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.     

行业资产的Black-Litterman模型配置研究——基于社交网络情绪文本挖掘算法

研究目标:构建反映行业股价走势的基于社交网络文本挖掘算法的行业投资者情绪指标，并改善嵌入行业投资者情绪指标的Black-Litterman模型对资产的配置结果。研究方法:基于社交网络文本挖掘算法度量投资者情绪，运用主成分分析法构建行业投资者情绪指标，并嵌入Black-Litterman模型中构建投资者观点矩阵，确定行业资产配置比。研究发现:基于行业投资者情绪的BL模型有效提高了资产配置的日均收益率和夏普比率。实证结果在样本外验证(除受新冠疫情影响阶段)、暴涨暴跌阶段以及经过允许卖空和交易成本调整后仍稳健，进而证实了投资者情绪对资产组合有显著影响。研究创新:基于社交网络文本挖掘算法构建投资者情绪指数，解决了仅依赖于预期收益或历史数据的预测模型无法直观揭示投资者心理认知和行为的局限性问题，从一个崭新的视角科学地解决Black-Litterman模型中投资者观点的生成问题。研究价值:扩展了Black-Litterman模型理论体系研究，并推动了行为金融理论在资产配置中的应用。     

Covariance estimation: do new methods outperform old ones?

This paper compares three new methods of estimating the asset returns covariance and evaluates their performances with the conventional covariance estimation methods. We find that taking a simple average of the historical sample covariance matrix and the covariance matrix estimated from the single-index model provides the best overall performance among all competing methods. In addition, we find that commonly used assessment criteria provide systematically different rankings, which explains the preferences to different types of estimation methods in the existing literature. We believe the difference between our results and those of previous studies may be partly due to the differences in the ratio of the time series observations to the number of stocks in the samples that have been used in different studies.     

A Stein-type shrinkage estimator of the covariance matrix for portfolio selections

The covariance matrix plays a crucial role in portfolio optimization problems as the risk and correlation measure of asset returns. An improved estimation of the covariance matrix can enhance the performance of the portfolio. In this paper, based on the Cholesky decomposition of the covariance matrix, a Stein-type shrinkage strategy for portfolio weights is constructed under the mean-variance framework. Furthermore, according to the agent’s maximum expected utility value, a portfolio selection strategy is proposed. Finally, simulation experiments and an empirical study are used to test the feasibility of the proposed strategy. The numerical results show our portfolio strategy performs satisfactorily.     

基于安全投资转移视角的风险相关性研究

投资者根据市场状态变化进行安全投资转移,引起资产间的资金流动和风险相关性变化。利用Markov状态转移模型识别市场状态,订单流差异衡量安全投资转移,基于CAPM的标准化协方差矩阵衡量风险相关性。研究发现:我国股市存在熊市、横盘和牛市三种状态,横盘状态下安全投资转移水平急剧提升。在时间维度上,横盘状态下安全投资转移对行业间风险相关性的影响最大;在截面维度上,同一状态下安全投资转移对安全型行业-风险型行业所组成行业对的风险相关性影响程度最大。结果表明,安全投资转移引起行业间风险相关性负向变化,使得行业间风险相关性减少。投资者同时配置受安全投资转移显著影响的安全型和风险型资产,可以降低投资组合系统性风险。     

金融资产配置、金融杠杆与现金流风险

金融资产会计安排是企业执行金融工具准则的重要环节,具有显著的经济后果。基于实体企业金融化现象,研究金融资产配置与现金流风险关系,分析金融杠杆的调节功能,探讨非效率资本配置的传导作用,研究发现：金融资产配置与现金流风险之间存在U型关系;金融杠杆能够调节金融资产配置与现金流风险的关系,使关系曲线拐点右移与扁平化。区分金融资产配置类型后发现：交易类金融资产与现金流风险呈U型关系;委托贷款等新兴金融资产负向影响现金流风险;投资性房地产和长期金融股权投资未显著影响现金流风险。考虑企业生命周期后发现,成长期与衰退期企业金融资产配置与现金流风险呈U型关系,成熟期企业金融资产配置负向影响现金流风险;按照产权性质分组检验发现,金融资产配置与现金流风险的关系以及金融杠杆的调节效应在非国有企业中更显著;机制检验发现,非效率资本配置在金融资产配置影响现金流风险的过程中发挥中介作用。     

Spatial spillover effects and risk contagion around G20 stock markets based on volatility network

Employing the spatial econometric model as well as the complex network theory, this study investigates the spatial spillovers of volatility among G20 stock markets and explores the influential factors of financial risk. To achieve this objective, we use GARCH-BEKK model to construct the volatility network of G20 stock markets, and calculate the Bonacich centrality to capture the most active and influential nodes. Finally, we innovatively use the volatility network matrix as spatial weight matrix and establish spatial Durbin model to measure the direct and spatial spillover effects. We highlight several key observations: there are significant spatial spillover effects in global stock markets; volatility spillover network exists aggregation effects, hierarchical structure and dynamic evolution features; the risk contagion capability of traditional financial power countries falls, while that of “financial small countries” rises; stock market volatility, government debt and inflation are positively correlated with systemic risk, while current account and macroeconomic performance are negatively correlated; the indirect spillover effects of all explanatory variables on systemic risk are greater than the direct spillover effects.     

基于极值分布理论的VaR与ES度量

本文应用极值分布理论对金融收益序列的尾部进行估计,计算收益序列的在险价值VaR和预期不足ES来度量市场风险。通过伪最大似然估计方法估计的GARCH模型对收益数据进行拟合,应用极值理论中的GPD对新息分布的尾部建模,得到了基于尾部估计产生收益序列的VaR和ES值。采用上证指数日对数收益数据为样本,得到了度量条件极值和无条件极值下VaR和ES的结果。实证研究表明:在置信水平很高(如99%)的条件下,采用极值方法度量风险值效果更好。而置信水平在95%下,其他方法和极值方法结合效果会很好。用ES度量风险能够使我们了解不利情况发生时风险的可能情况。     

Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation

Motivated by the need for a positive‐semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra‐high‐frequency asset prices in a state‐space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and expectation maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive‐semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations that mimic the liquidity and market microstructure characteristics of the S&P 500 universe as well as in a high‐dimensional application on US stocks. KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix

This paper considers spatial heteroskedasticity and autocorrelation consistent (spatial HAC) estimation of covariance matrices of parameter estimators. We generalize the spatial HAC estimator introduced by Kelejian and Prucha (2007) to apply to linear and nonlinear spatial models with moment conditions. We establish its consistency, rate of convergence and asymptotic truncated mean squared error (MSE). Based on the asymptotic truncated MSE criterion, we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug-in method. The finite sample performances of the spatial HAC estimator are evaluated via Monte Carlo simulation.     

Modeling the conditional distribution of financial returns with asymmetric tails

This paper proposes a conditional density model that allows for differing left/right tail indices and time-varying volatility based on the dynamic conditional score (DCS) approach. The asymptotic properties of the maximum likelihood estimates are presented under verifiable conditions together with simulations showing effective estimation with practical sample sizes. It is shown that tail asymmetry is prevalent in global equity index returns and can be mistaken for skewness through the center of the distribution. The importance of tail asymmetry for asset allocation and risk premia is demonstrated in-sample. Application to portfolio construction out-of-sample is then considered, with a representative investor willing to pay economically and statistically significant management fees to use the new model instead of traditional skewed models to determine their asset allocation.     

Forecasting stock market volatility: Can the risk aversion measure exert an important role?

In this paper, we predict realized volatility of stock return by utilizing time-varying risk aversion based on a simple linear autoregressive model. Our in-sample results suggest that time-varying risk aversion have significant impact for stock return volatility. In terms of out-of-sample forecasting performance, the empirical results indicate that the incorporation of time-varying risk aversion in the benchmark model can yield more accurate stock return volatility forecasts. Notably, the out-of-sample forecasting results confirm that our conclusions are robust when we apply alternative lag orders and alternative prediction evaluation periods. Finally, we study links between the prediction ability of time-varying risk aversion and the volatility of other stock indices and two kinds of crude oil, and find that the new predictor can effectively strengthen forecasting performance in most case. In view of the importance of volatility risk in the asset pricing process, our research is of great significance for financial asset participants.     

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.     

Minimax robust designs for field experiments

Experimental designs for field experiments are useful in planning agricultural experiments, environmental studies, etc. Optimal designs depend on the spatial correlation structures of field plots. Without knowing the correlation structures exactly in practice, we can study robust designs. Various neighborhoods of covariance matrices are introduced and discussed. Minimax robust design criteria are proposed, and useful results are derived. The generalized least squares estimator is often more efficient than the least squares estimator if the spatial correlation structure belongs to a small neighborhood of a covariance matrix. Examples are given to compare robust designs with optimal designs. The work was partially supported by research grants from the Natural Science and Engineering Research Council of Canada.     

Optimizing the spatial assignment of schools to reduce both inequality of educational opportunity and potential opposition rate through introducing random mechanism into proximity-based system

A serious spatial inequality of educational opportunity was revealed worldwide, for wealthy families can access good schools by buying real estate with good school' enrollment quota. Although the existing studies had revealed that random-based school assignment can significantly improve equality of opportunity allocation, random mechanism was adopted only in few places. Two major resistances of introducing random mechanism exist: the possibility of increased commuting distance to schools and the effected relative beneficiaries. In order to make the random-based allocation more feasible, this study proposes a spatial optimization model to take these two factors into account into proximity-based school assignment system. The proposed multi-objective allocation model, with the constraint conditions of assigning students to 3 closest schools and school capacities, was developed in this study to minimize the spatial disparity of educational opportunity and the potential opposition rate of introducing random mechanism into proximity-based assignment system. The model will be solved by a heuristic algorithm and applied to a case study area of Shijingshan District, Beijing. The results showed that the proposed model could improve spatial equality of educational opportunity significantly, but along with a minor increase on commuting distance to schools. In addition, potential opponents of introducing random mechanism decrease as the weight of parameters related to opposition rate increases in the model, reducing nearly 10% in the best case. Therefore, the solutions provided by proposed model may encounter less resistance in a democratic voting system. However, the results also indicated that there would be some relative beneficiaries who may oppose introducing random mechanism into proximity-based school system even in the best case. This implies that, to achieve equal educational opportunity in the context of proximity-based school system, optimized allocation is needed along with a more even distribution of educational resources.     

Asset allocation and multivariate position based trading

I add a second risky asset and a risk free bond to the univariate artificial market investigated by Lux and Marchesi (Int J Theor Appl Finance 3(4):675–702, 2000), keeping track of traders aggregate positions and wealth. Asset allocation and security selection are modeled as separate decision processes, as is common practice in financial institutions. Introducing position based trading avoids inconsistencies in traders inventories resulting from the order based setup of the original model, while preserving its ability to reproduce the stylized facts of financial return series.      

Predictability of stock returns and asset allocation under structural breaks

This paper adopts a new approach that accounts for breaks to the parameters of return prediction models both in the historical estimation period and at future points. Empirically, we find evidence of multiple breaks in return prediction models based on the dividend yield or a short interest rate. Our analysis suggests that model instability is a very important source of investment risk for buy-and-hold investors with long horizons and that breaks can lead to a negative slope in the relationship between the investment horizon and the proportion of wealth that investors allocate to stocks. Once past and future breaks are considered, an investor with medium risk aversion reduces the allocation to stocks from close to 100% at short horizons to 10% at the five-year horizon. Welfare losses from ignoring breaks can amount to several hundred basis points per year for investors with long horizons.     

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.     

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.     

Forecasting volatility with time-varying leverage and volatility of volatility effects

Predicting volatility is of primary importance for business applications in risk management, asset allocation, and the pricing of derivative instruments. This paper proposes a measurement model that considers the possibly time-varying interaction of realized volatility and asset returns according to a bivariate model to capture its major characteristics: (i) the long-term memory of the volatility process, (ii) the heavy-tailedness of the distribution of returns, and (iii) the negative dependence of volatility and daily market returns. We assess the relevance of the effects of “the volatility of volatility” and time-varying “leverage” to the out-of-sample forecasting performance of the model, and evaluate the density of forecasts of market volatility. Empirical results show that our specification can outperform the benchmark HAR–GARCH model in terms of both point and density forecasts.