Multivariate Modelling of 10-Day-Ahead VaR and Dynamic Correlation for Worldwide Real Estate and Stock Indices

Abstract

The Basel Committee regulations require the estimation of Value-at-Risk at 99% confidence level for a 10-trading-day-ahead forecasting horizon. The paper provides a multivariate modelling framework for multi-period VaR estimates for leptokurtic and asymmetrically distributed real-estate portfolio returns. The purpose of the paper is to estimate accurate 10-day-ahead 99% VaR forecasts for real estate markets along with stock markets for seven countries across the world (USA, UK, GERMANY, JAPAN, AUSTRALIA, HONG KONG and SINGAPORE) following the Basel Committee requirements for financial regulation.

A fourteen-dimensional multivariate Diag-VECH model for seven equity indices and their relative real estate indices is estimated. We evaluate the VaR forecasts over a period of two weeks in calendar time, or 10 trading days, and at 99% confidence level based on the Basle Committee on Banking Supervision requirements.

The Basel regulations require 10-day-ahead 99% VaR forecasts. This is the first study that provides successful evidence for 10-day-ahead 99% VaR estimations for real estate markets. Additionally, we provide evidence that there is a statistically significant relationship between the magnitude of the 10-day-ahead 99%VaR and the level of dynamic correlation for real estate and stock market indices; a valuable recommendation for risk managers who forecast risk across markets.

Risk managers, investors and financial institutions require dynamic multi-period VaR forecasts that will take into account properties of financial time series. Such accurate dynamic forecasts lead to successful decisions for controlling market risks.

Keywords: Basel Committee Requirements, Diag-VECH, Dynamic Correlation, Local Correlation Predictive Power, Multivariate ARCH, Risk Management, Real Estate Market, Value-at-Risk, Multi-Period Volatility Forecasting

JEL Classification: G1, C4, C5