Time Variation in the Covariance between Stock Returns and Consumption Growth

The conditional covariance between aggregate stock returns and aggregate consumption growth varies substantially over time. When stock market wealth is high relative to consumption, both the conditional covariance and correlation are high. This pattern is consistent with the “composition effect,” where agents' consumption growth is more closely tied to stock returns when stock wealth is a larger share of total wealth. This variation can be used to test asset‐pricing models in which the price of consumption risk varies. After accounting for variations in this price, the relation between expected excess stock returns and the conditional covariance is negative.     

On portfolio optimization: forecasting covariances and choosing the risk model

We evaluate the performance of models for the covariance structureof stock returns, focusing on their use for optimal portfolioselection. We compare the models' forecasts of future covariancesand the optimized portfolios' out-of-sample performance. A fewfactors capture the general covariance structure. Portfoliooptimization helps for risk control, and a three-factor modelis adequate for selecting the minimum-variance portfolio. Undera tracking error volatility criterion, which is widely usedin practice, larger differences emerge across the models. Ingeneral more factors are necessary when the objective is tominimize tracking error volatility.     

Expected Returns,Time-varying Risk,and Risk Premia

A new empirical model for intertemporal capital asset pricing is presented that allows both time-varying risk premia and betas where the latter are identified from the dynamics of the conditional covariance of returns. The model is more successful in explaining the predictable variations in excess returns when the returns on the stock market and corporate bonds are included as risk factors than when the stock market is the single factor. Although changes in the covariance of returns induce variations in the betas, most of the predictable movements in returns are attributed to changes in the risk premia.     

INTERTEMPORAL ASSET PRICING WITHOUT CONSUMPTION DATA: EMPIRICAL TESTS

In this paper I conduct tests of an intertemporal asset pricing model using variables that forecast stock returns as the risk factors. I document that the forecasting variables are priced so that expected excess returns are related to their conditional covariances with the forecasting variables. The variability in the covariance risk fails to explain the cross-sectional and time-series variation in expected stock returns. Evidence rejects restrictions on the prices of covariance risk imposed by the model with constant volatilities. I also find that an extended model that allows time-varying conditional volatilities is misspecified.     

ASYMMETRIC COVARIANCE,VOLATILITY, AND THE EFFECT OF NEWS

We propose that covariance (rather than beta) asymmetry provides a superior framework for examining issues related to changing risk premiums. Accordingly, we investigate whether the conditional covariance between stock and market returns is asymmetric in response to good and bad news. Our model of conditional covariance accommodates both the sign and magnitude of return innovations, and we find significant covariance asymmetry that can explain, at least in part, the volatility feedback of stock returns. Our findings are consistent across firm size, firm leverage, and temporal and cross‐sectional aggregations.     

Asymmetric Price and Volatility Adjustments in Emerging Asian Stock Markets

This paper tests the hypothesis that stock returns in emerging stock markets adjust asymmetrically to past information. The evidence suggests that both the conditional mean and the conditional variance respond asymmetrically to past information. In agreement with studies dealing with developed stock markets, the conditional variance is an asymmetrical function of past innovations, rising proportionately more during market declines. More importantly, the conditional mean is also an asymmetrical function of past returns. Specifically, positive past returns are more persistent than negative past returns of an equal magnitude. This behaviour is consistent with an asymmetric partial adjustment price model where news suggesting overpricing (negative returns) are incorporated faster into current prices than news suggesting underpricing (positive returns). Furthermore, the asymmetric adjustment of prices to past information could be partially responsible for the asymmetries in the conditional variance if the degree of adjustment and the level of volatility are positively related.     

Expected stock returns,common idiosyncratic volatility and average idiosyncratic correlation

Motivated by Herskovic et al. (2016), we examine the role of the average idiosyncratic correlation (ICOR) in two types of markets: an emerging market and a developed market. Examining daily stock data from the Chinese stock market for the period 1995 to 2020 and from the US for the period 1926 to 2019, we adopt high-dimensional principal component analysis (PCA) and thresholding methods to re-estimate ICOR. We find that ICOR plays an important role in explaining the expected stock returns, as the common idiosyncratic volatility (CIV) does in Herskovic et al. (2016). ICOR has been neglected in the literature due to large estimation error in the idiosyncratic covariance matrix and our analysis provides evidence that ICOR is nonnegligible in both markets when we control for several common market factors. We show that the average idiosyncratic covariance, which is the numerator of ICOR, exhibits the same pattern as CIV. Furthermore, our regression analyses of expected stock returns in response to ICOR change in both markets show that, in contrast to the negative result for CIV, the stocks’ high risk exposure to ICOR change comes with a higher risk premium, perhaps because of the synchronized but disproportionate changes in the monthly idiosyncratic covariance and idiosyncratic volatility.     

Returns synchronization and daily correlation dynamics between international stock markets

The use of close-to-close returns underestimates returns correlation because international stock markets have different trading hours. With the availability of 16:00 (London time) stock market series, we find dynamics of daily correlation and covariance, estimated using two non-synchroneity adjustment procedures, to be substantially different from their synchronous counterparts. Conditional correlation may have different signs depending on the model and data type used. Other findings include volatility spillover from the US to the UK (and France), and a reverse spillover which is not documented before. Also, unlike previous findings, we found the increase in daily correlation is prominent only under extremely adverse conditions when a large negative return has been registered.     

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multifactor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multifactor models.     

Time-varying stock returns and labor income risks in the US and UK

I propose and estimate conditional asset pricing models where the risk premiums of the markets are related to the conditional covariance of the markets with labor income growth within and across countries and the volatility of the markets are related to the shocks and interactions of stock returns and labor income growth. I document that the risk premiums for the US and UK stock markets are more related to the conditional covariance of returns with the labor income growth within countries than across countries. I also find significant interactions of volatilities between stock returns and labor income within countries but not across countries. The results are consistent with the hypothesis that prices of domestic stocks are determined to a greater extent by stochastic discount factors of domestic investors than foreign investors and vice versa.     

The Seasonal Stability of the Factor Structure of Stock Returns

This paper investigates the month-by-month stability of (a) daily returns and correlation coefficients of stock returns, (b) correlation and covariance matrices, (c) number of return-generating factors, and (d) the APT pricing relationship. The results show that there is a January effect and a small-firm effect in stock returns. Correlation matrices are more stable than covariance matrices, but both types of matrices are not stable across months and across the sample groups. The number of return-generating factors is rather stable most of the time and for most of the sample groups, but there is some significant instability that is related to the average correlation coefficients among stocks. The APT pricing relationship does not seem to be supported by the two-stage process using the maximum-likelihood factor analysis.     

Risk Reduction and Mean-Variance Analysis: An Empirical Investigation

Abstract:  I examine the performance of global minimum variance (GMV) and minimum tracking error variance (TEV) portfolios in UK stock returns using different models of the covariance matrix. I find that both GMV and TEV portfolios deliver portfolio risk reduction benefits in terms of significantly lower volatility and tracking error volatility relative to passive benchmarks for every model of the covariance matrix used. However, the GMV (TEV) portfolios do not provide significantly superior Sharpe (1966) (adjusted Sharpe) performance relative to passive benchmarks except for the restricted GMV portfolios. I find that a number of alternative covariance matrix models can improve the performance of the restricted TEV portfolio formed using the sample covariance matrix but not the restricted GMV portfolio. I also find that simpler covariance matrix models perform as well as the more sophisticated models.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

A note on the temporal variability of Canadian financial services stock returns

We show that Financial Services stock returns in Canada are covariance nonstationary with respect to any benchmark variable and vary negatively with interest rate levels. We find that the conditional correlation between financial services stock returns and the market returns varies directly and monotonically with market volatility. This result is robust to monetary regime shifts and other sources of high volatility. These findings, combined with those of Kane and Unal (1988) for the U.S., cast considerable doubt on the constant coefficient Two-Index model and its variants, to provide reliable estimates of usual risk measures.     

基于Copula函数的国际原油价格与股票市场收益的相关性研究

针对国际原油价格与金砖五国股票市场收益之间的相关性问题,使用 AR(p)-GARCH(1,1)-Copula 模型进行检验。运用广义误差分布(GED)获取收益残差序列,对 WTI 原油价格和金砖五国股市收益之间的相关性进行实证分析。研究结果表明,国际原油价格与中国股市收益呈现微弱的相关关系,而与其他四国股市收益的相关关系较为明显。用时变 SJC Copula 模型刻画国际原油价格与金砖五国股票市场收益的相关性最为合适。     

Stability and forecasting of the comovement measures of international stock market returns

The potential benefits to international diversification may be less if the comovement structure of international equity returns is non-stationary than if it is. This paper examines the intertemporal stability of the correlation and the covariance structure of the returns of ten major stock markets. Whilst empirical evidence supports the hypothesis that the correlation structure is stable over time, the empirical support for the stability of the covariance matrix is much weaker. Alternative forecasting models of the comovement structure are examined.     

Keep on smiling? The pricing of Quanto options when all covariances are stochastic

The paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.     

CO-MOVEMENTS IN INTERNATIONAL EQUITY MARKETS

We examine the co-movements of equity returns in four major international markets by characterizing the time-varying cross-country covariances and correlations. Using a generalized positive definite multivariate GARCH model, we find that the Japanese and U.S. stock markets have significant transitory covariance, but zero permanent covariance. The other pairs of markets examined display significant permanent and transitory covariance. We also find that, while conditional correlations between returns are generally small, they change considerably over time. An event analysis suggests that basing diversification strategies on these conditional correlations is potentially beneficial.     

Equilibrium moment restrictions on asset returns: normal and crisis periods

Empirically, the covariance between stock returns varies with their volatility. We seek a robust theoretical explanation of this. With minimal assumptions, we model stochastic properties of equilibrium returns which result from the interaction between inter-temporal traders and noisy, price-sensitive short-term traders. The inter-temporal traders can have arbitrary investment rules, preferences and information. In all cases we find a set of restrictions between second moments of equilibrium returns. With two assets there is also a bound on the correlation between asset returns. Estimation with second moments of global stock returns supports our theoretical framework. Higher volatility in at least one market can increase comovement among markets. With globalization, covariances between two stock markets can also affect covariances between two other stock markets. We also find that the changes in trader behavior between normal and crisis periods lead to changes in the moment restrictions between asset returns.     

Stock returns and economic forces—An empirical investigation of Chinese markets

This study finds evidence that a better macroeconomic climate and an improvement in liquidity help to explain Chinese stock returns. There is no evidence to support the hypothesis that growth in dividend yields can predict stock returns. The sectoral stock returns in China's markets are correlated with stock returns in the US markets as evidenced by: (i) a positive correlation with US stock returns; (ii) a significant negative error correcting term; (iii) a negative response of Chinese stocks to financial stress in the US market; and (iv) a positive correlation with a depreciation in the China/US exchange rate.