Contributions published at Empirical Finance (Marc Paolella)

In light of the growing use, acceptance of, and demand for, machine learning in many fields, notably data science, but also other fields such as finance- and this in both industry and academics, some university departments might wish, or find themselves forced to, accord to the winds of change and address this pressing issue. The goal of this document is to assist in designing relevant courses using material at the appropriate mathematical level. It protocols, sorts, evaluates, and contrasts, numerous viable books for a variety of possible courses. The subjects span several levels of, and different avenues in, linear algebra and real analysis, with briefer discussions of material in probability theory and mathematical finance.

The following thesis inquires into and compares selected methods of portfolio optimization accounting for turnover or transaction costs constraints. The focus lies on two optimization approaches introduced by Han, 2020, and Bonaccolto, 2021, respectively. The former presented a two stage portfolio optimization procedure allowing for the maximization of (quadratic) utility on the first stage of the procedure while penalizing a turnover measure on the second stage. Since this approach does not make any exante assumptions on the distribution of the error term, it can in a sense be considered a non-parametric approach. The second optimization approach studied considers a quantile regression based procedure introduced by Bonaccolto, 2021. This approach as well solves for an optimal portfolio in two distinct optimization stages. The first stage consists of a LASSO-penalized quantile regression that is used to perform model selection by restricting the universe of available assets. The second stage considers only the restricted set of assets on which it runs a standard quantile regression problem subject to a mean return constraint. The thesis furthermore attempts to combine the two approaches in different ways. These always include a LASSO-penalized quantile regression setup as the first stage to perform model selection. On the second stage different optimization approaches are employed. Either a quantile regression based method subject to a form of turnover constraint, or a quadratic programming problem with a turnover measure as its objective function subject to expected shortfall and mean return constraints. The resulting portfolios of the four optimization approaches are compared with respect to turnover, mean return and expected shortfall. In addition a variation of the Sharpe ratio is employed as a risk adjusted performance measure. It is found that the procedure by Han, 2020, outperforms all other three with respect to having minimal turnover, the best expected shortfall value, the best performance as measured by the Sharpe Ratio, and the same target mean return. A trade-off is found between minimizing turnover and achieving a better expected shortfall value comparing the procedure of Bonaccolto, 2021, with the one of the combined approaches in form of a quadratic programming problem with a turnover measure as its objective function. The combined approach in form of a quantile regression based method subject to a turnover constraint is found not to work as intended.

Financial time series sequences are non-stationary and dominated by noise, which makes stock prediction one of the most challenging problems. Nowadays, it has been a trend that researchers have turned to techniques in the computer science fields of big data and machine learning for stock price forecasting. This thesis applies Independent Component Analysis (ICA) method to reduce the influence of noise. Together with ICA, this thesis applies Support Vector Machine (SVM) to predict stock performance. In order to evaluate the proposed method, the simulated data generated by Monte Carlo Simulation is used as illustrative data sample. Apart from simulated data, the SSE Composite Index is also used to evaluate the method. The results show that the combination of ICA and SVM performs better than forecasting by SVM without denoising data. Key words: Monte Carlo Simulation, Independent Component Analysis, Support Vector Machine

Investors and researchers use various performance tests to compare the performance of different portfolio strategies. Many apply the tests directly without checking the properties of them. Here, we aim to investigate the properties of Ledoit-Wolf test based on multiple settings and come up with an alternative performance test based on the abnormal rate of return. We find that Ledoit-Wolf test is more sensitive to the change of Sharpe ratio that comes from change of mean but not volatility, but has low power in both case. Besides, the test results in a less power along with a higher Sharpe ratio out-performance in the strategy of minimum-variance with constraints. The alternative test is built up on simple linear regression and HAC covariance estimators, which has a higher power than Ledoit-Wolf test in different designs and for different observation periods. Keywords: Ledoit-Wolf test, Sharpe ratios

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 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 principal 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. When applied to portfolio optimization, it generates strategies with lower turnover and maximum drawdown, and superior risk-adjusted returns net of transaction costs. Moreover, unlike its competitors, it performs well in the sudden market downturn triggered by the global COVID-19 pandemic.

Interest in the use of machine learning methods continues unabated, notably in empiri-cal finance and financial time series prediction. The recent advent of powerful machine learning methods combined with the availability of vast amounts of computational re-sources form an attractive basis for researchers and practitioners. This thesis applies four methods for stock price movement prediction and algorithmic trading, with the fourth method belonging to the field of deep learning. Concretely, a simple momen-tum model, an autoregressive AR(1) model combined with prediction smoothing, a linear 1 trend filter based model with adaptive hyperparameter optimization, and a Long Short-Term Memory neural network are employed on 1 min high-frequency price data. The objective is to attain high accuracies for price movement predictions and to find profitable trading strategies net of transaction costs. The LSTM-based pre-diction model utilizes 1 min price data and extracts features based on handcrafted basis functions fitted to tick price data using the least-squares method, which are then further processed using a LSTM neural network for prediction. The model delivered the best performance with a prediction accuracy of 72% based on average prices for the considered stocks and period, and outperformed the other approaches net of trans-actions costs, although the performance was still negative overall. These findings are encouraging and support further research using modern machine learning methods for high-frequency financial time series prediction and algorithmic trading applications. It is expected that a bet sizing mechanism on top of price movement predictions would significantly improve strategy performance net of transaction costs.

The purpose of this master’s thesis is to assess the profitability in the U.S. market of a newly-proposed asset selection technique, which is suitable in a high-dimensional con-text, i.e., when the number of assets is at least equal to the total number of observations. We focus on the out-of-sample portfolio performances, showing that the approach can potentially deliver good returns, but is unable to deal with bad market phases, when volatility increases. To overcome this limitation, we propose a risk-managed version of the asset selection technique that delivers much larger returns over the time frame ana-lyzed and overwhelms the performance of the commonly employed momentum strategy, even accounting for transaction costs.

We replicated the vol-of-vol measure (VOIV) by Baltussen et al. (2018) and analyzed how a portfolio based on this measure performs after the initial publication of their results in 2014 (Baltussen et al. (2014)). We were able to qualitatively replicate most of their findings, but found no significant excess returns for the period from 1996 to 2014. For the period from 2014 to 2019, we observed, that the relationship between VOIV and portfolio returns turned from negative to positive, showing significant excess returns. We created Efficient Sorting portfolios (Ledoit et al.(2019)), but we were not able to improve risk adjusted returns using this methodology.

Real-world applications of Markowitz’ portfolio theory often deliver mediocre results in terms of performance and practicability of the optimal weights. This phenomenon has been attributed to estimation errors in the input parameters of the optimization problem which can get magnified when the optimal weights are computed numerically. In this thesis, one examines the smoothing with the exponential weighting moving average of the ex-post Markowitz portfolio weights with a rolling windows backtesting approach along with three benchmark strategies, one of them being the Ledoit and Wolf (2003) shrinkage approach. The findings show an appealing performance using the ex-post weights smoother, especially when considering transaction costs.

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Over the last decades, the utilization of high-frequency data in financial modelling has gained in popularity. Compared to lower frequency equivalents, it conveys more precise information about the fine-structure of the underlying stochastic processes. Working with an extensive set of 5-minute candlestick data, we exploit its informational content to forecast the conditional co-variance structure. Combining the strands of literature on high-frequency econometrics and optimal currency exposure we develop a novel currency hedging strategy. The currency and asset data are examined for the presence of jumps. Moreover, we aim to identify the adequate jump type - finite or infinite activity - in order to forecast jump robust, conditional co-variation. To this end, suitable non-parametric measures, such as realized power and truncated power variations, are employed. The co-variation’s decomposition into a continuous part and a jump part as well as into signed semi-covariances is assessed in terms of improving forecast quality using the parsimonious HAR-model and adaptations thereof. Time-varying jump adjusted optimal currency exposures are derived from the predicted conditional co-variation employing a range of portfolios and currencies. We show that the optimally dynamically hedged portfolio outperforms the unhedged as well as the fully hedged portfolio, in terms of Sharpe ratios, on a monthly rebalancing horizon both in- and out-of-sample.

This thesis investigates the benefits of a joint optimization approach to international portfolio optimization in the mean-variance framework. In this joint approach, asset weights and currency exposures, which are modeled through currency forward contracts, are determined in a single optimization. This optimization solves the classical mean-variance problem (based on the sample covariance matrix) in an international setting, while also employing several extensions to the mean-variance framework that have been proposed in the literature. These extensions aim at reducing the parameter uncertainty related to the input parameters. This is achieved by either shrinking the optimization parameters [Ledoit and Wolf, 2003, 2004] or constraining the norms of the portfolio-weight vector [Li, 2015, DeMiguel et al., 2009a]. Furthermore, a general framework is created to formulate these rules in the international setting with the possibility to add additional constraints. These portfolio rules are then extended by two further rules, which are inspired by practical considerations that govern the maximal net exposure to foreign currencies. The thesis also motivates the joint approach through an in-sample analysis that is able to show its potential benefits. A total of nine different portfolio rules are then tested out-of-sample on three different data sets and compared to the 1/N benchmark. For each rule a portfolio is created using the joint approach proposed in this thesis, as well as another portfolio that follows a separate overlay approach, which first optimizes the assets and then chooses the currency exposure weights in a second step. The performance of the portfolios is evaluated empirically using different portfolio performance measures that are also translated into the context of international portfolio optimization. Using these measures, it was found that, across different portfolio rules and data sets, the joint optimization approach is not able to improve the portfolio performance consistently.

The US dollar and also increasingly the euro and in some instances the Swiss franc exhibit risk-minimizing capabilities in a wide range of international portfolios. From 1975 until the end of 2019, these currencies moved against both equity markets as well as additional asset classes such as bonds, real estate and commodities. This presents the possibility of holding specific amounts of currencies in an attempt to reduce risk in international portfolios. Given the expected return structure of an initial investment, a risk-minimizing investor can include such positions in a portfolio in order to reduce overall volatility. The financing of these long positions can be established by short selling other foreign exchange positions that are positively correlated with an investor’s initial investment. This is especially the case for the Australian and Canadian dollars as well as most emerging market currencies when investing in equities and beyond. Optimal hedging demands largely depend on investor sentiment, return expectations and preferred risk exposure. Defining these metrics alongside preferred asset classes can lead to substantial risk reduction, primarily in more aggressive portfolios. In the empirical part of the work, we show that di↵erent asset classes exhibit similar hedging demands but deviate substantially in the amount of currency held. This leads to a real estate or commodities investor holding a considerably larger amount of US dollars compared to an equity or bond investor. Moreover, we demonstrate that currency demands also tend to change over time, leading to sizeably distinct optimal allocations for di↵erent time periods.

Risk factors in stock markets are of great interest in investments. Baltussen et al. (2018) proposed that the uncertainty about risk also determines stock returns. They measured the uncertainty about risk of stocks as the volatility of implied volatility (vol of vol). The vol of vol has been proved to be a distinct risk characteristic of stocks, but not a significant risk factor. We propose a new measure of vol of vol. Our measure is quantified as the length of the confidence interval of the expected shortfall (LBCI). We show that the LBCI is a sensitive risk characteristic of stocks. The portfolio of stocks with the largest LBCI outperforms the portfolio of stocks with the smallest LBCI by 10.47% per year among 30 stock choices and by 47% per year among 501 stock choices. The portfolio of stocks with the largest LBCI has larger system risk, a larger abnormal return, and larger total volatility than the portfolio of stocks with the smallest LBCI. After running an asset pricing model with panel data, we find that the LBCI is a priced risk factor with statistical significance. Keywords: Confidence interval, expected shortfall, bootstrap, APARCH, non-central student’s t, CAPM, panel regression

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate ARCH-type models. This model class is the workhorse tool for modelling the conditional volatility of financial assets. Their distinguishing feature is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study.

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This thesis primarily investigate the improvement of financial indicators based on the dynamically varying covariances. In previous research and papers, financial indicators are usually calculated by convariance matrix based on i.i.d Gaussian assumptions. Here I employ two indicators, financial turbulence and absorption ratio and estimate them based on related covariance matrix obtained by 7 models, i.i.d. Gaussian model, multivariate student’s t model, DCC-GARCH based on multivariate normal model, DCC-GARCH based on multivariate student’t model, Go-GARCH based on multivariate normal model, Go-GARCH based on NIG model, MCD covariance estimator. I refer to the turbulenceresistant portfolio and portfolio based on absorption ratio to estimate the performance of the portfolios to assess the financial indicators accordingly. Then I evaluate the improvement of the DCC-GARCH models on the two financial indicators. Keywords: financial indicators; financial turbulence; absorption ratio; covariance matrix; DCC-GARCH model; Go-GARCH model.

Generative adversarial networks (GANs) provide a novel training approach to deep generative models by introducing two neural networks acting as agents in an adversarial game. The models have been successful in a wide range of applications in computer vision and audio synthesis and are highly regarded as a powerful approach for learning complex distributions when sampling from a distribution is of interest, rather than estimating an explicit form of the density; However, GANs are notably unstable and very difficult to train with acknowledged issues such as mode collapse and convergence problems. This work explores the ability and uses recurrent and convolutional based GANs to learn the underlying stochastic process of financial asset returns. Recent research has provided promising results in generating. univariate return series. This thesis extends the application to a multivariate setting with the goal of generating realistic multivariate sample paths of a basket of assets. Empirical experiments show that the models are able to capture the temporal as well as the cross-asset dependencies of the return series. Also, an application in a mean-variance optimization framework demonstrates that making use of the ability to sample synthetic samples with the same statistical properties as the realized paths, is useful for constructing more robust investment portfolios.