The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.     

Granger causality in risk and detection of extreme risk spillover between financial markets

Controlling and monitoring extreme downside market risk are important for financial risk management and portfolio/investment diversification. In this paper, we introduce a new concept of Granger causality in risk and propose a class of kernel-based tests to detect extreme downside risk spillover between financial markets, where risk is measured by the left tail of the distribution or equivalently by the Value at Risk (VaR). The proposed tests have a convenient asymptotic standard normal distribution under the null hypothesis of no Granger causality in risk. They check a large number of lags and thus can detect risk spillover that occurs with a time lag or that has weak spillover at each lag but carries over a very long distributional lag. Usually, tests using a large number of lags may have low power against alternatives of practical importance, due to the loss of a large number of degrees of freedom. Such power loss is fortunately alleviated for our tests because our kernel approach naturally discounts higher order lags, which is consistent with the stylized fact that today’s financial markets are often more influenced by the recent events than the remote past events. A simulation study shows that the proposed tests have reasonable size and power against a variety of empirically plausible alternatives in finite samples, including the spillover from the dynamics in mean, variance, skewness and kurtosis respectively. In particular, nonuniform weighting delivers better power than uniform weighting and a Granger-type regression procedure. The proposed tests are useful in investigating large comovements between financial markets such as financial contagions. An application to the Eurodollar and Japanese Yen highlights the merits of our approach.     

Coherent risk measures in general economic models and price bubbles

In this article we study coherent risk measures in general economic models where the set of financial positions is an ordered Banach space E$E$ and the safe asset an order unit _x0$x_0$ of E$E$. First we study some properties of risk measures. We show that the set of normalized (with respect to _x0$x_0$) price systems is weak star compact and by using this result we prove a maximum attainment representation theorem which improves the one of Jaschke and Küchler (2001). Also we study how a risk measure changes under different safe assets and we show a kind of equivalence between these risk measures. In the sequel we study subspaces of E$E$ consisting of financial positions of risk greater or equal to zero and we call these subspaces unsure. We find some criteria and we give examples of these subspaces. In the last section, we combine the unsure subspaces with the theory of price-bubbles of Gilles and LeRoy (1992).     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.