Granularity Adjustment for Efficient Portfolios

This article considers large portfolios of assets submitted to both systematic and unsystematic (or idiosyncratic) risks. The idiosyncratic risks can be fully diversified if the portfolio size is infinite, but only partly diversified otherwise. The granularity adjustment measures the effect of partly diversifying idiosyncratic risks. We derive the granularity adjustments for a portfolio with naive diversification and for the efficient mean-variance portfolio allocation. We consider in particular the Sharpe performances, with and without short-sale restrictions and we highlight the effect of concentration risk.     

How risky is the optimal portfolio which maximizes the Sharpe ratio?

In this paper, we investigate the properties of the optimal portfolio in the sense of maximizing the Sharpe ratio (SR) and develop a procedure for the calculation of the risk of this portfolio. This is achieved by constructing an optimal portfolio which minimizes the Value-at-Risk (VaR) and at the same time coincides with the tangent (market) portfolio on the efficient frontier which is related to the SR portfolio. The resulting significance level of the minimum VaR portfolio is then used to determine the risk of both the market portfolio and the corresponding SR portfolio. However, the expression of this significance level depends on the unknown parameters which have to be estimated in practice. It leads to an estimator of the significance level whose distributional properties are investigated in detail. Based on these results, a confidence interval for the suggested risk measure of the SR portfolio is constructed and applied to real data. Both theoretical and empirical findings document that the SR portfolio is very risky since the corresponding significance level is smaller than 90 % in most of the considered cases.     

High-dimensional Markowitz portfolio optimization problem: empirical comparison of covariance matrix estimators

We compare the performance of recently developed regularized covariance matrix estimators for Markowitz's portfolio optimization and of the minimum variance portfolio (MVP) problem in particular. We focus on seven estimators that are applied to the MVP problem in the literature; three regularize the eigenvalues of the sample covariance matrix, and the other four assume the sparsity of the true covariance matrix or its inverse. Comparisons are made with two sets of long-term S&P 500 stock return data that represent two extreme scenarios of active and passive management. The results show that the MVPs with sparse covariance estimators have high Sharpe ratios but that the naive diversification (also known as the ‘uniform (on market share) portfolio’) still performs well in terms of wealth growth.     

On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio

We consider the problem of estimating the portfolio weights obtained by maximizing the Sharpe ratio. Assuming that the underlying asset returns are independent and multivariate normally distributed, Okhrin and Schmid (J. Econom. 134:235–256, 2006) showed that the frequently used sample estimators of these weights do not have a first moment. This paper proves that an unbiased estimator of the Sharpe ratio portfolio weights does not exist at all. Moreover, we show that there is no asymptotically unbiased estimator of these weights within the family of estimators which are bounded by cylinder functions.     

金融危机传染效应的资产动态组合视角解析

由金融危机三阶段视角透视跨国投资组合供需动态变化过程中金融危机的传染特性。以跨国投资者投资决策与投资业绩互动为突破点,剖析在金融危机三阶段内调整跨国资产组合配置的微观交易行为所引致的金融危机传染性。经由9个国家金融危机期间基金交易数据的计量检验得出：金融危机中跨国投资者资产组合再分配是金融危机重要的传染渠道;与金融危机发源国分享风险偏好型跨国投资者的国家最容易被危机感染;金融危机三阶段传染效应的强度呈动态变化;金融市场上投资者的信息搜集在化解市场风险方面具有重要作用。     

零息收益率曲线期限结构变化的主成分分析

文章认为运用主成分分析方法能极大地简化对利率曲线变化的分析,便于准确了解利率曲线结构变动的模式。同时运用主成分分析方法能为金融机构计算投资组合资产VaR提供切实可行的方法,为金融机构风险管理提供依据。     

A descent algorithm for constrained LAD-Lasso estimation with applications in portfolio selection

To improve the out-of-sample performance of the portfolio, Lasso regularization is incorporated to the Mean Absolute Deviance (MAD)-based portfolio selection method. It is shown that such a portfolio selection problem can be reformulated as a constrained Least Absolute Deviance problem with linear equality constraints. Moreover, we propose a new descent algorithm based on the ideas of ‘nonsmooth optimality conditions’ and ‘basis descent direction set’. The resulting MAD-Lasso method enjoys at least two advantages. First, it does not involve the estimation of covariance matrix that is difficult particularly in the high-dimensional settings. Second, sparsity is encouraged. This means that assets with weights close to zero in the Markovwitz's portfolio are driven to zero automatically. This reduces the management cost of the portfolio. Extensive simulation and real data examples indicate that if the Lasso regularization is incorporated, MAD portfolio selection method is consistently improved in terms of out-of-sample performance, measured by Sharpe ratio and sparsity. Moreover, simulation results suggest that the proposed descent algorithm is more time-efficient than interior point method and ADMM algorithm.     

Latent class models for financial data analysis: some statistical developments

I exploit the potential of latent class models for proposing an innovative framework for financial data analysis. By stressing the latent nature of the most important financial variables, expected return and risk, I am able to introduce a new methodological dimension in the analysis of financial phenomena. In my proposal, (i) I provide innovative measures of expected return and risk, (ii) I suggest a financial data classification consistent with the latent risk-return profile, and (iii) I propose a set of statistical methods for detecting and testing the number of groups of the new data classification. The results lead to an improvement in both risk measurement theory and practice and, if compared to traditional methods, allow for new insights into the analysis of financial data. Finally, I illustrate the potentiality of my proposal by investigating the European stock market and detailing the steps for the appropriate choice of a financial portfolio.     

Statistical Inference for High‐Dimensional Global Minimum Variance Portfolios

Many studies demonstrate that inference for the parameters arising in portfolio optimization often fails. The recent literature shows that this phenomenon is mainly due to a high‐dimensional asset universe. Typically, such a universe refers to the asymptotics that the sample size n + 1 and the sample dimension d both go to infinity while d ∕ n → c ∈ (0,1). In this paper, we analyze the estimators for the excess returns’ mean and variance, the weights and the Sharpe ratio of the global minimum variance portfolio under these asymptotics concerning consistency and asymptotic distribution. Problems for stating hypotheses in high dimension are also discussed. The applicability of the results is demonstrated by an empirical study. Copyright © 2014 John Wiley & Sons, Ltd.     

Common-factor stochastic volatility modelling with observable proxy

Multi-asset modelling is of fundamental importance to financial applications such as risk management and portfolio selection. In this article, we propose a multivariate stochastic volatility modelling framework with a parsimonious and interpretable correlation structure. Building on well-established evidence of common volatility factors among individual assets, we consider a multivariate diffusion process with a common-factor structure in the volatility innovations. Upon substituting an observable market proxy for the common volatility factor, we markedly improve the estimation of several model parameters and latent volatilities. The model is applied to a portfolio of several important constituents of the S&P500 in the financial sector, with the VIX index as the common-factor proxy. We find that the prediction intervals for asset forecasts are comparable to those of more complex dependence models, but that option-pricing uncertainty can be greatly reduced by adopting a common-volatility structure. The Canadian Journal of Statistics 48: 36–61; 2020 © 2020 Statistical Society of Canada     

Adjusted empirical likelihood for value at risk and expected shortfall

Value at risk (VaR) and expected shortfall (ES) are widely used risk measures of the risk of loss on a specific portfolio of financial assets. Adjusted empirical likelihood (AEL) is an important non parametric likelihood method which is developed from empirical likelihood (EL). It can overcome the limitation of convex hull problems in EL. In this paper, we use AEL method to estimate confidence region for VaR and ES. Theoretically, we find that AEL has the same large sample statistical properties as EL, and guarantees solution to the estimating equations in EL. In addition, simulation results indicate that the coverage probabilities of the new confidence regions are higher than that of the original EL with the same level. These results show that the AEL estimation for VaR and ES deserves to recommend for the real applications.     

GSH Dependence Modeling with an Application to Risk Management

The generalized secant hyperbolic distribution (GSH) can be used to represent financial data with heavy tails as an alternative to the Student-t, because it guarantees the existence of all moments, also with a high kurtosis value. In order to obtain a multivariate extension of the GSH distribution, in this article we present two approaches to model the dependence, the copula approach and independent component analysis. Since the methodologies considered allow to simulate the GSH dependence, we show also the empirical results obtained in the estimation of risk of a financial portfolio by the Monte Carlo method.     

Production Frontiers and Panel Data

Value at risk (VaR) is the standard measure of market risk used by financial institutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, the conditional autoregressive value at risk (CAViaR) model specifies the evolution of the quantile over time using an autoregressive process and estimates the parameters with regression quantiles. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the dynamic quantile test. Applications to real data provide empirical support to this methodology.     

我国保险投资组合的模拟和金融风险测量研究

 本文利用Copula函数的概念研究了保险投资组合多元金融数据的统计模拟。根据我国保险投资的特殊性，我们选用沪深300指数、基金指数、企债指数和国债指数四种风险资产来模拟保险投资组合中的股票、基金、企债和国债收益。基于模拟的结果分别利用传统近似方法（Add-VaR、N-VaR和H-VaR）和Copula方法计算了投资组合的总风险；相对于Copula-VaR方法，Add-VaR显著高估了风险，N-VaR显著低估了风险，H-VaR对于Copula-VaR的近似效果比较好，但其也高估了风险，即H-VaR相对于Copula-VaR是一种比较保守的方法。另外，我们分析了投资组合权重变化和Copula函数的选择对投资组合总风险的影响。     

A comparison of risk transfer strategies for a portfolio of life annuities based on RORAC

This paper aims to compare different reinsurance arrangements in order to reduce the longevity and financial risk originated by a life insurer while managing a portfolio of annuities policies. Linear and nonlinear reinsurance strategies as well as swap like agreements are evaluated via a discrete-time actuarial risk model. Specifically, longevity dynamics are represented by Lee–Carter type models, while interest rate is modeled by Cox–Ingersoll–Ross model. The reinsurance strategies effectiveness is evaluated according to the Return on Risk Adjusted Capital under a ruin probability constrain.     

基于小波多分辨分析的高阶矩CAPM

 为改进传统Beta系数测量系统风险的不足，反映系统风险的动态特征，讨论了四阶矩的资本资产定价模型(CAPM)并将小波分析引入到高阶矩CAPM研究中。利用小波多分辨分析的特点，给出了小波高阶中心矩和高阶混合中心矩的定义，基于此给出了多分辨系统风险测度Beta、Gamma、Theta的计算方法和多分辨CAPM，并从行为金融理论出发，给出多分辨高阶矩CAPM的金融背景解释。实证结果支持了多分辨系统风险假说和多分辨高阶矩CAPM的成立，为构建动态投资组合分散金融风险的动态影响提供了证据。     

基于贝叶斯方法的信用评级模型构建与违约概率估计

以贝叶斯方法为基础构建了信用评级和违约概率模型,指出金融机构利用已有评级信息提高债务人信用风险评估准确性的途径,并以单个债务人违约概率度量方法和Merton理论为基础,考虑异质性导致的宏观经济冲击对债务人的不同影响,度量资产组合违约风险。利用相关数据对贝叶斯模型应用给出例证,结果表明贝叶斯方法具有更为灵活的框架和较好的预测能力。     

Robust bootstrap densities for dynamic conditional correlations: implications for portfolio selection and Value-at-Risk

ABSTRACT

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions depend on the forecasts covariance matrix little is known about effects of outliers on the uncertainty associated with these forecasts. In this paper we analyse these effects on the context of dynamic conditional correlation models when the uncertainty is measured using bootstrap methods. We also propose a bootstrap procedure to obtain forecast densities for return, volatilities, conditional correlation and Value-at-Risk that is robust to outliers. The results are illustrated with simulated and real data.     

Multiple Regression Model Averaging and the Focused Information Criterion With an Application to Portfolio Choice

ABSTRACT

We consider multiple regression (MR) model averaging using the focused information criterion (FIC). Our approach is motivated by the problem of implementing a mean-variance portfolio choice rule. The usual approach is to estimate parameters ignoring the intention to use them in portfolio choice. We develop an estimation method that focuses on the trading rule of interest. Asymptotic distributions of submodel estimators in the MR case are derived using a localization framework. The localization is of both regression coefficients and error covariances. Distributions of submodel estimators are used for model selection with the FIC. This allows comparison of submodels using the risk of portfolio rule estimators. FIC model averaging estimators are then characterized. This extension further improves risk properties. We show in simulations that applying these methods in the portfolio choice case results in improved estimates compared with several competitors. An application to futures data shows superior performance as well.     

基于高维波动率网络模型的股票市场风险特征研究

波动率是金融风险管理研究的重要内容之一。本文基于复杂网络理论和数据挖掘技术提出股票市场的高维波动率网络模型。首先运用互信息度量不同股票价格波动之间的相关关系,其次对股票市场不同周期下的波动情况建立度的中心势、平均距离、幂律分布等网络拓扑指标,再次根据这些指标利用Prim算法构建出高维波动率网络模型,最后运用Newman-Girvan算法对股票价格波动率的相关性进行分层研究。高维波动率网络模型突破了传统波动率模型关于变量维数的限制,能够在依赖少量假设的基础上,挖掘出多个金融市场主体间的相互关系,反映金融市场的风险特征及网络拓扑性质。实证结果发现：与常用的Pearson相关系数法相比,在互信息框架下,股价波动的非线性相关关系得到了更好的度量;股票市场的整体波动性与个股波动率相关性变化趋势相反,市场处在高波动时期资产组合分散化效果较好;网络中存在少量度数大的关键节点和中心节点,风险通过这些节点可以迅速传递到整个市场;股票市场的运行具有明显的行业聚集现象;网络分层研究进一步直观的展现了风险在层与层之间的传递规律和与之对应的行业特征。高维波动率网络模型为挖掘股票市场的风险特征与管理金融风险提供了一个新的工具。