Contributions published at Empirical Finance (Marc Paolella)

This thesis compares GARCH models, Stochastic Volatility (SV) models, and Markov-switching GARCH (MSGARCH) models in terms of forecasting one-day-ahead Value-at-Risk (VaR) for industrial metals futures. GARCH and MSGARCH models are estimated with three innovation distributions: normal, student-t, and generalized error distributions (GED). For in-sample analysis, we implement these models to compare the Akaike information criterion (AIC) as well as their in-sample conditional volatility. Out-of-sample VaR forecasting performance is evaluated based on conditional coverage test. The results show MSGARCH models outperform the other models in predicting a one-day-ahead VaR for both long and short trading positions.

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models have gained considerable attention since the contributions of Engle (1982) and Bollerslev (1986). These pioneers showed the time-varying volatility in financial asset returns. Building upon this, Duan (1995) further expanded the applicability of GARCH models by elucidating the framework and conditions necessary for integrating them into option pricing. In 2000, the well-know affine GARCH model (HN-GARCH), which was elaborated by S. L. Heston and Nandi (2000), brought an innovation by introducing closedform option pricing formulas, while capturing several stylized fact such as the price of risk, leverage effect (Black (1976) and Christie (1982)), news effect (Campbell and Hentschel (1992) and Bekaert and G. Wu (2000)), and time-varying conditional variances as expressed by a discrete-time GARCHtype process. As a consequence, many extensions have been emerged, which are called the affine GARCH family of models. Some examples : the GARCH(p,q) of Bollerslev (1986), the aysmmetric GARCH of Engle and Ng (1993) and the threshold GARCH of Glosten et al. (1993); for the empirical application into option pricing see Christoffersen, Jacobs, and Ornthanalai (2013); for comparisons between affine and non-affine GARCH models, see Hsieh and Ritchken (2006), Christoffersen, Jacobs, and Mimouni (2006) and Christoffersen, Dorion, et al. (2010). These affine GARCH extensions incorporate non-Gaussianity by Gaussian innovations (Christoffersen, Steve Heston, et al., 2006) or Levy jumps (Ornthanalai, 2014); and multivariate extensions which allows fast and accurate pricing of multi-asset options see Escobar-Anel, Rastegari, et al. (2020). Recently, the literature indicate the importance to include the stochastic jump into the stochastic volatility structure (see Chernov et al. (2003), Eraker et al. (2003), Eraker (2004) and Todorov and Tauchen (2011)) but is missing in GARCH models except for the model proposed by Chan and J. Maheu (2002) and J. M. Maheu and McCurdy (2004). The multivariate model combining GARCH and Stochastic Volatility by introducing a latent component is proposed by Paolella and Polak (2015) : A common market factor non-Gaussian returns model (COMFORT).

This paper examines the effectiveness of environmental, social, and governance (ESG) momentum in trading Brazilian securities. It tests several trading strategies employ ing both top-decile and time-series momentum, including long-only, long-short, and reverse strategies, which invest in stocks with low ESG momentum. Brazilian results are then compared with those in Chinese, Indian, and South African markets, with overperformance seen in the Brazilian and South African markets and underperformance in Chinese and Indian markets. These results of this paper highlight the complex relationship between ESG momentum and stock returns, contributing insights to the ongoing debate on ESG investing efficacy.

Based on the data of S&P 500 index from 2008-04-01 to 2022-12-30, four different models, namely Black-Scholes, Variance-Gamma (VG), GARCH, and COMFORT-GARCH models are employed to make options pricing, and the pricing quality of these models are compared. The results show that the COMFORT-GARCH model combines GARCH-type dynamics with an SV structure, it can better capture the volatility characteristics of S&P 500 index, yields a more stable price change with a smaller magnitude. The research confirms the applicability of COMFORT-GARCH model in the multivariate setting for potentially large numbers of assets.

This paper explores an ARFIMA-based momentum trading strategy, extending the work of Chitsiripanich et al. (2022) and aiming to refine predictive accuracy and enhance profitability by incorporating long-memory attributes into stock returns modelling. Our focus revolved around the Sowell (1992) Maximum Likelihood Estimation methodology, targeting its benefits and limitations while suggesting enhancements. Notably, the ARFIMA(2, 0.4 + d2, 2) model outperformed other advanced strategies, showing promising risk-adjusted returns, less volatility, and minimal market dependence. However, the results should be considered with caution due to computational constraints and the scope of the data sample. Future research could leverage more substantial computing resources, extend the stock selection, or apply alternate estimation methodologies.

We study the effect of using fractional returns instead of log returns on improving portfolio optimization. The fractional return is defined as a fractional difference of log prices. The rationale behind the substitution lies in the fractional return’s similarity to log returns and its memory richness nature. We conduct extensive experiments on 8 groups of stocks with Gaussian and COMFORT models, with the optimization objective of maximizing the Sharpe ratio, with or without short-selling. Our findings are the following. First, qualitatively, portfolios using fractional returns behave generally more turbulent. Second, the Sharpe ratio demonstrates a pattern of first increasing and then decreasing with respect to degrees of fractional returns. Third, application of fractional returns yields improved Sharpe ratios in most groups. Fourth, the improvement effect is greater for portfolios with short selling. We also give an interpretation of the findings and conclude with future directions.

Secured Overnight Financing Rate (SOFR) and CME Term SOFR Rates will replace LIBOR as the new reference rate for U.S. Dollar financial contracts. This thesis investigates the feasibility of replicating CME Term SOFR Rates Benchmark. We develop a new approach for calculating SOFR Futures prices and follow the methodology from CME Group. The empirical results show that our estimation is close to the real Term SOFR with less than one basis point error. Our findings suggest that CME Term SOFR Rates can be replicated with small errors using free and accessible data, and contributes to hedge the risk of forward SOFR rate in further study.

This paper implements systematic research on the holiday effect in China stock market. First, considering other anomalies in the stock market, this paper analyzes the overall holiday effect on the two main stock indices of SSE and SZSE, SSCI and SZSCI, from January 2000 to December 2021. During this period, the pre-and post-holiday effect can be observed in both SSE and SZSE. Subsequently, several influencing potential factors of the holiday effect are considered: Sophisticated investors seem to be impacted less by the holiday effects. The holiday effects also demonstrate enormous divergences in various industries. The holiday effects are correlated to the firm sizes. Further, the holidays in China are distinguished into seven different statutory holidays, and their effects on the stock returns are analyzed respectively. Then, this paper finds that no holiday effect (except the post-QM holiday effect) exists when there is no holiday on a specific day through special case analysis. At last, three periods of analyses indicate that most holiday effects are alleviated over time in SSCI, except for the post-QM effect. The methodologies in this paper are descriptive statistics, non-parametric tests, OLS models, Stable Paretian Distribution, Noncentral t Distribution, ARMA-eGARCH-sstd, and ARMA-apARCH-(M)-sstd. Key Words: Holiday Effect, China Stock Market, SSCI, SZSCI, Statutory Holidays, descriptive statistics, non-parametric tests, OLS models, Stable Paretian Distribution, Noncentral t Distribution, and ARMA-GARCH-clusters

This thesis examines the value at risk (VaR) forecasting ability of various univariate and multivariate models for a long equity portfolio. All of the considered models involve a generalized autoregressive conditional heteroskedasticity (GARCH)-type structure. The resulting forecasts are checked for desirable properties using violation-based backtests and compared in terms of predictive ability. We find that the VaR forecasts of almost all univariate models are inadequate, while the multivariate models have few problems passing these backtests. However, we do not find evidence that the multivariate models systematically outperform their univariate counterparts with regards to predictive accuracy, or vice versa.

Although momentum strategies are widely used and discussed in the finance literature, the issue of look-back period selection is often put on the back burner. Based on the idea of Levy and Lopes (2021), various methodologies will be used in order to dynamically choose the most effective look-back period. Compared to the above-mentioned paper, different statistically based strategies will be analysed and the case of cross-sectional strategies will also be explored. The results say that more or less complex statistical models lead to better performance for both the time-series and cross-sectional approaches.

Unexpected and abnormal discontinuities in price evolution have been acknowledged as a substantial component of price time series generated on financial markets. This thesis aims to identify these extreme movements and define them as trigger points for tactically induced portfolio optimization. For this purpose, a high-frequency data set was examined for price jumps using different detection procedures. The categorized price jumps were set as points in time at which a portfolio underwent rebalancing processes. The findings indicate that price jumps are prevalent, but their occurrence does not qualify for determining rebalancing points in time.

A multivariate heterogeneous tail distribution for asset return modelling will be presented, together with several approaches to construct a portfolio, based solely on the estimated model. The focus lies on computational efficiency and feasibility of such portfolio constructions. As an optimization criteria, the left-tail risk measure of Expected Shortfall will be used, where the return-risk-ratio is being maximized, or — similar to Markowitz — risk under a predefined expected return is being minimized. A backtesting exercise of the proposed portfolio optimization will be conducted for the period of 2016-2020, showing that the proposed approaches have a promising return structure.

This article proposes a weighted maximum likelihood approach for fitting DCC-GARCH with finite Gaussian mixtures. At its foundation, the method requires component separation to be conducted at an earlier step via either the conventional expectation-maximization algorithm for the MLE or the robust Minimum Covariance Determinant estimator. The overall compu-tational routine allows for parameter shrinkage via a quasi-Bayesian prior and can be further augmented with traditional time-based weighting schemes (e.g. hyperbolic) to account for model misspecificiation. It is shown in a backtesting exercise with DJIA data that portfolios built with this estimation approach consistently outperform their IID equivalents. Moreover, it is shown that the more complex DCC model doesn’t produce any improvements over the com-putationally faster CCC variant for a universe of 30 assets. By changing the assets considered for allocation along with the index composition over the years, the results also reveal the large influence that Survivorship Bias can exert on portfolio strategies in general if not accounted for when backtesting.

The significance of the pre-selection of high-quality assets before the official formation cannot be ignored during the portfolio optimization process. Therefore, with the top 30 most discussed Chinese A-share stocks in GUBA, this thesis has tried to combine deep learning techniques for predicting the stock price to select high-quality stocks, with different portfolio allocation strategies to see the portfolio performance of the combinations. In the first place, LSTM with benchmark inputs, LSTM with subjective sentiment extracted from comments data of GUBA, and LSTM with objective sentiment extracted from market-based indexes were separately constructed to predict the stock price. The results have shown that adding investors’ sentiment in a subjective way or in an objective way can significantly elevate the prediction performance. In the second stage, high-quality stocks screened from those three models in the first stage and randomly-chosen stocks were respectively combined with three portfolio allocation strategies, including "Equal Weights", "Global Minimum Variance Optimization(GMV) without short-selling", and "Global Minimum CVaR(GMC) without short-selling". The results have validated the importance of the pre-selection of high-quality assets before the official formation of a portfolio. The combination of LSTM and GMC has achieved the highest return. The combination of LSTM considering investors’ sentiment extracted from comments data of GUBA and equal weights strategy has shown the highest Sharpe ratio. Keywords: Stock Price Prediction, Deep Learning, LSTM, Portfolio Optimization, Sentiment Analysis, Markowitz Mean-Variance Optimization, CVaR

Following the line of classification-based two-sample testing, tests based on the Random Forest classifier are proposed. The developed tests are easy to use, require almost no tuning, and are applicable for any distribution on R^d. Furthermore, the built-in variable importance measure of the Random Forest gives potential insights into which variables make out the difference in distribution. An asymptotic power analysis for the proposed tests is conducted. Finally, two real-world applications illustrate the usefulness of the introduced methodology. To simplify the use of the method, the R-package “hypoRF” is provided.

The present paper combines nonlinear shrinkage with the Multivariate Generalized Hyperbolic (MGHyp) distribution to account for heavy tails in estimating the first and second moments in high dimensions. An Expectation-Maximization (EM) algorithm is developed that is fast, stable, and applicable in high dimensions. Theoretical arguments for the monotonicity of the proposed algorithm are provided and it is shown in simulations that it is able to accurately retrieve parameter estimates. Finally, in an extensive Markowitz portfolio optimization analysis, the approach is compared to state-of-the-art benchmark models. The proposed model excels with a strong out-of-sample portfolio performance combined with a comparably low turnover.

This thesis examines how investors can optimise the level of gross leverage in their portfolios according to arbitrary investment objectives. An approach based on ARIMA modelling is proposed that generalises methods found in existing academic literature. Through regular hyper-parameter selection, this method allows for changing dynamics of optimal shorting limits to reflect different market conditions. Various combinations of hyper-parameter selec-tion methods and objective functions are examined to see the impact on the estimated shorting limits. The results show that the choice of objective func-tion has a major impact on the dynamics of the optimal gross leverage limit, which in turn has a significant impact on portfolio behaviour. The results give a clear indication to the effectiveness of long-only portfolios when comparing various performance metrics. When considering transaction costs, portfolios that have gross leverage limits also see further improvements due to lower portfolio turnover.

This thesis investigates a recent idea on the allocation of financial assets by Gerber et al. (2021). These authors proposed a new co-movement measure, the Gerber statistic, to estimate the covariance matrix. The Gerber statistic is a nonparametric statistic based on Kendall’s Tau (1938), is an extension of it, which is expected to provide more robust and better results than the historical covariance and the shrinkage method of Ledoit and Wolf (2004). In this work, their methodology is applied to related but different data and performance is compared with commonly used benchmark methods. In general, the statistical quality of the method is verified, and the results of the original paper are supported by different data.

A multivariate normal mean-variance heterogeneous tails mixture distribution is proposed for the joint distribution of financial factors and asset returns (referred to as Factor-HGH). The proposed latent variable model incorporates a Cholesky decomposition of the dispersion matrix to ensure a rich dependency structure for capturing the stylized facts of the data. It generalizes several existing model structures, with or without financial factors. It is further applicable in large dimensions due to a fast ECME estimation algorithm of all the model parameters. The advantages of modelling financial factors and asset returns jointly under non-Gaussian errors are illustrated in an empirical comparison study between the proposed Factor-HGH model and classical financial factor models. While the results for the Fama-French 49 industry portfolios are in line with Gaussian-based models, in the case of highly tail heterogeneous cryptocurrencies, the portfolio based on the Factor HGH model doubles the average return while keeping the volatility, the maximum drawdown, the turnover, and the expected-shortfall at a low level.

In dieser Arbeit wird das von Piotroski (2000) geschaffene Scoring Modell « F Score » , rend auf Kennzahlen, für Value Aktien am Schweizer Aktienmarkt untersucht. Im ersten Teil erfolgt eine theoretische Analyse, welche zum Schluss kommt, dass die von Piotroski doku- mentierte Üb errendite aus der Inkongruenz zwischen der Einschätzung durch die Investoren und dem Fundamentalwert resultiert. In der empirischen Analyse im zweiten Teil wird der F Score auf dem Schweizer Markt nach Vorbild dem Piotroskis angewendet. Dabei vermochte der F Sc ore Gewinner von Verliererakti en zu unterscheiden . Das Portfolio mit den aktien konnte eine um 6.82% höhere jährliche Rendite als der SPI erzielen, wies jedoch im Vergleich zu weiteren Value Konstruktionen keine bessere Performance auf. Die Überrendite zeigte dabei keine Signifikanz. Im dritten Teil wurde der F Score schrittweise durch den Ein- bezug weiterer Kennzahlen und Marktdaten modifiziert. Dabei wurden auch weitere Bewer- tungskennzahlen miteinbezogen. Schliesslich erfolgte eine Gewichtung durch Equal Risk Con- tribution. Schrittweise konnten die Renditen gesteigert werden, während die Risiko Masse san ken. So konnten verschiedene Portfolios signifikante Überrenditen aufweisen.