Evarist Stoja

A Simplified Approach to Modelling the Comovement of Asset Returns

This paper proposes a simplified multivariate GARCH model that involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The model that we propose is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. We use the simplified multivariate GARCH model to estimate the minimum-variance hedge ratio for the FTSE 100 index portfolio, hedged using index futures, and compare it to four of the most widely used multivariate GARCH models. The simplified multivariate GARCH model performs at least as well as the other models that we consider, and in some cases better than them.

Multidimensional Risk and Risk Dependence

Evaluating multiple sources of risk is an important problem with many applications in finance and economics. In practice this evaluation remains challenging. We propose a simple non-parametric framework with several economic and statistical applications. In an empirical study, we illustrate the flexibility of our technique by applying it to the evaluation of multidimensional density forecasts, multidimensional Value at Risk and dependence in risk.

Incorporating Higher Moments into Value at Risk Estimation

Value-at-Risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a new simple approach to estimation of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with time-varying higher moments. We allow the first four moments of the GCE to depend on past information, which leads to a more accurate approximation of the tails of the distribution. The results unambiguously show that our GCE-based VaR forecasts provide accurate and robust estimates of the realised VaR, outperforming those generated by the constant-higher-moments models.

Systematic Tail Risk

We propose new systematic tail risk measures constructed using two different approaches. The first extends the canonical downside beta and co-moment measures, while the second is based on the sensitivity of stock returns to innovations in market crash risk. Both tail risk measures are associated with a significantly positive risk premium after controlling for other measures of downside risk, including downside beta, co-skewness and co-kurtosis. Using these measures, we examine the relevance of the tail risk premium for investors with different investment horizons.

Extreme Downside Risk and Financial Crises

We investigate the dynamics of the relationship between returns and extreme downside risk in different states of the market by combining the framework of Bali, Demirtas, and Levy (2009) with a Markov switching mechanism. We show that the risk-return relationship identified by Bali, Demirtas, and Levy (2009) is highly significant in the low volatility state but disappears during periods of market turbulence. This is puzzling since it is during such periods that downside risk should be most prominent. We show that the absence of the risk-return relationship in the high-volatility state is due to leverage and volatility feedback effects arising from increased persistence in volatility. To better filter out these effects, we propose a simple modification that yields a positive tail risk-return relationship under all states of market volatility.

Extreme Risk Interdependence

Tail interdependence is defined as the situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multi-information to quantify tail interdependence at different levels of extremity, decompose it into systemic and residual part and measure the contribution of a constituent to the interdependence of a system. Further, we devise statistical procedures to test: a) tail independence; b) whether an empirical interdependence structure is generated by a theoretical model; and c) symmetry of the interdependence structure in the tails. The application of this approach to multidimensional financial data confirms some known and uncovers new stylized facts on extreme returns.

Day-of-the-Month Effects in the Performance of Momentum Trading Strategies in the Foreign Exchange Market

This article documents a very strong day-of-the-month effect in the performance of momentum strategies in the foreign exchange market. It shows that this seasonality in trading strategy performance is attributable to seasonality in the conditional volatility of foreign exchange returns, and in the volatility of conditional volatility. Indeed, a two-factor model employing conditional volatility and the volatility of conditional volatility explains as much as 70% of the intra-month variation in the Sharpe ratio. The article further shows that the seasonality in volatility is in turn closely linked to the pattern of U.S. macroeconomic news announcements, which tend to be clustered around certain days of the month.