Chaotic behavior in national stock market indices: New evidence from the close returns test

Attempts have been made to detect chaotic behaviour in financial markets data using techniques which require large, clean data sets. Although such data are common in the physical sciences where these tests were developed, financial returns data typically do not conform. The close returns test is a recent innovation in the literature and is better suited to testing for chaos in financial markets. This paper tests for the presence of chaos in a wide range of major national stock market indices using the close returns test. The results indicate that the data are not chaotic, although considerable nonlinearities are present. The commonly used BDS test is also applied to the data and, in comparison, the close returns test provides substantially more evidence of nonlinearity compared to the BDS test.     

The Determinants of Conditional Autocorrelation in Stock Returns

We investigate whether return volatility, trading volume, return asymmetry, business cycles, and day‐of‐the‐week are potential determinants of conditional autocorrelation in stock returns. Our primary focus is on the role of feedback trading and the interplay of return volatility. We present empirical evidence using conditional autocorrelation estimates generated from multivariate generalized autoregressive conditional heteroskedasticity (M‐GARCH) models for individual U.S. stock and index data. In addition to return volatility, we find that trading volume and market returns are important in explaining the time‐varying patterns of return autocorrelation.     

Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

The Random Walk Hypothesis in the Emerging Indian Stock Market

This paper examines the random walk hypothesis in the emerging Indian stock market using daily data on individual stocks. The statistical evidence in this paper rejects the random walk hypothesis. The results suggest that daily returns earned by individual stocks and by an equally weighted portfolio show significant non–linear dependence and persistent volatility effects. The non–linear dependence takes the form of ARCH–type conditional heteroskedasticity and does not appear to be caused by nonstationarity of underlying economic variables. Though conditional volatility is time varying, it does not explain expected returns.     

Accounting Ratios and the Cross‐section of Expected Stock Returns

Under clean‐surplus accounting, the log return on a stock can be decomposed into a linear function of the contemporaneous log return on equity, the contemporaneous log dividend–price ratio (if the stock pays a dividend), and both the contemporaneous and lagged values of the log book‐to‐market equity ratio. This paper studies the implications of this decomposition for the cross‐section of conditional expected stock returns. The empirical analysis reveals that the log accounting ratios capture cross‐sectional variation in both the conditional mean and conditional variance of log stock returns, which is consistent with the decomposition. It also brings fresh insights to the relation between firm size (market equity) and conditional expected stock returns. The evidence indicates that the conditional median return increases with firm size, while the conditional return skewness decreases with firm size. Empirically, the skewness effect outweighs the median effect, leading to the well‐documented inverse relation between size and average returns. The results of out‐of‐sample tests suggest that investors could use the information provided by the observed values of the log accounting ratios to formulate more effective portfolio strategies.     

Deterministic nonlinearity in the stock returns of major European equity markets and the United States

By using recently developed statistical tools designed to overcome some of the limitations often associated with financial data, this study attempts to detect low-dimensional deterministic chaos in five major European stock markets and the United States. Country indexes exhibiting low-dimensional deterministic chaos may contain some informational inefficiency; thus, it may be possible to use nonlinear dynamics to predict future stock returns. The results do not provide evidence of the existence of low-dimensional chaotic systems in any of the examined indexes. As such, the notion of market efficiency in the examined indexes is not threatened by the findings of this study.     

Evaluating the Forecast Accuracy of Emerging Market Stock Returns

This paper analyzes the forecast performance of emerging market stock returns using standard autoregressive moving average (ARMA) and more elaborated autoregressive conditional heteroskedasticity (ARCH) models. Our results indicate that the ARMA and ARCH specifications generally outperform random walk models. Models that allow for asymmetric shocks to volatility are better for in-sample estimation (threshold autoregressive conditional heteroskedasticity for daily returns and exponential generalized autoregressive conditional heteroskedasticity for longer periods), and ARMA models are better for out-of-sample forecasts. The results are valid using both U. S. dollar and domestic currencies. Overall, the forecast errors of each Latin American market can be explained by the forecasts of other Latin American markets and Asian markets. The forecast errors of each Asian market can be explained by the forecasts of other Asian markets, but not by Latin American markets. Our predictability results are economically significant and may be useful for portfolio managers to enter or leave the market.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

NONLINEAR DYNAMICS AND THE DISTRIBUTION OF DAILY STOCK INDEX RETURNS

Three alternative models of daily stock index returns are considered: (1) a diffusion-jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non-nested tests between the diffusion-jump process and a GARCH(1.1) process with t-distributed errors reject the diffusion-jump process, but do not always reject the GARCH process. Kolmogorov-Smirnov tests of fit, however, reject the GARCH(1,1)-t process for all cases. Nonlinear dependence is not removed for the value-weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.     

Asset Pricing at the Millennium

This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the trade-off between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor (SDF) that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance.     

Heteroskedasticity in Stock Returns

We use predictions of aggregate stock return variances from daily data to estimate time-varying monthly variances for size-ranked portfolios. We propose and estimate a single factor model of heteroskedasticity for portfolio returns. This model implies time-varying betas. Implications of heteroskedasticity and time-varying betas for tests of the capital asset pricing model (CAPM) are then documented. Accounting for heteroskedasticity increases the evidence that risk-adjusted returns are related to firm size. We also estimate a constant correlation model. Portfolio volatilities predicted by this model are similar to those predicted by more complex multivariate generalized-autoregressive-conditional-heteroskedasticity (GARCH) procedures.     

Effects of Price of Gold on Bombay Stock Exchange Sectoral Indices: New Evidence for Portfolio Risk Management

Using daily data, this paper examines the relationship between the returns of gold and seven sectoral indices in the Bombay Stock Exchange (BSE) for the period from January 2000 to May 2018. Given the importance of gold in India, there are significant issues in a portfolio selection in that country. By addressing the hedged robust portfolio problems, this paper focuses on three vanilla portfolio problems: the maximum return portfolio allocation, the global minimum variance portfolio problem, and the Markowitz portfolio allocation by using various multiple generalized autoregressive conditional heteroskedasticity (GARCH) models. The paper finds that gold returns are significantly independent of the returns of the BSE sectoral indices. Besides, gold returns can help predict the future returns of the Consumer Durables and the Fast-Moving Consumer Goods indices as well as the Oil & Gas equity indices. Finally, the findings also show that gold hedges against the information technology stock index and serves as a robust portfolio diversification tool. With these new results, this paper offers several implications for investors and risk management purposes.     

Non-linear Dependence in Stock Returns: Does Trading Frequency Matter?

The UK has a quote-driven pure dealer market structure that is very different from order driven markets such as the NYSE and Japanese markets. This paper investigates non-linear dependence in stock returns for an exhaustive sample of UK stocks for a 21 year period. The results are analysed on the basis of trading frequency. It is found that non-linear dependence is highly significant in all cases for both individual stocks and stock portfolios formed on the basis of trading frequency. The non-linear dependence is primarily over a one day interval, although statistically significant non-linear dependence exists consistently even up to five trading days. Most of the non-linear dependence is in the form of ARCH-type conditional heteroskedasticity. However, statistically significant non-linearity in addition to an EGARCH(1,1) dependence also appears to be present. This additional non-linearity is greater for individual stocks than for portfolios and greater for smaller, less-liquid portfolios. Non-linear dependence does not appear to be caused by non-stationarity in underlying economic fundamentals or by non-linearity in the conditional mean. However, low dimensional chaos is not generally supported. The limited evidence on chaotic behaviour is stronger for portfolios with long price adjustment delays across component stocks. The main results are consistent with US studies on stock indices, suggesting that the process generating non-linear dependence is not dependent on market microstructure characteristics.     

Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market

The Markowitz portfolio optimization model, popularly known as the Mean-Variance model, assumes that stockreturns follow normal distribution. But when stock returns do not follow normal distribution, this model wouldbe inadequate as it would prescribe sub-optimal portfolios. Stock market literature often deliberates that stock returns are non-normal. In such context the Markowitz model would not be sufficient to estimate the portfolio risks. The purpose of this paper is to expand the original Markowitz portfolio theory (mean-variance) via adding the higher order moments like skewness (third moment about the mean) and kurtosis (fourth moment about the mean) in the return characteristics. The research paper investigates the impact of including higher moments using multi-objective programming model for portfolio stock selection and optimization. The empirical results indicate that the inclusion of higher moments had a considerable impact in estimating the returns behavior of portfolios. The portfolios optimized using all the four moments, generated higher returns for the given level of risk in comparison to the returns of the Markowitz model during the study period 2000–2011. The results of this study would be immensely useful to fund managers, portfolio managers and investors as it would help them in understanding the Indian stock market behavior better and also in selecting alternative portfolio selection models.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

An examination of nonlinear dependence in exchange rates,using recent methods from chaos theory

Interest in the relevance of nonlinear dynamics to finance and economics has spurred the evolution of new ways to analyze time series data. Tests for chaos, based on a metric approach which measures spatial correlations, led to the development of the correlation dimension test for chaos and the BDS test for nonlinearity. More recently, a topological method has been introduced into the scientific literature which employs a simple qualitative test for chaos that is adaptable to the characteristics of financial data. A quantitative version is also presented here. Conflicting evidence exists about the presence of chaotic behavior in exchange-rate data. The qualitative topological test does not support evidence of a chaotic generating mechanism in these series. The quantitative form finds nonlinear dependence and is a useful diagnostic to determine the adequacy of ARCH-type models for this nonlinear structure.     

Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach

To analyze the intertemporal interaction between the stock andbond market returns, we assume that the conditional covariancematrix follows a multivariate GARCH process. We allow for asymmetriceffects in conditional variances and covariances. Using dailydata, we find strong evidence of conditional heteroskedasticityin the covariance between stock and bond market returns. Theresults indicate that not only variances, but also covariancesrespond asymmetrically to return shocks. Bad news in the stockand bond market is typically followed by a higher conditionalcovariance than good news. Cross asymmetries, that is, asymmetriesfollowed from shocks of opposite signs, appear to be importantas well. Covariances between stock and bond returns tend tobe relatively low after bad news in the stock market and goodnews in the bond market. A financial application of our modelshows that optimal portfolio shares can be substantially affectedby asymmetries in covariances. Moreover, our results show sizablegains due to asymmetric volatility timing.     

Emerging Markets and Stock Market Bubbles: Nonlinear Speculation?

Daily returns of stock markets in emerging markets in Asia, Africa, South America, and Eastern Europe from the early 1990s through 2006 are analyzed for the possible presence of nonlinear speculative bubbles. The absence of these is tested for by studying residuals of vector autoregressive-based fundamentals, using the Hamilton regimeswitching model and the rescaled range analysis of Hurst. For the first test, absence of bubbles is rejected for twenty-four countries (except Mexico, Sri Lanka, and Taiwan); for the second test, it is rejected for twenty-six countries (except Malaysia). BDS testing on these residuals after autoregressive conditional heteroskedasticity (ARCH) effects are removed fails to reject further nonlinearity (except for Israel). Policy issues are discussed, noting that what is appropriate varies from country to country and time period to time period.     

ARE LONG-HORIZON STOCK RETURNS PREDICTABLE? A BOOTSTRAP ANALYSIS

This paper examines empirical evidence of predictability of long-horizon real and excess stock returns in the UK using univariate as well as multivariate Variance Ratio tests. In order to estimate the sampling distribution of the test statistics, artificial histories ofstock returns are generated from their empirical distribution using the bootstrap method. This allows the construction of significance levels of the test statistic which are free from distributional assumptions. The empirical results indicate that there is no evidence of mean reversion in stock prices even if a wider information set to forecast stock returns is used and that the significance of historical Variance Ratio statistics has been overstated by previous studies.     

EXCESS RETURNS AND RISK AT THE LONG END OF THE TREASURY MARKET: AN EGARCH-M APPROACH

In this paper we model weekly excess returns of ten-year Treasury notes and long-term Treasury bonds from 1968 through 1993 using an exponential generalized autoregressive conditional heteroskedasticity in mean (EGARCH-M) approach. The results indicate the presence of conditional heteroskedasticity and a strong tendency for the ex-ante volatility of excess returns to increase more following negative excess return innovations compared with positive innovations of equal magnitude. In addition, increases in ex-ante volatility are associated in some subperiods with rising excess returns on longer-term instruments, although the slope of the yield curve and lagged excess returns generally remain significant predictors of excess returns.