Contributions published at Empirical Finance (Marc Paolella)

A fast method for estimating the parameters of a stable-APARCH not requiring likelihood or iteration is proposed. Several powerful tests for the (asymmetric) stable Paretian distribution with tail index 1<α<2 are used for assessing the appropriateness of the stable assumption as the innovations process in stable-GARCH-type models for daily stock returns. Overall, there is strong evidence against the stable as the correct innovations assumption for all stocks and time periods, though for many stocks and windows of data, the stable hypothesis is not rejected.

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A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time tt is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration.

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Several graphical methods for testing univariate composite normality from an i.i.d. sample are presented. They are endowed with correct simultaneous error bounds and yield size-correct tests. As all are based on the empirical CDF, they are also consistent for all alternatives. For one test, called the modified stabilized probability test, or MSP, a highly simplified computational method is derived, which delivers the test statistic and also a highly accurate p-value approximation, essentially instantaneously. The MSP test is demonstrated to have higher power against asymmetric alternatives than the well-known and powerful Jarque-Bera test. A further size-correct test, based on combining two test statistics, is shown to have yet higher power. The methodology employed is fully general and can be applied to any i.i.d. univariate continuous distribution setting.

Review of asset allocation techniques: what does one century of historical data suggest? The purpose of this paper is to shed some light on the different approaches and to find out the most appropriate one in the context of Asset and Liability Management (ALM) for insurance companies, through an extensive backtesting exercise using one century of historical data. In order to address weaknesses in the Markowitz optimization approach, some portfolio construction techniques which disregard the assets expected returns and only focus on the assets volatilities have been developed. These techniques are also known as risk-based allocations. In this paper we study under which conditions risk-based allocations would outperform the mean-variance approach and show that in disagreement with the recent literature, which advocates in favour of the risk-based allocation, we find that the mean-variance portfolio is still the best performing one. Risky asset allocation across the cycle from the perspective of insurance asset management The allocation of risky assets through the business cycle is one of the key questions raised to an insurance company. Utilizing 40 years of historical data, two investment approaches are compared: A static approach targeting a long-term stable allocation to investment risks, and a dynamic approach which rebalances the allocation to investment risks over time. The analysis of the two approaches is performed under the assumption of efficient markets, i.e. no outperformance due to market insight is considered. The two approaches show entirely different asset allocation behaviours over the cycle. In terms of performance, there is no clear preference. Benefits for both strategies are identified. Empirical investigation of CO2 Emission prices and their supposed Economic Drivers In this paper we intend to study the dependence between the emission allowances and some supposed price drivers. In particular, we would like to verify if the prices of the emission allowances are influenced by the prices of coal, gas and crude oil. First we identify the relevant prices among the different indexes available. Then we try to explain the fundamental relationships between the different time series, showing some trading strategies and non-arbitrage arguments. In the second part of the paper, we conduct a statistical analysis of the returns based on univariate and multivariate GARCH models. In addition to measuring dependence through standard univariate measures, we check whether the information included in a multivariate dataset leads to more accurate forecasts for the emission allowances series. We find that the information carried by the supposed drivers does not greatly increase the predictive power when used in traditional multivariate models, but a fundamental trading strategy indicates some potential influence. Überprüfung von Asset Allocation Strategien: Was kann man aus den historischen Daten eines Jahrhunderts ableiten? Im vorliegenden Artikel untersuchen wir verschiedene Asset Allocation Strategien und versuchen mit Hilfe einer umfangreichen Backtesting-Übung, welche historische Daten eines Jahrhunderts auswertet, den für Versicherungsunternehmen am besten geeignete Ansatz für das Asset and Liability Management (ALM) zu finden. Um Schwachstellen im Markowitz-Optimierungsansatz zu umgehen wurden einige Portfolio-Bautechniken entwickelt, welche die Erwartungswerte der Kapitalanlagen ausser Achtlassen und sich nur auf die Volatilitäten konzentrieren. Diese Techniken werden auch als risikoorientierte Allokationen bezeichnet. Mit dieser Arbeit untersuchen wir, unter welchen Bedingungen risikobasierte Allokationen das Mittelwert-Varianz Portfolio übertreffen und zeigen auf, dass in Abweichung von der neueren Literatur, welche die risikoorientierte Allokation favorisiert, das Mittelwert-Varianz Portfolio immer noch die beste Leistung erbringt. Risikobereitschaft über den Zyklus aus der Perspektive des Versicherungs-Asset-Managements Die Verteilung von risikobehafteten Vermögenswerten über den Konjunkturzyklus ist eine der Schlüsselfragen für ein Versicherungsunternehmen. Mit Hilfe von historischen Daten der letzten 40 Jahre werden zwei Investitionsansätze verglichen: ein statischer Ansatz, der auf eine langfristig stabile Allokation der Anlagerisiken abzielt und einen dynamischen Ansatz, der die Allokation der Anlagerisiken über die Zeit verteilt. Die Analyse der beiden Ansätze wird unter der Annahme effizienter Märkte durchgeführt, d.h. es wird keine Outperformance aufgrund der Marktbeobachtung in Betracht gezogen. Die beiden Ansätze zeigen völlig unterschiedliche Asset Allocation Verhaltensweisen über den Zyklus. Hinsichtlich der Leistung gibt es keine eindeutige Präferenz. Die Vorteile für beide Strategien werden identifiziert. Empirische Untersuchung der CO2-Emissionspreise und ihrer angeblichen Wirtschaftstreiber In dieser Arbeit wollen wir die Abhängigkeit zwischen den Emissionsberechtigungen und einigen angeblichen Preistreibern untersuchen. Insbesondere möchten wir überprüfen, ob die Preise der Emissionsberechtigungen von den Preisen für Kohle, Gas und Rohöl beeinflusst werden. Zuerst identifizieren wir die relevanten Preise unter den verschiedenen Indizes. Dann versuchen wir die grundlegenden Beziehungen zwischen den verschiedenen Zeitreihen zu erläutern in dem wir einige Handelsstrategien und No-Arbitrage Argumente aufzeigen. Im zweiten Teil der Arbeit führen wir eine statistische Analyse der Renditen auf der Basis von univariaten und multivariaten GARCH-Modellen durch. Zusätzlich zur Messung der Abhängigkeit durch standardisierte univariate Masse prüfen wir, ob die in einem multivariaten Datensatz enthaltenen Informationen zu genaueren Prognosen für die Emissionsberechtigungsreihen führen. Wir finden heraus, dass die von den angeblichen Treibern getragenen Informationen die Vorhersagekraft nicht stark erhöhen, wenn sie in traditionellen multivariaten Modellen verwendet werden, aber eine grundlegende Handelsstrategie weist auf einen potenziellen Einfluss hin.

It is well-known in empirical finance that virtually all asset returns, whether monthly, daily, or intraday, are heavy-tailed and, particularly for stock returns, are mildly but often significantly negatively skewed. However, the tail indices, or maximally existing moments of the returns, can differ markedly across assets. To accommodate these stylized facts when modeling the joint distribution of asset returns, an asymmetric extension of the meta-elliptical t distribution is proposed. While the likelihood is tractable, for high dimensions it will be impractical to use for estimation. To address this, a fast, two-step estimation procedure is developed, based on a saddlepoint approximation to the noncentral Student's t distribution. The model is extended to support a CCC-(I)GARCH structure and demonstrated by modeling and forecasting the return series comprising the DJIA. The techniques of shrinkage, time-varying tail dependence, and weighted likelihood are employed to further enhance the forecasting performance of the model with no added computational burden.

The use of mixture distributions for modeling asset returns has a long history in finance. New methods of demonstrating support for the presence of mixtures in the multivariate case are provided. The use of a two-component multivariate normal mixture distribution, coupled with shrinkage via a quasi-Bayesian prior, is motivated, and shown to be numerically simple and reliable to estimate, unlike the majority of multivariate GARCH models in existence. Equally important, it provides a clear improvement over use of GARCH models feasible for use with a large number of assets, such as constant conditional correlation, dynamic conditional correlation, and their extensions, with respect to out-of-sample density forecasting. A generalization to a mixture of multivariate Laplace distributions is motivated via univariate and multivariate analysis of the data, and an expectation–maximization algorithm is developed for its estimation in conjunction with a quasi-Bayesian prior. It is shown to deliver significantly better forecasts than the mixed normal, with fast and numerically reliable estimation. Crucially, the distribution theory required for portfolio theory and risk assessment is developed.

Simple, fast methods for modeling the portfolio distribution corresponding to a non-elliptical, leptokurtic, asymmetric, and conditionally heteroskedastic set of asset returns are entertained. Portfolio optimization via simulation is demonstrated, and its benefits are discussed. An augmented mixture of normals model is shown to be superior to both standard (no short selling) Markowitz and the equally weighted portfolio in terms of out of sample returns and Sharpe ratio performance.

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A fast method is developed for value-at-risk and expected shortfall prediction for univariate asset return time series exhibiting leptokurtosis, asymmetry and conditional heteroskedasticity. It is based on a GARCH-type process driven by noncentral t innovations. While the method involves the use of several shortcuts for speed, it performs admirably in terms of accuracy and actually outperforms highly competitive models. Most remarkably, this is the case also for sample sizes as small as 250.

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A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. The model is straightforwardly extended to the multivariate setting by using an independent component analysis framework. The tractability of the relevant characteristic function then facilitates portfolio optimization using expected shortfall as the downside risk measure.

The class of mixed normal conditional heteroskedastic (MixN-GARCH) models, which couples a mixed normal distributional structure with GARCH-type dynamics, has been shown to offer a plausible decomposition of the contributions to volatility, as well as excellent out-of-sample forecasting performance, for financial asset returns. In this paper, we generalize the MixN-GARCH model by relaxing the assumption of constant mixing weights. Two different specifications with time--varying mixing weights are considered. In particular, by relating current weights to past returns and realized (component-wise) likelihood values, an empirically reasonable representation of Engle and Ng's (1993) news impact curve with an asymmetric impact of unexpected return shocks on future volatility is obtained. An empirical out-of-sample study confirms the usefulness of the new approach and gives evidence that the leverage effect in financial returns data is closely connected, in a non-linear fashion, to the time--varying interplay of mixture components representing, for example, various groups of market participants.

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