Multivariate rotated ARCH models

This paper introduces a new class of multivariate volatility models which is easy to estimate using covariance targeting, even with rich dynamics. We call them rotated ARCH (RARCH) models. The basic structure is to rotate the returns and then to fit them using a BEKK-type parameterization of the time-varying covariance whose long-run covariance is the identity matrix. This yields the rotated BEKK (RBEKK) model. The extension to DCC-type parameterizations is given, introducing the rotated DCC (RDCC) model. Inference for these models is computationally attractive, and the asymptotics are standard. The techniques are illustrated using data on the DJIA stocks.     

Estimation Bias and Inference in Overlapping Autoregressions: Implications for the Target‐Zone Literature*

Samples with overlapping observations are used for the study of uncovered interest rate parity, the predictability of long‐run stock returns and the credibility of exchange rate target zones. This paper quantifies the biases in parameter estimation and size distortions of hypothesis tests of overlapping linear and polynomial autoregressions, which have been used in target‐zone applications. We show that both estimation bias and size distortions of hypothesis tests are generally larger, if the amount of overlap is larger, the sample size is smaller, and autoregressive root of the data‐generating process is closer to unity. In particular, the estimates are biased in a way that makes it more likely that the predictions of the Bertola–Svensson model will be supported. Size distortions of various tests also turn out to be substantial even when using a heteroskedasticity and autocorrelation‐consistent covariance matrix.     

The conditional autoregressive Wishart model for multivariate stock market volatility

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes an autoregressive moving average structure for the scale matrix of the Wishart distribution. It accounts for positive definiteness of covariance matrices without imposing parametric restrictions, and can be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to realized variances and covariances for five New York Stock Exchange stocks.     

Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data

We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi–Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data.     

Are the profitability and investment factors valid ICAPM risk factors? Pre-1963 evidence

We empirically evaluate whether the profitability and investment factors from Novy-Marx (2013) and Fama and French (2015, 2018) are compatible with Merton’s (1973) intertemporal CAPM (ICAPM) framework in the pre-1963 period. We show that: (i) the covariance risk price estimates of the profitability factors are positive and statistically significant, which indicates that they have explanatory power with respect to the cross-section of stock returns; (ii) the investment factors carry insignificant covariance risk prices and are therefore not valid ICAPM risk factors; and (iii) the profitability factors forecast the first moment of the aggregate stock return and economic activity with the correct sign, which is consistent with their positive covariance risk price estimates and satisfies the sign restrictions associated with the ICAPM.     

Explaining movements in UK stock prices

We examine movements in aggregate UK stock prices by decomposing the variance of unexpected real stock returns into components due to revisions in expectations of future dividends, discount rates, and the covariance between the two. The contribution of news about future discount rates is about four times that of news about future dividends, with no significant covariance between them. Our analysis of excess returns uncovers a positive covariance between news about dividends and news about real interest rates. Since these two elements have opposite effects on current stock prices, their combined effect is negligible. Persistence in expected returns, as well as predictability, are found to be important in explaining stock price movements.     

Analysis of high dimensional multivariate stochastic volatility models

This paper is concerned with the Bayesian estimation and comparison of flexible, high dimensional multivariate time series models with time varying correlations. The model proposed and considered here combines features of the classical factor model with that of the heavy tailed univariate stochastic volatility model. A unified analysis of the model, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of the estimation algorithm (which relies on MCMC methods) are: (1) a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and (2) a special method for sampling the parameters of the univariate SV process. The resulting algorithm is scalable in terms of series and factors and simulation-efficient. Methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations are also provided. The performance and effectiveness of the inferential methods are extensively tested using simulated data where models up to 50 dimensions and 688 parameters are fit and studied. The performance of our model, in relation to various multivariate GARCH models, is also evaluated using a real data set of weekly returns on a set of 10 international stock indices. We consider the performance along two dimensions: the ability to correctly estimate the conditional covariance matrix of future returns and the unconditional and conditional coverage of the 5% and 1% value-at-risk (VaR) measures of four pre-defined portfolios.     

Predicting stock splits with the help of firm-specific experiences

Evidence exists of abnormal stock returns at and following stock split announcements. The successful prediction of splits may therefore enhance investor returns, yet few studies attempt such forecasts. We note a neglected aspect of prior prediction studies—that companies enjoying a favorable stock market response to a previous split are more likely to split again. Firms in industries with a record of favorable post-split performance may also be more likely to split. We find that inclusion of these factors enhances split prediction accuracy. We also find that with these factors our split prediction model generates significant abnormal returns.     

Portfolio selection based on semivariance and distance correlation under minimum variance framework

In the minimum variance model, the covariance matrix plays an important role because it measures the risk and relationship of asset returns simultaneously under the normality assumption. However, in practice, the distribution of asset returns is nonnormal and has an obvious fat‐tail nature. In addition, the risk is one‐sided. In this paper, the main objective is to propose a better tool to replace the covariance matrix. The covariance matrix can be decomposed into two parts: a diagonal variance matrix and a square matrix with its elements being the Pearson correlation coefficient. A substitution of the covariance matrix is presented by replacing the variance and Pearson correlation coefficient in the decomposition of the covariance matrix with a semivariance and distance correlation coefficient, respectively. The proposed portfolio optimization strategy is applied to empirical data, and the numerical studies show the strategy performs well.     

High dimensional covariance matrix estimation using a factor model

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p$p$ tends to ∞$\infty$ as the sample size n$n$ increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K$K$ is allowed to grow with p$p$. We investigate the impact of p$p$ and K$K$ on the performance of the model-based covariance matrix estimator. Under mild assumptions, we have established convergence rates and asymptotic normality of the model-based estimator. Its performance is compared with that of the sample covariance matrix. We identify situations under which the factor approach increases performance substantially or marginally. The impacts of covariance matrix estimation on optimal portfolio allocation and portfolio risk assessment are studied. The asymptotic results are supported by a thorough simulation study.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

Lagged order flows and returns: A longer-term perspective

In this paper, we consider the large-sample relation between returns and lagged order flows over horizons of up to 2 months. The analysis is motivated by work in market microstructure which suggests that the effects of inventory control on stock returns should be discernible over horizons longer than those considered in the literature. We begin our analysis by developing a simple model of inventory effects in the presence of public information. Using mid-quote return data, we then find some evidence of return predictability using order flows, even after controlling for lagged returns, which is consistent with our theoretical setting. The relation is present only for negative imbalances and is stronger in large firms rather than small ones. Overall, the analysis is consistent with the notion that inventory control effects span several weeks.     

Non‐linear Predictability of UK Stock Market Returns*

Linear predictability of stock market returns has been widely reported. However, recently developed theoretical research has suggested that due to the interaction of noise and arbitrage traders, stock returns are inherently non‐linear, whereby market dynamics differ between small and large returns. This paper examines whether an exponential smooth transition threshold model, which is capable of capturing this non‐linear behaviour, can provide a better characterization of UK stock market returns than either a linear model or an alternate non‐linear model. The results of both in‐sample and out‐of‐sample specification tests support the exponential smooth transition threshold model and hence the belief that investor behaviour does differ between large and small returns.     

Co-determination of capital structure and stock returns—A LISREL approach: An empirical test of Taiwan stock markets

Titman and Wessels (1988) utilize a structural-equations model (LISREL) to find out the latent determinants of capital structure. Maddala and Nimalendran (1996) indicate that the problematic model specification causes the poor results in Titman and Wessels’ research. Chang, Lee, & Lee (2009) apply a Multiple Indicators and Multiple Causes (MIMIC) model to re-examine the same issue as Titman and Wessels did but found more convincing results. We extend Titman and Wessels’ research from using a single-equation approach to a multi-equations approach. In addition to the determinants of firms’ capital structure, those of stock returns are determined simultaneously. Literature indicates that a firm's capital structure may affect its stock returns (Bhandari, 1988), and the reverse is true too (Baker and Wurgler, 2002, Lucas and McDonald, 1990, Welch, 2004). Hence, a firm's determinants of its capital structure and those of its stock returns should be decided simultaneously, rather than independently. By solving the simultaneous equations, we examine the empirical relationship between the two endogenous variables: capital structure and stock returns and find out their common determinants as well. Our results show that stock returns, expected growth, uniqueness, asset structure, profitability, and industry classification are the main factors of capital structure, while the primary determinants of stock returns are leverage, expected growth, profitability, value and liquidity. The level of debt ratios and stock returns are mutually determined by the aforementioned factors and themselves.     

Estimating and predicting multivariate volatility thresholds in global stock markets

We propose a general double tree structured AR‐GARCH model for the analysis of global equity index returns. The model extends previous approaches by incorporating (i) several multivariate thresholds in conditional means and volatilities of index returns and (ii) a richer specification for the impact of lagged foreign (US) index returns in each threshold. We evaluate the out‐of‐sample forecasting power of our model for eight major equity indices in comparison to some existing volatility models in the literature. We find strong evidence for more than one multivariate threshold (more than two regimes) in conditional means and variances of global equity index returns. Such multivariate thresholds are affected by foreign (US) lagged index returns and yield a higher out‐of‐sample predictive power for our tree structured model setting. Copyright © 2006 John Wiley & Sons, Ltd.     

Exact Skewness–Kurtosis Tests for Multivariate Normality and Goodness‐of‐Fit in Multivariate Regressions with Application to Asset Pricing Models*

We study the problem of testing the error distribution in a multivariate linear regression (MLR) model. The tests are functions of appropriately standardized multivariate least squares residuals whose distribution is invariant to the unknown cross‐equation error covariance matrix. Empirical multivariate skewness and kurtosis criteria are then compared with a simulation‐based estimate of their expected value under the hypothesized distribution. Special cases considered include testing multivariate normal and stable error distributions. In the Gaussian case, finite‐sample versions of the standard multivariate skewness and kurtosis tests are derived. To do this, we exploit simple, double and multi‐stage Monte Carlo test methods. For non‐Gaussian distribution families involving nuisance parameters, confidence sets are derived for the nuisance parameters and the error distribution. The tests are applied to an asset pricing model with observable risk‐free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over 5‐year subperiods from 1926 to 1995.     

Model averaging by jackknife criterion in models with dependent data

The past decade witnessed a literature on model averaging by frequentist methods. For the most part, the asymptotic optimality of various existing frequentist model averaging estimators has been established under i.i.d. errors. Recently, Hansen and Racine [Hansen, B.E., Racine, J., 2012. Jackknife model averaging. Journal of Econometrics 167, 38–46] developed a jackknife model averaging (JMA) estimator, which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors. In this paper, we broaden Hansen and Racine’s scope of analysis to encompass models with (i) a non-diagonal error covariance structure, and (ii) lagged dependent variables, thus allowing for dependent data. We show that under these set-ups, the JMA estimator is asymptotically optimal by a criterion equivalent to that used by Hansen and Racine. A Monte Carlo study demonstrates the finite sample performance of the JMA estimator in a variety of model settings.     

Pricing unexpected illiquidity

The well documented positive relation between returns and lagged illiquidity suggests that illiquidity is a priced characteristic of stocks. Recent studies suggest that stock returns are inversely related to the contemporaneous unexpected illiquidity, which is consistent with price revisions to reflect realized illiquidity. This study analyzes the relations between stock returns and illiquidity innovations and finds that that the negative illiquidity shock premium persists beyond the contemporaneous interval. However, transaction costs overwhelm any potential profits from strategies that attempt to exploit the price adjustments to the shocks, suggesting the markets are efficient with respect to illiquidity information.     

Asymptotics of the principal components estimator of large factor models with weakly influential factors

This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose an estimator of the number of factors for which the PC estimator works reasonably well. For the special case when the idiosyncratic terms are cross-sectionally but not temporally correlated (or vice versa), we show that the coefficients in the OLS regressions of the PC estimates of factors (loadings) on the true factors (true loadings) are asymptotically normal, and find explicit formulae for the corresponding asymptotic covariance matrix. We explain how to estimate the parameters of the derived asymptotic distributions. Our Monte Carlo analysis suggests that our asymptotic formulae and estimators work well even for relatively small n$n$ and T$T$. We apply our theoretical results to test a hypothesis about the factor content of the US stock return data.