Moments Of Asset Returns Research Articles

Valuing Financial Data

Abstract How should an investor value financial data? The answer is complicated because it depends on the characteristics of all investors. We develop a sufficient statistics approach that uses equilibrium asset return moments to summarize all relevant information about others’ characteristics. Our approach values public or private data, data about one or many assets, and data relevant for dividends or sentiment. While different data types, of course, have different valuations, heterogeneous investors also value the same data very differently. This finding suggests a low price elasticity for data demand. Heterogeneous investors’ data valuations are also affected very differentially by market illiquidity.

Climate risks and the realized higher-order moments of financial markets: Evidence from China

The return distribution of energy assets deviates from the normal distribution, making volatility a partial measure of risk, and climate risk tend to affect the skewness preferences of environmentally conscious investors. However, limited evidence exists on the impact of climate risk on higher-order moments of asset returns, especially in China. Using data from December 2013 to June 2022, we study the time-varying Granger causal flow from two Chinese climate uncertainty indices (Chinese climate policy uncertainty (CPU) and Chinese climate uncertainty (CU)) to the realized high-order moments (volatility, skewness, and kurtosis) of various Chinese assets covering green energy, carbon emission allowances, and brown energy indices. The main results show evidence of time-variation in the causal flows from climate risks, without ignoring the heterogeneity between the two climate risk measures and across the three assets under study. Granger causality spans various time periods, and is generally more significant for the realized volatility. These results are robust to the specification of the time-varying causality analysis. They also remain significant when accounting for the impact of Chinese economic policy uncertainty, which further supports their robustness. These findings highlight the ability of climate risk to affect higher-order moments of asset returns through the channels of strong deviation of returns from the normal distribution, the preference of investors for skewness, and the frequent occurrence of crisis periods.

Asset pricing with long-run disaster risk.

Traditional disaster models with time-varying disaster risk are not perfect in explaining asset returns. We redefine rare economic disasters and develop a novel disaster model with long-run disaster risk to match the asset return moments observed in the U.S. data. The difference from traditional disaster models is that our model contains the long-run disaster risk by treating the long-run ingredient of consumption growth as a function of time-varying disaster probability. Our model matches the U.S. data better than the traditional disaster model with time-varying disaster risk. This study uncovers an additional channel through which disaster risk affects asset returns and bridges the gap between long-run risk models and rare disaster models.

Optimal Portfolio Diversification via Independent Component Analysis

A natural approach to enhance portfolio diversification is to rely on factor-risk parity, which yields the portfolio whose risk is equally spread among a set of uncorrelated factors. The standard choice is to take the variance as risk measure, and the principal components (PCs) of asset returns as factors. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice: any rotation of the PCs results in uncorrelated factors. This is problematic because we demonstrate that any portfolio is a factor-variance-parity portfolio for some rotation of the PCs. More importantly, choosing the PCs does not account for the higher moments of asset returns. To overcome these issues, we propose using the independent components (ICs) as factors, which are the rotation of the PCs that are maximally independent, and care about higher moments of asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on value at risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and several state-of-the-art benchmarks.

Quantile forecasting based on a bivariate hysteretic autoregressive model with GARCH errors and time ‐varying correlations

AbstractTo understand and predict chronological dependence in the second‐order moments of asset returns, this paper considers a multivariate hysteretic autoregressive (HAR) model with generalized autoregressive conditional heteroskedasticity (GARCH) specification and time‐varying correlations, by providing a new method to describe a nonlinear dynamic structure of the target time series. The hysteresis variable governs the nonlinear dynamics of the proposed model in which the regime switch can be delayed if the hysteresis variable lies in a hysteresis zone. The proposed setup combines three useful model components for modeling economic and financial data: (1) the multivariate HAR model, (2) the multivariate hysteretic volatility models, and (3) a dynamic conditional correlation structure. This research further incorporates an adapted multivariate Student t innovation based on a scale mixture normal presentation in the HAR model to tolerate for dependence and different shaped innovation components. This study carries out bivariate volatilities, Value at Risk, and marginal expected shortfall based on a Bayesian sampling scheme through adaptive Markov chain Monte Carlo (MCMC) methods, thus allowing to statistically estimate all unknown model parameters and forecasts simultaneously. Lastly, the proposed methods herein employ both simulated and real examples that help to jointly measure for industry downside tail risk.

Optimal Portfolio Diversification via Independent Component Analysis

A natural approach to enhance portfolio diversification is to rely on factor-risk parity, which yields the portfolio whose risk is equally spread among a set of uncorrelated factors. The standard choice is to take the variance as risk measure, and the principal components (PCs) of asset returns as factors. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice: any rotation of the PCs results in uncorrelated factors. This is problematic because we demonstrate that any portfolio is a factor-variance-parity portfolio for some rotation of the PCs. More importantly, choosing the PCs does not account for the higher moments of asset returns. To overcome these issues, we propose to use the independent components (ICs) as factors, which are the rotation of the PCs that are maximally independent, and care about higher moments of asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on Value-at-Risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and several state-of-the-art benchmarks.

Do Commodities Add Economic Value in Asset Allocation? New Evidence from Time-Varying Moments

We conduct a comprehensive out-of-sample assessment of the economic value adding of commodities in multiasset investment strategies that exploit the predictability of asset return moments. We find that predictability makes the inclusion of commodities profitable even when short selling and high leverage are not permitted. For instance, a mean-variance (non-mean-variance) investor with moderate risk aversion and leverage, rebalancing quarterly, would be willing to pay up to 108 (155) basis points per year after transaction cost for adding commodities to her stock, bond, and cash portfolio. Previous research had reached mixed or even opposite conclusions, especially in an out-of-sample context.

Large Dynamic Covariance Matrices

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.

The Diversification Delta: A Different Perspective

In a 2012 article published in The Journal of Portfolio Management, Vermorken, Medda, and Schroder introduce a new measure of diversification, the Diversification Delta (DD), based on the entropy of the portfolio return distribution. Entropy as a measure of uncertainty has been used successfully in several frameworks and takes into account the entire statistical distribution, rather than just the first two moments. In this article, the authors highlight some drawbacks of the DD measure and go on to propose an alternative measure based on exponential entropy that overcomes the identified shortcomings. The authors present the properties of this new measure and propose it as an alternative for portfolio optimization that incorporates higher moments of asset returns, such as skewness and excess kurtosis.

Recent Developments in Copula Models

Copula models have become very popular and well studied among the scientific community.[...]

Disaster risk and asset returns: An international perspective

Recent studies have shown that disaster risk can generate asset return moments similar to those observed in the U.S. data. However, these studies have ignored the cross-country asset pricing implications of the disaster risk model. This paper shows that standard U.S.-based disaster risk model assumptions found in the literature lead to counterfactual international asset pricing implications. Given consumption pricing moments, disaster risk from this literature cannot explain the range of equity premia and government bill rates. Furthermore, the independence of disasters presumed in some studies generates counterfactually low cross-country correlations in equity markets. Alternatively, if disasters are all shared, the model generates correlations that are excessively high. We show that common and idiosyncratic components of disaster risk are needed to explain the pattern in consumption and equity co-movements.

Disaster Risk and Asset Returns: An International Perspective

Recent studies have shown that disaster risk can generate asset return moments similar to those observed in the U.S. data. However, these studies have ignored the cross-country asset pricing implications of the disaster risk model. This paper shows that standard U.S.-based disaster risk model assumptions found in the literature lead to counterfactual international asset pricing implications. Given consumption pricing moments, disaster risk cannot explain the range of equity premia and government bill rates nor the high degree of equity return correlation found in the data. Moreover, the independence of disasters presumed in some studies generates counterfactually low cross-country correlations in equity markets. Alternatively, if disasters are all shared, the model generates correlations that are excessively high. We show that common and idiosyncratic components of disaster risk are needed to explain the pattern in consumption and equity co-movements.

ON OPTIMAL STRATEGIES FOR UTILITY MAXIMIZERS IN THE ARBITRAGE PRICING MODEL

We consider a popular model of microeconomics with countably many assets: the Arbitrage Pricing Model. We study the problem of optimal investment under an expected utility criterion and look for conditions ensuring the existence of optimal strategies. Previous results required a certain restrictive hypothesis on the tails of asset return distributions. Using a different method, we manage to remove this hypothesis, at the price of stronger assumptions on the moments of asset returns.

Large Dynamic Covariance Matrices

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper aims to marry these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices.

Investor sentiment and portfolio selection

We provide a theoretical framework to examine how investor sentiment impacts the mean-variance tradeoff. We derive a sentiment-adjusted Markowitz efficient frontier in which investor sentiment alters the first two moments of asset returns, the minimum-variance frontier as well as the Capital Market Line. Our theoretical results are consistent with empirical findings that heightened sentiment-related noise trading activity drives perceived prices away from fundamental and increases market volatility. A rational investor neglecting the effect of investor sentiment may end up selecting a sub-optimal portfolio.

Risk-free rate effects on conditional variances and conditional correlations of stock returns

This paper investigates whether the risk-free rate may explain the movements observed in the conditional second moments of asset returns. Original results are derived, within the C-CAPM framework, that attest the existence of a channel connecting these seemingly unrelated quantities. The empirical results, involving 165 time series of stock returns quoted at the NYSE, show that the risk-free rate does contain information that is relevant in predicting the 165 conditional variances and 13,530 conditional correlations. These findings are particularly pronounced at lower frequencies where the persistence of the conditional second moments is significantly weaker.

Size matters: Optimal calibration of shrinkage estimators for portfolio selection

We carry out a comprehensive investigation of shrinkage estimators for asset allocation, and we find that size matters—the shrinkage intensity plays a significant role in the performance of the resulting estimated optimal portfolios. We study both portfolios computed from shrinkage estimators of the moments of asset returns (shrinkage moments), as well as shrinkage portfolios obtained by shrinking the portfolio weights directly. We make several contributions in this field. First, we propose two novel calibration criteria for the vector of means and the inverse covariance matrix. Second, for the covariance matrix we propose a novel calibration criterion that takes the condition number optimally into account. Third, for shrinkage portfolios we study two novel calibration criteria. Fourth, we propose a simple multivariate smoothed bootstrap approach to construct the optimal shrinkage intensity. Finally, we carry out an extensive out-of-sample analysis with simulated and empirical datasets, and we characterize the performance of the different shrinkage estimators for portfolio selection.

Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications

This article solves the portfolio choice problem in a multi-asset jump-diffusion model. We decompose the optimal portfolio weight into components that correspond to a collection of fictitious economies, one of which is a standard diffusion economy, and the others of which are pure-jump economies. We derive a semi-closed-form solution for the optimal portfolio weight, and investigate its properties with or without ambiguity aversion. We find that an investor may not reduce her investment in risky assets when facing more frequent jumps, as suggested by a single-asset jump-diffusion model. Moreover, an investor who is extremely cautious about her estimates of higher moments of asset returns may still hold risky assets, contrary to the prediction of a pure-diffusion model with ambiguity aversion to the first moment.

Assessing misspecified asset pricing models with empirical likelihood estimators

Hansen and Jagannathan (1997) compare misspecified asset pricing models based on least-square projections on a family of admissible stochastic discount factors. We extend their fundamental contribution by considering Minimum Discrepancy projections where misspecification is measured by a family of convex functions that take into account higher moments of asset returns. The Minimum Discrepancy problems are solved on dual spaces producing a family of estimators that captures the least-square problem as a particular case. We derive the asymptotic distributions of the estimators for the Cressie–Read family of discrepancies, and illustrate their use with an assessment of the Consumption Asset Pricing Model.

Why does bad news increase volatility and decrease leverage?

A recent literature shows how an increase in volatility reduces leverage. However, in order to explain pro-cyclical leverage it assumes that bad news increases volatility, that is, it assumes an inverse relationship between first and second moments of asset returns. This paper suggests a reason why bad news is more often than not associated with higher future volatility. We show that, in a model with endogenous leverage and heterogeneous beliefs, agents have the incentive to invest mostly in technologies that become more volatile in bad times. Agents choose these technologies because they can be leveraged more during normal times. Together with the existing literature this explains pro-cyclical leverage. The result also gives a rationale to the pattern of volatility smiles observed in stock options since 1987. Finally, the paper presents for the first time a dynamic model in which an asset is endogenously traded simultaneously at different margin requirements in equilibrium.