Dynamic Density Forecasts for Multivariate Asset Returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time-varying) non-central co-moments of assets. We estimate the coefficients of the polynomial via the Method of Moments for a carefully selected set of co-moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed technique to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the negative tail of the joint distribution.Time-varying higher co-moments, Joint Density Forecasting, Method of Moments, Multivariate Value-at-Risk.

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts with an Application to Risk Management

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.Multivariate Density Forecast Evaluation, Probability Integral Transformation, Multidimensional Value at Risk, Monte Carlo Simulations

Forecasting multidimensional tail risk at short and long horizons

We define the Multidimensional Value at Risk (MVaR) as a natural generalization of VaR. This generalization makes a number of important applications possible. For example, many techniques developed for VaR can be applied to MVaR directly. As an illustration, we employ VaR forecasting and evaluation techniques. One of our forecasting models builds on the progress made in the volatility literature and decomposes MVaR into long-term trend and short-term cycle components. We compute short- and long-term MVaR forecasts for several multidimensional time series and discuss their (un)conditional accuracy

Extreme risk interdependence

We define tail interdependence as a situation where extreme outcomes for some variables are informative about such outcomes for other variables. We extend the concept of multiinformation to quantify tail interdependence, decompose it into systemic and residual interdependence 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. We outline some additional extensions and illustrate this framework by applying it to several datasets

A Cyclical Model of Exchange Rate Volatility

In this paper, we investigate the long run dynamics of the intraday range of the GBP/USD, JPY/USD and CHF/USD exchange rates. We use a non-parametric filter to extract the low frequency component of the intraday range, and model the cyclical deviation of the range from the long run trend as a stationary autoregressive process. We find that the long run trend is time-varying but highly persistent, while the cyclical component is strongly mean reverting. This has important implications for modelling and forecasting volatility over both short and long horizons. As an illustration, we use the cyclical volatility model to generate out-of-sample forecasts of exchange rate volatility for horizons of up to one year under the assumption that the long run trend is fully persistent. As a benchmark, we compare the forecasts of the cyclical volatility model with those of the two-factor intraday range-based EGARCH model of Brandt and Jones (2006). Not only is the cyclical volatility model significantly easier to estimate than the EGARCH model, but it also offers a substantial improvement in out-of-sample forecast performance.Conditional volatility, Intraday range, Hodrick-Prescott filter

A cyclical model of exchange rate volatility

Draft version issued as working paper by University of Exeter Business School. Final version published by Elsevier. Available online at http://www.journals.elsevier.com/journal-of-banking-and-finance/In this paper, we investigate the long run dynamics of the intraday range of the GBP/USD, JPY/USD and CHF/USD exchange rates. We use a non-parametric filter to extract the low frequency component of the intraday range, and model the cyclical deviation of the range from the long run trend as a stationary autoregressive process. We find that the long run trend is time-varying but highly persistent, while the cyclical component is strongly mean reverting. This has important implications for modelling and forecasting volatility over both short and long horizons. As an illustration, we use the cyclical volatility model to generate out-of-sample forecasts of exchange rate volatility for horizons of up to one year under the assumption that the long run trend is fully persistent. As a benchmark, we compare the forecasts of the cyclical volatility model with those of the two-factor intraday range-based EGARCH model of Brandt and Jones (2006). Not only is the cyclical volatility model significantly easier to estimate than the EGARCH model, but it also offers a substantial improvement in out-of-sample forecast performance

Day-of-the-month effects in the performance of momentum trading strategies in the foreign exchange market

Draft version dated October 2008; due for publication in Journal of Trading, Winter 2009This 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

An unconventional FX tail risk story

We examine how the tail risk of currency returns over the past 20 years were impacted by central bank (monetary and liquidity) measures across the globe with an original and unique dataset that we make publicly available. Using a standard factor model, we derive theoretical measures of tail risks of currency returns which we then relate to the various policy instruments employed by central banks. We find empirical evidence for the existence of a cross-border transmission channel of central bank policy through the FX market. The tail impact is particularly sizeable for asset purchases and swap lines. The effects last for up to 1 month, and are proportionally higher for joint QE actions. This cross-border source of tail risk is largely undiversifiable, even after controlling for the U.S. dollar dominance and the effects of its own monetary policy stance

Extreme downside risk and market turbulence

This is the author accepted manuscript. The final version is available from Taylor & Francis (Routledge) via the DOI in this record.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 riskreturn 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 in all states of market volatility

An unconventional FX tail risk story

We examine how the tail risk of currency returns over the past 20 years were impacted by central bank monetary and liquidity measures across the globe with an original and unique dataset that we make publicly available. Using a standard factor model, we derive theoretical measures of tail risks of currency returns which we then relate to the various policy instruments employed by central banks. We find empirical evidence for the existence of a cross-border transmission channel of central bank policy through the FX market. The tail impact is particularly sizeable for asset purchases and swap lines. The effects last for up to 1 month, and are proportionally higher for joint QE actions. This cross-border source of tail risk is largely undiversifiable, even after controlling for the U.S. dollar dominance and the effects of its own monetary policy stance