Covariance Of Returns Research Articles

Regularizing stock return covariance matrices via multiple testing of correlations

This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock returns. The approach involves simultaneous testing of all pairwise correlations, followed by setting non-statistically significant elements to zero. This adaptive thresholding is achieved through sign-based Monte Carlo resampling within multiple testing procedures, controlling either the traditional familywise error rate, a generalized familywise error rate, or the false discovery proportion. Subsequent shrinkage ensures that the final covariance matrix estimate is positive definite and well-conditioned while preserving the achieved sparsity. Compared to alternative estimators, this new regularization method demonstrates strong performance in simulation experiments and real portfolio optimization.

Stock returns and monetary policy stance

This paper investigates the structural relationships between monetary policy and stock returns. We build an asset pricing model incorporating a standard Taylor rule into a consumption-CAPM framework. Our model quantitatively explains the negative risk premium of expansionary monetary policy. As monetary policy plays a role of insurance, (expansionary) monetary policy beta is negatively related to covariances of returns with output gap and inflation theoretically and empirically. In addition, while systematic responses mainly account for the negative risk premium, pure monetary policy shocks have little influence under plausible calibrations. We also provide theoretical predictions on how the slope of the Phillips curve and the response parameters of monetary policy affect the cross-section of returns.

Who participates in corporate income tax consolidation?: Evidence from Japan

When a group of affiliated corporations can file a single tax return based on a combined income, what types of groups would take up the option? This study empirically analyzes decisions to participate in a single-jurisdiction consolidated tax filing. The data consists of 2,782 Japanese corporate groups headed by publicly-traded corporations observed from 2002 to 2007. Results indicate a higher likelihood of participation among groups characterized by low correlation in returns among group members, high variance in returns, many subsidiaries, and losses accumulated in parents. The significant influence of variance and covariance of returns suggests that a consolidation scheme improves the efficiency of a corporate income tax by reducing profit shifting.

The sources of portfolio volatility and mutual fund performance

We conduct a volatility decomposition to identify the source of performance differences between low volatility and high volatility mutual funds. Higher return covariances between fund holdings are associated with more fund-level exposure to the idiosyncratic volatility effect. The average security-level variance of fund holdings is only weakly associated with idiosyncratic volatility but is closely tied to a fund's exposure to the beta anomaly. We demonstrate that our measure of the within-portfolio covariance of fund holdings is useful in evaluating fund-level performance measures and exposure to volatility anomalies.

Climate change news risk and corporate bond returns in China

By constructing a climate change news index based on the textual analysis of newspapers and estimations of the covariance of bond returns, this paper investigates whether climate change news risk is “priced in” in Chinese corporate bonds. We find that bonds with a higher climate change news beta are associated with lower future returns. Moreover, the low climate change news beta premium originates from the transition news beta. Additionally, the low climate change news beta premium is more obvious during times of heightened climate change news risk, which is consistent with the asset pricing theory of intertemporal hedging demand.

Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage

Abstract We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive models with the least absolute shrinkage and selection operator. Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios.

Which factor model? A systematic return covariation perspective

We examine which factor model best captures systematic return covariation by focusing on the economic implications for portfolio risk control. The pairwise variance equality test and the model confidence set procedure suggest that the Fama and French (2015) five-factor model, the Barillas and Shanken (2018) six-factor model, and the Fama and French (2018) six-factor model are the top performers for the factor model-implied minimum risk portfolios in the out-of-sample. When it comes to the minimum tracking error portfolios, the Barillas and Shanken (2018) six-factor model and the Fama and French (2018) six-factor model are the overall winners in the horse race.

Who Owns What? A Factor Model for Direct Stockholding

ABSTRACTWe build a cross‐sectional factor model for investors' direct stockholdings and estimate it using data from almost 10 million retail accounts in the Indian stock market. Our model identifies strong investor clienteles for stock characteristics, most notably firm age and share price, and for particular clusters of stock characteristics. These clienteles are intuitively associated with investor attributes such as account age, size, and diversification. Coheld stocks tend to have higher return covariance, inconsistent with simple models of diversification but suggestive that clientele demands influence stock returns.

Modeling and forecasting dynamic conditional correlations with opening, high, low, and closing prices

Models for variances and covariances of asset returns are crucial in risk management and asset allocation. Traditionally, these models were based on daily returns. Daily opening, high, low and closing (OHLC) prices have been sometimes used in multivariate volatility models for variances, but not for correlations. We therefore suggest a new version of the Dynamic Conditional Correlation (DCC) model wherein information from daily OHLC prices is utilized in both variance and correlation equations. The model is evaluated for two datasets: five exchange traded funds and five currencies. The results show that in terms of conditional covariance matrix estimates and forecasts the proposed model significantly outperforms, not only the standard DCC model, but also models that incorporate OHLC prices only in the variance equation.

TESTING THE APPLICABILITY OF THE CAPM MODEL USING SELECTED SHARES LISTED ON THE BELGRADE STOCK EXCHANGE

One of the basic types of portfolio valuation as well as valuation of individual company shares is the CAPM (Capital Asset Pricing) model, which uses a well-known measure of systemic risk in its analysis, which is beta. The CAPM model in its analysis uses the link between the systemic risk measure (beta) and the expected market return. Guided by this model, the analysis of monthly returns of selected shares on the Belgrade Stock Exchange in the period from 2011 to 2021 was performed in this research. In the research, the beta coefficient of selected shares was calculated with the help of the covariance of market return and stock return. The results and their statistical value were confirmed by the linear regression test. The rest of the research tests the applicability of the CAPM model to selected actions and in the same way, the SML (security market line) is devised, which is a graphical representation of the model. The research indicated that the basic assumptions of the CAPM model are not applicable as a predictor of future expected returns of selected shares on the Belgrade Stock Exchange due to various other elements that affect price movements and returns of selected shares not covered by the model.

Dynamic portfolio selection with linear control policies for coherent risk minimization

This paper is concerned with a linear control policy for dynamic portfolio selection. We develop this policy by incorporating time-series behaviors of asset returns on the basis of coherent risk minimization. Analyzing the dual form of our optimization model, we demonstrate that the investment performance of linear control policies is directly connected to the intertemporal covariance of asset returns. To mitigate overfitting to training data (i.e., historical asset returns), we apply robust optimization. For this optimization, we prove that the worst-case coherent risk measure can be decomposed into the empirical risk measure and the penalty terms. Numerical results demonstrate that when the number of assets is small, linear control policies deliver good out-of-sample investment performance. When the number of assets is large, the penalty terms improve the out-of-sample investment performance.

Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimization

Portfolio optimization requires sophisticated covariance estimators that are able to filter out estimation noise. Non-linear shrinkage is a popular estimator based on how the Oracle eigenvalues can be computed using only data from the calibration window. Contrary to common belief, NLS is not optimal for portfolio optimization because it does not minimize the right cost function when the asset dependence structure is non-stationary. We instead derive the optimal target. Using historical data, we quantify by how much NLS can be improved. Our findings reopen the question of how to build the covariance matrix estimator for portfolio optimization in realistic conditions.

Do risk exposures explain accounting anomalies? A new testing method

AbstractI quantitatively evaluate how much of the cross‐sectional return predictive ability of a range of accounting anomalies can be attributed to firm‐specific stock return covariances with market risk factors. Using a novel two‐step regression‐based testing method, I find robust evidence that the risk factor exposures do not explain a meaningful fraction of the time‐series variations in the return predictive coefficients of the anomaly variables. Out‐of‐sample tests further confirm that it is the mispricing component of the accounting anomalies that is mainly responsible for the return predictability.

Bayesian nonparametric portfolio selection with rolling maximum drawdown control

We present a novel approach to the portfolio selection problem for a multiperiod investor facing multiple risky assets, trading constraints, and return predictability. Our objective is to maximize mean-variance utility while addressing the computational challenges arising from the curse of dimensionality associated with dynamic programming in the presence of trading constraints. To overcome this, we employ model predictive control, a computationally efficient method for solving the problem. Additionally, we propose the use of a non-parametric Bayesian model, specifically the hierarchical Dirichlet process based Hidden Markov Model (HDP-HMM), to predict the multiperiod mean and covariance of returns. Then, we consider a time-varying maximum drawdown to adjust the risk aversion, which can effectively cope with the limit loss problems. Through extensive simulation studies and empirical analysis, we demonstrate that trading strategies based on our proposed method outperform existing approaches in out-of-sample performance.

Realized semibetas: Disentangling “good” and “bad” downside risks

We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the “right” semibetas.

Analysis of Global Fixed-Income Returns Using Multilinear Tensor Algebra

Global fixed income returns exhibit highly structured correlations across maturities and economies (data modes), and their modeling therefore requires analysis tools that are capable of directly capturing the inherent multi-way couplings present in such multimodal data. Yet, current analyses typically employ “flat-view” multivariate matrix models and their associated linear algebras; these are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, we first show that global fixed income returns naturally reside on multi-modal lattice data structures, referred to as tensors. This serves as a basis to introduce a multilinear algebraic approach, inherent to tensors, to the modeling of the global term structure underlying multiple interest rate curves. Owing to the enhanced flexibility of multilinear algebra, statistical descriptors, such as correlations, exist between tensor columns and rows (fibers), as opposed to between individual entries in standard matrix analysis. This allows us to express the covariance of global returns as a joint multilinear decomposition of the maturity-domain and country-domain covariances. This not only drastically reduces the number of parameters required to fully capture the global returns covariance structure, but also makes it possible to devise rigorous and tractable global portfolio management strategies; we tailor these specifically to each of the data domains and thereby fully exploit the lattice structure of global fixed income returns. The ability of the proposed multilinear tensor approach to compactly describe the macroeconomic environment through economically meaningful factors is validated via empirical analysis that demonstrates the existence of maturity-domain and country-domain covariances underlying the interest rate curves of eight developed economies. TOPICS:Fixed income and structured finance, quantitative methods, statistical methods, portfolio construction, global markets Key Findings ▪ We show that global fixed income returns naturally reside on multi-modal lattice data structures, referred to as tensors, which exhibit highly structured correlations across maturities and economies. ▪ We introduce a multilinear algebraic approach to the modeling of the global term structure underlying multiple interest rate curves, which allows us to express the covariance of global returns as a joint multilinear decomposition of the maturity-domain and country-domain covariances. ▪ This drastically reduces the number of parameters required to fully capture the global returns covariance structure, and makes it possible to devise rigorous and tractable global portfolio management strategies which are tailored to each of the data domains.

Multi-Asset Market Impact and Order Flow Commonality

The empirical finding that market movements in stock prices may be correlated with the order flow of other stocks has led to the notion of and has prompted the development of multivariate models of market impact. These models are parametrized by a matrix of impact coefficients whose off-diagonal elements are meant to capture how trades in one asset influence the price of other assets, leading to a large number of 'cross-impact' parameters which may not be identified solely based on the covariance of returns with order flow. Moreover, empirical evidence suggests that these cross-impact terms are unstable and change sign randomly over time, which poses a problem for their interpretation and use. We reexamine this empirical evidence from a causal standpoint and offer a simpler explanation for the observed correlation between the returns of an asset and the order flow imbalance of other assets, in terms of common components in order flow across stocks which may naturally arise from multi-asset trading strategies. We provide empirical evidence from order flow and price changes of NASDAQ-100 stocks to support this explanation. Our results show the main determinants of impact to be idiosyncratic order flow imbalance as well as a market order flow factor common across stocks. Additional ‘cross-impact’ terms account for less than 1% of market impact. This leads to a parsimonious approach for causal modelling of multi-asset impact, which does not require introducing any concept of cross-impact.

Оптимальная ликвидность и безрисковый портфель активов

Monetary financing of huge spending aimed to fight the pandemic had taken place under the unique and extremal circumstances. However, it also has long-term implications due largely to the accelerated increases in the value of financial assets. A simple model is proposed to study the complex and prolong process of normalizing money and finance. The latter is viewed as restructuring of the macro-financial portfolio of assets, which is subject to the stochastic dynamic of broad money. Such a model is focused on one of the most important macro-financial relationships: the optimal amount of liquidity must be adequately collateralized by the value of real wealth. If this condition is realized then an effective financial system could be formed. The provision of loans in such a system is secured and revenues of a risk-free asset portfolio are ade quate to repay all liabilities outstanding. In the short term, the riskless rate of return is similar to the rate of a macro-financial repo transaction. In the long run, the risk-free rate of return correspondence to a «neutral» interest rate has to be justified by the zero covariance of returns with the stochastic discount factor. Large deviations from the optimum of money, by disrupting the best configuration of assets and liabilities, cause undesirable consequences: either an illiquidity crisis or the credit expansion ending in a complete breakdown of the financial system.

Stock Returns and Monetary Policy Stance

This paper investigates the structural relationships between monetary policy and stock returns. We build an asset pricing model incorporating a standard monetary policy rule into a consumption-CAPM framework. Our model quantitatively explains the negative risk premium of expansionary monetary policy. It also suggests that (expansionary) monetary policy beta is negatively related to covariances of returns with output gap and inflation. In addition, related to the premise of its stabilization role, a hawkish monetary policy stance predicts rises in future consumption growth and inflation. These results are consistent with empirical evidence. Furthermore, we provide theoretical predictions on how the slope of the Phillips curve and the response parameters of monetary policy affect the cross-section of returns.

Who Owns What? A Factor Model for Direct Stockholding

We build a cross-sectional factor model for investors' direct stockholdings, by analogy with standard time-series factor models for stock returns. We estimate the model using data from almost 10 million retail accounts in the Indian stock market. We find that stock characteristics such as firm age and share price have strong investor clienteles associated with them. Similarly, account attributes such as account age, account size, and extreme underdiversification (holding a single stock) are associated with particular characteristic preferences. Coheld stocks tend to have higher return covariance, suggestive of the importance of clientele effects in the stock market.