Contributions published at Empirical Finance (Marc Paolella)

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In recent years, interest in factor-based investment strategies has grown immensely, and with the rising supply of factor-based exchange traded funds, these strategies are more accessible than ever before. Therefore, knowing about the statistical and distributional characteristics of factor-based investment returns is of great importance not only for academics but also for practitioners. A vast amount of studies research the existence of various statistical properties of nancial asset returns. Properties that are consistent over dierent nancial instruments are commonly referred to as stylized facts. In this thesis, we follow the ndings of Cont (2001), and studies referred to therein, and examine these properties in factor returns. Factor-based investment instruments are an asset class that have not been researched in the named paper. Furthermore, we take a closer look at the distributional characteristics of the factor returns and compare those with three hypothetical distributions; the Gaussian distribution, the Student's t distribution and the normal inverse Gaussian distribution. Additionally, the factors are analysed over two periods; a time of crisis and a time characterized by strong economic growth. Another aim of this thesis is researching and discussing the statistical dierences of the factors and how their statistical properties change over time. Last, we review the ndings and discuss their implication on risk management. We nd evidence that the stylized empirical properties found in the returns of other nancial in- struments also exist in factor-based investment returns. Additionally, we nd some dierences in their statistical characteristics. Furthermore, we nd that the statistical properties signicantly change over time. Finally, we observe that the NIG distribution seems to best reproduce the return distributions of various factors and is therefore well-suited for risk management applications.

A non-Gaussian multivariate regime switching dynamic correlation model for financial asset returns is proposed. It incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns. All model parameters are estimated consistently using a new two-stage expectation–maximization algorithm that also allows for incorporation of shrinkage estimation via quasi-Bayesian priors. It is shown that use of Markov switching correlation dynamics not only leads to highly accurate risk forecasts, but also potentially reduces the regulatory capital requirements during periods of distress. In terms of portfolio performance, the new regime switching model delivers consistently higher Sharpe ratios and smaller losses than the equally weighted portfolio and all competing models. Finally, the regime forecasts are employed in a new dynamic risk control strategy that avoids most losses during the financial crisis and vastly improves risk-adjusted returns.

Covariance matrix forecasts for portfolio optimization have to balance sensitivity to new data points with stability in order to avoid excessive rebalancing. To achieve this, a new robust orthogonal GARCH model for a multivariate set of non-Gaussian asset returns is proposed. The conditional return distribution is multivariate generalized hyperbolic and the dispersion matrix dynamics are driven by the leading factors in a principle component decomposition. Each of these leading factors is endowed with a univariate GARCH structure, while the remaining eigenvalues are kept constant over time. Joint maximum likelihood estimation of all model parameters is performed via an expectation maximization algorithm, and is applicable in high dimensions. The new model generates realistic correlation forecasts even for large asset universes and captures rising pairwise correlations in periods of market distress better than numerous competing models. Moreover, it leads to improved forecasts of an eigenvalue-based financial systemic risk indicator. Crucially, it generates portfolios with much lower turnover and superior risk-adjusted returns net of transaction costs, outperforming the equally weighted strategy even under high transaction fees.

This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate p-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

This Master thesis examines the impact of weather forecasts on energy prices in the United States. For this purpose, ve dierent weather variables are created, their benchmark is a monthly average temperature forecast. The Holt-Winters, rather than the seasonal ARIMA and cumulative average model, provides most accurate predictions. After testing all the in- cluded variables for the presence of a unit root, a robust linear regression model is applied. The study shows that strongest price reactions occur 3 to 7 and 18 to 24 trading days prior to a weather event. Analyses taking into account seasonal weather forecasts further suggest that the heating fuel markets behave Informationally Ecient. Winter temperature condi- tions of the East, rather than the Midwest were found to be strongest correlated with Mont Belvieu Propane prices. Summer temperature conditions of the South region have been found to be most correlated with Henry Hub Natural Gas prices. The price behavior of natural gas, heating oil and propane, spot and future prices can be explained through the immediacy of consumption, or storage respectively. Spot and future prices react strongest to weather condi- tions at the beginning of a season; in November and December for the winter period, June and July for the summer season. A Two-Stage Least Squares analysis using Arctic Oscillation and North Atlantic Oscillation index values as instrumental variables partially conrmed results of the regression analyses.

A mean–variance heterogeneous tails mixture distribution is proposed for modeling financial asset returns. It captures, along with the obligatory leptokurtosis, different tail behavior among the assets. Its construction allows for joint maximum likelihood estimation of all model parameters via an expectation–maximization algorithm and thus is applicable in high dimensions. A useful and unique feature of the model is that the tail behavior of the individual assets is driven by asset-specific news effects. In the bivariate iid case, the model corresponds to the standard CAPM model, but enriched with a filter for capturing the news impact associated with both the market and asset excess returns. An empirical application using a portfolio of highly tail-heterogeneous cryptocurrencies and realistic transaction costs shows superior out-of-sample portfolio performance compared to numerous competing models. A model extension to capture asset-specific asymmetry is also discussed.

A new foreign currency hedging strategy for international investors is motivated and studied. Model-free optimal foreign currency exposures for a risk averse investor are derived. Based on those, and assuming a very flexible non-Gaussian returns model for currency and portfolio returns, we build a dynamic currency hedging strategy. In the context of our model, each element of the vector return at time $t$ is endowed with a common univariate shock, interpretable as a common market factor. It is shown that this mixing random variable plays the role of ambiguity (uncertainty about the return distribution), where its magnitude is expressed through the size of the market factor's conditional variance. Using the derived theoretical model and the proposed dynamic hedging strategy, an out of sample back test on the historical market data is performed. The results show that the approach yields a robust and highly risk reductive hedging strategy, obtainable with low transaction costs.

The choice of optimal currency exposure for a risk and ambiguity averse international investor is derived and studied. Robust mean-variance preferences, explicitly capturing investor’s dislike for model uncertainty, are used in order to derive the model-free optimal currency exposure in the presence of both risk and ambiguity aversion. Additionally, we show that the sample efficient currency demand is found as a vector of generalized ridge regression coefficients of fully hedged portfolio returns on excess currency returns, where the model uncertainty corresponds to the penalty term in the regression. The empirical analysis of the currency hedging strategy is conducted using the foreign exchange, stock, and bond returns over the period 1999 to 2018. We find that the proposed hedging strategy leads to significant improvements of the portfolio performance and examine the effect of model uncertainty on equilibrium currency allocations.

The choice of optimal currency exposure for a risk and ambiguity averse international investor is derived and studied. Robust mean-variance preferences, explicitly capturing investor’s dislike for model uncertainty, are used in order to derive the model-free optimal currency exposure in the presence of both risk and ambiguity aversion. Additionally, we show that the sample efficient currency demand is found as a vector of generalized ridge regression coefficients of fully hedged portfolio returns on excess currency returns, where the model uncertainty corresponds to the penalty term in the regression. The empirical analysis of the currency hedging strategy is conducted using the foreign exchange, stock, and bond returns over the period 1999 to 2018. We find that the proposed hedging strategy leads to significant improvements of the portfolio performance and examine the effect of model uncertainty on equilibrium currency allocations.

We present an application of Independent Component Analysis to financial portfolio allocation based on daily data. The independent components are, like the financial asset returns, time series that exhibit volatility clustering and heavy tails. Unlike the initial set of returns the components are stochastically independent. The scale terms of the independent components are modeled by a GARCH-type process and the innovation sequence is taken to be either (non-Gaussian) stable Paretian or normal inverse Gaussian, depending on the result of a test for the former. The convolutions of stable Paretian and normal inverse Gaussian random variables remain in the domain of attraction of a stable law, thus ensuring a heavy tailed portfolio returns distribution. In particular, even as the number of assets tends towards infinity, the classic central limit theorem is not applicable to the independent components and instead the generalized central limit theorem applies. The portfolio distribution based on risk minimization for a specified target return results from characteristic function inversions and is validated using simulation studies. An empirical example demonstrates the validity of the procedure and presents its advantage over its competitor models.

Countless test statistics can be written as quadratic forms in certain random vectors, or ratios thereof. Consequently, their distribution has received considerable attention in the literature. Except for a few special cases, no closed-form expression for the cdf exists, and one resorts to numerical methods. Traditionally the problem is analyzed under the assumption of joint Gaussianity; the algorithm that is usually employed is that of Imhof (1961). The present manuscript generalizes this result to the case of multivariate generalized hyperbolic (MGHyp) random vectors. The MGHyp is a very flexible distribution which nests, among others, the multivariate t, Laplace, and variance gamma distributions. An expression for the first partial moment is also obtained, which plays a vital role in financial risk management. The proof involves a generalization of the classic inversion formula due to Gil-Pelaez (1951). Two numerical applications are considered: first, the finite-sample distribution of the 2SLS estimator of a structural parameter. Second, the Value at Risk and Expected Shortfall of a quadratic portfolio with heavy-tailed risk factors. An empirical application is examined, where a portfolio of of Dow Jones Industrial Index (DJIA) stock options is optimised by minimising the expected shortfall. The empirical results show the benefits of the analytical expression.

It is well established that daily or higher frequency nancial asset returns exhibit volatility clustering and non-Gaussian behavior, notably so-called heavy tails. These features have enormous implications for both passive risk management (such as measuring the value at risk of a given portfolio) and active risk management (portfolio optimization). While many models have been proposed in a univariate setting to address these features, far fewer constructs are available in the large-scale multivariate case. Among such multivariate con- structs, most are based on Gaussianity, and are inappropriate for accurate risk assessment. In this work, not only is the Gaussianity assumption relaxed, but each asset is allowed to have its own tail behavior, allowing more accurate modeling and portfolio risk assessment. A further, independent development in nancial economics and empirical asset pricing is the use of so-called factors, or exogenous variables, that are assumed to have predictive ability for the asset returns. Research in this area, and search for new factors, continues unabated, since the seminal work of Eugene Fama and Ken- neth French in the early 1990s. Such models are an extension of the famous CAPM construction, and its use for portfolio construction diers completely from the alternative approach of using a multivariate predictive distribution of the returns and application of a Markowitz-type of optimization. This work combines the two strands of literature by proposing a mathematically elegant stochastic process that allows the joint time series modeling of nancial asset returns and factors. Such a construction appears to be new in the academic literature, and subsumes numerous previously proposed approaches. It allows for volatility clustering and heterogeneous tail behavior among the assets. In doing so, the eect of including factors can in uence both the mean prediction of returns, as well as their covariance structure, and thus in uence also risk prediction. The mathematical overhead required for its implementation needs to go beyond basic regressions and other simple statistical procedures. For example, it entails use of more sophisticated time series ltering mechanisms, use of distribution inversion theorems, and deeper concepts in optimization, though it is still computationally feasible. Importantly, the methodology is applicable in reasonably high dimensions, as is necessary in a realistic investment environment. A limited empirical example using ve daily value-weighted industry portfolio returns, along with the classic three Fama-French factors is conducted, in a long-only investment setting, comparing the performance with and without conditioning on the factors. Future research will expand upon the model and, crucially, conduct extensive backtesting exercises with various and larger data sets.

A non-Gaussian multivariate regime switching dynamic correlation model for financial asset returns is proposed. It incorporates the multivariate generalized hyperbolic law for the conditional distribution of returns. All model parameters are estimated consistently using a new two-stage expectation-maximization algorithm that also allows for incorporation of shrinkage estimation via quasi-Bayesian priors. It is shown that use of Markov switching correlation dynamics not only leads to highly accurate risk forecasts, but also potentially reduces the regulatory capital requirements during periods of distress. In terms of portfolio performance, the new regime switching model delivers consistently higher Sharpe ratios and smaller losses than the equally weighted portfolio and all competing models. Finally, the regime forecasts are employed in a dynamic risk control strategy that avoids most losses during the financial crisis and vastly improves risk-adjusted returns.

We follow the line of using classifiers for two-sample testing and propose several tests based on the Random Forest classifier. The developed tests are easy to use, require no tuning and are applicable for any distribution on Rp, even in high-dimensions. We provide a comprehensive treatment for the use of classification for two-sample testing, derive the distribution of our tests under the Null and provide a power analysis, both in theory and with simulations. To simplify the use of the method, we also provide the R-package "hypoRF".

Empirical evidence shows that market betas vary substantially over time, hence time-varying beta models are of interest in the eld of nancial modeling. This thesis reexamines the ndings of Bali et al. (2017) of a positive link between the dynamic conditional beta and the cross section of daily stock returns. Their investment strategy takes a long position in stocks in the highest beta decile and a short position in stocks in the lowest beta decile, and produces average returns and alphas in the range of 0.60%{0.80% per month. We are able to replicate their ndings based on the DCC-GARCH construct and show that the value-weighted High- Low dierence portfolio yields even higher monthly excess returns and alphas in the range of 1.7%{1.9% on our sample data. Replacing DCC- GARCH with the so-called COMFORT model, which is statistically more advanced and accounts for major stylized facts of nancial asset returns, does not increase performance, nor does it result in lower portfolio risk due to model estimation errors and a longer estimation window.

In this paper I conduct an autoregressive multivariate regression analysis of stock returns, which includes the use of lower sampled macroeconomic inputs. I apply the Mixed Data Sampling (MIDAS) weighting scheme to handle the frequency mismatch between the higher sampled daily return data and the lower sampled monthly macroeconomic variables, which allows me to parsimoniously weigh the higher frequency variable. This so-called reverse MIDAS approach is rather new to the literature, as typically mostly the inverse relationship is considered. I compare this model with multiple dierent vector autoregressive (VAR) congurations. I nd that the Gaussian based approach with homoscedastic errors does not adequately model the underlying nancial data. Additionally, the inclusion of macroeconomic regressors does not increase the performance of the model. Increasing the lag length of the autoregressive component does not lead to an increased performance either. As a potentially more suitable conguration I outline the use of a non-Gaussian model that is based on a generalized hyperbolic distribution, which accounts for non-normality and GARCH eects among others.

A saddlepoint approximation for evaluating the expected shortfall of financial returns under realistic distributional assumptions is derived. This addresses a need that has arisen after the Basel Committee’s proposed move from Value at Risk to expected shortfall as the mandated risk measure in its market risk framework. Unlike earlier results, the approximation does not require the existence of a moment generating function, and is therefore applicable to the heavy-tailed distributions prevalent in finance. A link is established between the proposed approximation and mean-expected shortfall portfolio optimization. Numerical examples include the noncentral t, generalized error, and α-stable distributions. A portfolio of DJIA stocks is considered in an empirical application.

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This thesis contributes to the growing literature of modeling financial re-turns at the intra-day level by considering its ability to predict the daily structure for asset allocation purposes. We test, whether the VG-iid model calibrated on the 30min time scale is beneficial for daily portfolio optimiza-tion by minimizing the next day ES. The VG-iid model lowers portfolio turnover, fits the return data quite well and allows for an easy deriva-tion of daily parameter estimates based on intra-day returns (Podg´orski and Wallin (2016)). However, the assumption of iid returns is quite ques-tionable at the intra-day level (Voev and Lunde (2006)), which stresses our focus on the practical benefit of this approach. Without transaction costs, we present an outperformance of all our strategies using 30min data instead of daily returns. The benefits are quite stable and remain even under simplifying assumptions. One of the 30min strategies also reduces the turnover rate, which stresses the practical significance of our findings.