surge of stock prices in the 90s, the increased portfolio diversification could at least partly account for the decrease in the equity premium and the unprecedented increase in market valuations. A third, fundamental explanation for the surge of the stock market that has been proposed is a shift in corporate practice from paying dividends to repurchasing shares as an alternative measure to distribute cash to shareholders. In this case dividends do not measure appropriately the profitability of the asset and such a shift in corporate practice explains, at least partly, an increase in price-earnings or price-dividend ratios or equivalently a decrease of the risk premium. Further evidence on this issue is provided by Fama and French (2001).

Some recent papers attempt a quantitative evaluation of the decrease in the equity premium. Fama and French (2002) argue that, based on average dividend growth, the real risk premium has significantly decreased from 4.17% in the period 1872-1950 to 2.5% after 1950. Jagannathan, McGrattan, and Scherbina (2000) go even further and, comparing the equity yield to a long-term bonds yield, reach the conclusion that the risk premium from 1970 onwards was approximately 0.7%. That is, investors require almost the same return to invest in stocks and in 20 years government bonds. The explanations above indicate structural, fundamental reasons for a long-horizon tendency of the risk premium to decrease, or equivalently for an increase of the valuation of the aggregate stock market. However, to quantify the decrease in the equity premium is difficult and the estimates provided earlier are questionable. Although fundamental reasons may partly explain an increase of stock prices, the dramatic movements e.g. in the nineties are hard to interpret as an adjustment of stock prices toward a new fundamental value.

Another strand of recent literature has provided empirical evidence on market inefficiencies and proposed a behavioral explanation. Hirshleifer (2001) and Barberis and Thaler (2003) contain extensive surveys of behavioral finance and empirical results both for the cross-section of returns and for the aggregate stock market. Much attention has been paid to the continuation of short-term returns and their reversal in the long-run. This was documented both for the cross-section of returns by de Bondt and Thaler (1985), and Jegadeesh and Titman (1993) and for the aggregate market by Cutler, Poterba, and Summers (1991). At short run horizons of 6-12 months, past winners outperform past losers, whereas at longer horizons of e.g. 3-5 years, past losers outperform past winners.

A behavioral explanation of this phenomenon is that at horizons from 3 months to a year, investors underreact to news about fundamentals of a company or the economy. They slowly adjust their valuations to incorporate the news and create positive serial correlation in returns. However, in the adjustment process they drive prices too far from what is warranted by the fundamental news. This shows up in returns as negative correlation at longer horizons. Several behavioral models have been developed to explain the empirical evidence. Barberis, Shleifer, and Vishny (1998), henceforth BSV, assume that agents are affected by psychological biases in forming expectations about future cash flows. BSV consider a model with a representative risk-neutral investor in which the true earnings process is a random walk, but investors believe that earnings are generated by one of two regimes, a mean-reverting regime and a trend regime. When confronted with positive fundamental news investors are too conservative in extrapolating the appropriate implication for the immediate asset valuation. However, they overreact to a stream of positive fundamental news because they interpret it as representative of a new regime of higher growth.

The model is able to replicate the empirical observation of continuation and reversal of stock returns. Another behavioral model that aims at explaining the same stylized facts is Daniel, Hirshleifer, and Subrahmanyam (1998), henceforth DHS. Their model stresses the importance of biases in the interpretation of private information. DHS assume that investors are overconfident and overestimate the precision of the private signal they receive about the asset pay-off. The overconfidence increases if the private signal is confirmed by public information, but decreases slowly if the private signal contrasts with public in- formation. The model of BSV assumes that all information is public and that investors misinterpret fundamental news. In contrast, DHS emphasize overconfidence concerning private information compared to what is warranted by the public signal. These models aim to explain the continuation and reversal in the cross-section of returns. However, as suggested by Barberis and Thaler (2003), both models are also suitable to explain the aggregate market dynamics.

In this paper we consider an asset pricing model with behavioral heterogeneity and estimate the model using yearly S&P 500 data from 1871 to 2003. The model is a reformu- lation, in terms of price-to-cash flow ratios, of the asset pricing model with heterogeneous beliefs introduced by Brock and Hommes (1997, 1998). Agents are boundedly rational and have heterogeneous beliefs about future pay-offs of a risky asset. Beliefs about future cash flows are homogeneous and correct, but agents disagree on the speed the asset price will mean-revert back towards its fundamental value. A key feature of the model is the endogenous, evolutionary selection of beliefs or expectation rules based upon their relative past performance, as proposed by Brock and Hommes (1997). The estimation of our model on yearly S&P 500 data suggests that behavioral heterogeneity is significant and that there are two different regimes, a “mean reversion” regime and a “trend following” regime. To each regime, there corresponds a different (class of) investor types: fundamentalists and trend followers. These two investor types co-exist and their fractions show considerable fluctuations over time. The mean-reversion regime corresponds to the situation when the market is dominated by fundamentalists, who recognize a mispricing of the asset and expect the stock price to move back towards its fundamental value. The other trend following regime represents a situation when the market is dominated by trend followers, expecting continuation of say good news in the (near) future and expect positive stock returns. Before the 90s, the trend regime is activated only occasionally and never persisted for more than two consecutive years. However, in the late 90s the fraction of investors believing in a trend increased close to one and persisted for a number of years. The prediction of an explosive growth of the stock market by trend followers was confirmed by annual returns of more than 20% for four consecutive years. These high realized yearly returns convinced many investors to also adopt the trend following belief thus reinforcing an unprecedented deviation of stock prices from their fundamental value.

The outline of the paper is as follows. Section I discusses some closely related literature. Section II describes the asset pricing model with heterogeneous beliefs and endogenous switching, while Section III presents the estimation results. Section IV discusses empirical implications of our model, in particular the impulse response to a permanent positive shock to the fundamental and a simulation based prediction of how likely or unlikely high valuation ratios are in the future. Finally, Section V concludes.

Corresponding author: Sebastiano Manzan, Center for Nonlinear Dynamics in Economics and Finance (CeNDEF), Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, NL-1018 WB Amsterdam, The Netherlands; e-mail: s.manzan@uva.nl, webpage: http://www.fee.uva.nl/cendef/.

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