Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

Shuangzhe Liu,Tiefeng Ma,Ruili Sun,Milind Sathye

doi:10.3390/jrfm12010048

Shuangzhe Liu, Tiefeng Ma + Show 2 more

Open Access

https://doi.org/10.3390/jrfm12010048

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Abstract

The literature on portfolio selection and risk measurement has considerably advanced in recent years. The aim of the present paper is to trace the development of the literature and identify areas that require further research. This paper provides a literature review of the characteristics of financial data, commonly used models of portfolio selection, and portfolio risk measurement. In the summary of the characteristics of financial data, we summarize the literature on fat tail and dependence characteristic of financial data. In the portfolio selection model part, we cover three models: mean-variance model, global minimum variance (GMV) model and factor model. In the portfolio risk measurement part, we first classify risk measurement methods into two categories: moment-based risk measurement and moment-based and quantile-based risk measurement. Moment-based risk measurement includes time-varying covariance matrix and shrinkage estimation, while moment-based and quantile-based risk measurement includes semi-variance, VaR and CVaR.

Highlights

This paper is motivated by three stylized facts about the operation of real-world financial markets
Asai (2008) studied two models for describing fat tail and volatility dependence: autoregressive stochastic volatility model with Student t distribution (ARSV-T) and multifactor stochastic volatility (MFSV) model, and the results showed that ARSV-T model provided a better fit than MFSV model based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)
Lioui and Poncet (2016) proposed a new portfolio decomposition formula to reveal the economics of investor portfolio selection according to the mean-variance criterion and noted that the number of components of the dynamic portfolio strategy could be reduced to two: the first was to hedge the risk of discounted bonds maturing within the investor’s time limit without preference, while the second was to hedge against time variation in pseudo relative risk tolerance

Summary

Introduction

This paper is motivated by three stylized facts about the operation of real-world financial markets. Considering the difference between multivariate normal distribution and multivariate t distribution in the description of market risk factors, Albanese and Campolieti (2006) proposed the probability density function for calculating the change of option portfolio value and the Monte Carlo simulation method for estimating the multivariate VaR at a given confidence level and explored the relationship between a normal distribution and a fat tail distribution. Lafosse and Rodríguez (2018) combined stochastic volatility model with GH Skew Student t distribution to characterize the skewness and fat tail of financial data and showed the evidence of asymmetries and heavy tails of daily stocks returns data. Gunay and Khaki (2018) noted that capturing conditional distributions, fat tails and price spikes was the key to measuring risk and accurately simulating and predicting the volatility of energy futures These researchers tried to model the volatility of energy futures under different distributions

The Dependence of Financial Data

Portfolio Selection: A Review of Common Models

Mean-Variance Model

Global Minimum Variance Model

Factor Model

Single Factor Models

Multi-Factor Models

Portfolio Risk Measure

Time-Varying Covariance Matrix

Shrinkage Estimation

VaR and CVaR

Findings