Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails

Survey of quantitative investment strategies in the Russian stock market : Special interest in tactical asset allocation

Russia’s financial markets have been an uncharted area when it comes to exploring the performance of investment strategies based on modern portfolio theory. In this thesis, we focus on the country’s stock market and study whether profitable investments can be made while at the same time taking uncertainties, risks, and dependencies into account. We also pay particular interest in tactical asset allocation. The benefit of this approach is that we can utilize time series forecasting methods to produce trading signals in addition to optimization methods. We use two datasets in our empirical applications. The first one consists of nine sectoral indices covering the period from 2008 to 2017, and the other includes altogether 42 stocks listed on the Moscow Exchange covering the years 2011 – 2017. The strategies considered have been divided into five sections. In the first part, we study classical and robust mean-risk portfolios and the modeling of transaction costs. We find that the expected return should be maximized per unit expected shortfall while simultaneously requiring that each asset contributes equally to the portfolio’s tail risk. Secondly, we show that using robust covariance estimators can improve the risk-adjusted returns of minimum variance portfolios. Thirdly, we note that robust optimization techniques are best suited for conservative investors due to the low volatility allocations they produce. In the second part, we employ statistical factor models to estimate higher-order comoments and demonstrate the benefit of the proposed method in constructing risk-optimal and expected utility-maximizing portfolios. In the third part, we utilize the Almgren–Chriss framework and sort the expected returns according to the assumed momentum anomaly. We discover that this method produces stable allocations performing exceptionally well in the market upturn. In the fourth part, we show that forecasts produced by VECM and GARCH models can be used profitably in optimizations based on the Black–Litterman, copula opinion pooling, and entropy pooling models. In the final part, we develop a wealth protection strategy capable of timing market changes thanks to the return predictions based on an ARIMA model. Therefore, it can be stated that it has been possible to make safe and profitable investments in the Russian stock market even when reasonable transaction costs have been taken into account. We also argue that market inefficiencies could have been exploited by structuring statistical arbitrage and other tactical asset allocation-related strategies.Venäjän rahoitusmarkkinat ovat olleet kartoittamatonta aluetta tutkittaessa moderniin portfolioteoriaan pohjautuvien sijoitusstrategioiden käyttäytymistä. Tässä tutkielmassa keskitymme maan osakemarkkinoihin ja tarkastelemme, voidaanko taloudellisesti kannattavia sijoituksia tehdä otettaessa samalla huomioon epävarmuudet, riskit ja riippuvuudet. Kiinnitämme erityistä huomiota myös taktiseen varojen kohdentamiseen. Tämän lähestymistavan etuna on, että optimointimenetelmien lisäksi voimme hyödyntää aikasarjaennustamisen menetelmiä kaupankäyntisignaalien tuottamiseksi. Empiirisissä sovelluksissa käytämme kahta data-aineistoa. Ensimmäinen koostuu yhdeksästä teollisuusindeksistä kattaen ajanjakson 2008–2017, ja toinen sisältää 42 Moskovan pörssiin listattua osaketta kattaen vuodet 2011–2017. Tarkasteltavat strategiat on puolestaan jaoteltu viiteen osioon. Ensimmäisessä osassa tarkastelemme klassisia ja robusteja riski-tuotto -portfolioita sekä kaupankäyntikustannusten mallintamista. Havaitsemme, että odotettua tuottoa on syytä maksimoida suhteessa odotettuun vajeeseen edellyttäen samalla, että jokainen osake lisää sijoitussalkun häntäriskiä yhtä suurella osuudella. Toiseksi osoitamme, että minimivarianssiportfolioiden riskikorjattuja tuottoja voidaan parantaa robusteilla kovarianssiestimaattoreilla. Kolmanneksi toteamme robustien optimointitekniikoiden soveltuvan parhaiten konservatiivisille sijoittajille niiden tuottamien matalan volatiliteetin allokaatioiden ansiosta. Toisessa osassa hyödynnämme tilastollisia faktorimalleja korkeampien yhteismomenttien estimoinnissa ja havainnollistamme ehdotetun metodin hyödyllisyyttä riskioptimaalisten sekä odotettua hyötyä maksimoivien salkkujen rakentamisessa. Kolmannessa osassa käytämme Almgren–Chrissin viitekehystä ja asetamme odotetut tuotot suuruusjärjestykseen oletetun momentum-anomalian mukaisesti. Havaitsemme, että menetelmä tuottaa vakaita allokaatioita menestyen erityisen hyvin noususuhdanteessa. Neljännessä osassa osoitamme, että VECM- että GARCH-mallien tuottamia ennusteita voidaan hyödyntää kannattavasti niin Black–Littermanin malliin kuin kopulanäkemysten ja entropian poolaukseenkin perustuvissa optimoinneissa. Viimeisessä osassa laadimme varallisuuden suojausstrategian, joka kykenee ajoittamaan markkinoiden muutoksia ARIMA-malliin perustuvien tuottoennusteiden ansiosta. Voidaan siis todeta, että Venäjän osakemarkkinoilla on ollut mahdollista tehdä turvallisia ja tuottavia sijoituksia myös silloin kun kohtuulliset kaupankäyntikustannukset on huomioitu. Toiseksi väitämme, että markkinoiden tehottomuutta on voitu hyödyntää suunnittelemalla tilastolliseen arbitraasiin ja muihin taktiseen varojen allokointiin pohjautuvia strategioita

Risk Management in Environment, Production and Economy

The term "risk" is very often associated with negative meanings. However, in most cases, many opportunities can present themselves to deal with the events and to develop new solutions which can convert a possible danger to an unforeseen, positive event. This book is a structured collection of papers dealing with the subject and stressing the importance of a relevant issue such as risk management. The aim is to present the problem in various fields of application of risk management theories, highlighting the approaches which can be found in literature

Measuring the risk of financial portfolios with nonlinear instruments and non-Gaussian risk factors

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The focus of my research has been computationally efficient means of computing measures of risk for portfolios of nonlinear financial instruments when the risk factors might be possibly non-Gaussian. In particular, the measures of risk chosen have been Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR). I have studied the problem of computation of risk in two types of financial portfolios with nonlinear instruments which depend on possibly non-Gaussian risk factors: 1. Portfolios of European stock options when the stock return distribution may not be Gaussian; 2. Portfolios of sovereign bonds (which are nonlinear in the underlying risk factor, i.e. the short rate) when the risk factor may or may not be Gaussian. Addressing both these problems need a wide array of mathematical tools both from the field of applied statistics (Delta-Gamma-Normal models, characteristic function inversion, probability conserving transformation) and systems theory (Vasicek stochastic differential equation model, Kalman filter). A new heuristic is proposed for addressing the first problem, while an empirical study is presented to support the use of filter-based models for addressing the second problem. In addition to presenting a discussion of these underlying mathematical tools, the dissertation also presents comprehensive numerical experiments in both cases, with simulated as well as rea

Quantification of uncertainty of geometallurgical variables for mine planning optimisation

Interest in geometallurgy has increased significantly over the past 15 years or so because of the benefits it brings to mine planning and operation. Its use and integration into design, planning and operation is becoming increasingly critical especially in the context of declining ore grades and increasing mining and processing costs. This thesis, comprising four papers, offers methodologies and methods to quantify geometallurgical uncertainty and enrich the block model with geometallurgical variables, which contribute to improved optimisation of mining operations. This enhanced block model is termed a geometallurgical block model. Bootstrapped non-linear regression models by projection pursuit were built to predict grindability indices and recovery, and quantify model uncertainty. These models are useful for populating the geometallurgical block model with response attributes. New multi-objective optimisation formulations for block caving mining were formulated and solved by a meta-heuristics solver focussing on maximising the project revenue and, at the same time, minimising several risk measures. A novel clustering method, which is able to use both continuous and categorical attributes and incorporate expert knowledge, was also developed for geometallurgical domaining which characterises the deposit according to its metallurgical response. The concept of geometallurgical dilution was formulated and used for optimising production scheduling in an open-pit case study.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Robust optimization of algorithmic trading systems

GAs (Genetic Algorithms) and GP (Genetic Programming) are investigated for finding robust Technical Trading Strategies (TTSs). TTSs evolved with standard GA/GP techniques tend to suffer from over-fitting as the solutions evolved are very fragile to small disturbances in the data. The main objective of this thesis is to explore optimization techniques for GA/GP which produce robust TTSs that have a similar performance during both optimization and evaluation, and are also able to operate in all market conditions and withstand severe market shocks. In this thesis, two novel techniques that increase the robustness of TTSs and reduce over-fitting are described and compared to standard GA/GP optimization techniques and the traditional investment strategy Buy & Hold. The first technique employed is a robust multi-market optimization methodology using a GA. Robustness is incorporated via the environmental variables of the problem, i.e. variablity in the dataset is introduced by conducting the search for the optimum parameters over several market indices, in the hope of exposing the GA to differing market conditions. This technique shows an increase in the robustness of the solutions produced, with results also showing an improvement in terms of performance when compared to those offered by conducting the optimization over a single market. The second technique is a random sampling method we use to discover robust TTSs using GP. Variability is introduced in the dataset by randomly sampling segments and evaluating each individual on different random samples. This technique has shown promising results, substantially beating Buy & Hold. Overall, this thesis concludes that Evolutionary Computation techniques such as GA and GP combined with robust optimization methods are very suitable for developing trading systems, and that the systems developed using these techniques can be used to provide significant economic profits in all market conditions

Multi Level Monte Carlo Methods for Uncertainty Quantification and Robust Design Optimization in Aerodynamics

The vast majority of problems that arise in aircraft production and operation require decisions to be made in the presence of uncertainty. An effective and accurate quantification and control of the level of uncertainty introduced in the design phase and during the manufacturing and operation of aircraft vehicles is imperative in order to design robust and risk tolerant systems. Indeed, the geometrical and operational parameters, that characterize aerodynamic systems, are naturally affected by aleatory uncertainties due to the intrinsic variability of the manufacturing processes and the surrounding environment. Reducing the geometrical uncertainties due to manufacturing tolerances can be prohibitively expensive while reducing the operational uncertainties due to atmospheric variability is simply impossible. The quantification of those two type of uncertainties should be available in reasonable time in order to be effective and practical in an industrial environment. The objective of this thesis is to develop efficient and accurate approaches for the study of aerodynamic systems affected by geometric and operating uncertainties. In order to treat this class of problems we first adapt the Multi Level Monte Carlo probabilistic approach to tackle aerodynamic problems modeled by Computational Fluid Dynamics simulations. Subsequently, we propose and discuss different strategies and extensions of the original technique to compute statistical moments, distributions and risk measures of random quantities of interest. We show on several numerical examples, relevant in compressible inviscid and viscous aerodynamics, the effectiveness and accuracy of the proposed approach. We also consider the problem of optimization under uncertainties. In this case we leverage the flexibility of our Multi Level Monte Carlo approach in computing different robust and reliable objective functions and probabilistic constraints. By combining our approach with single and multi objective evolutionary strategies, we show how to optimize the shape of transonic airfoils in order to obtain designs whose performances are as insensitive as possible to uncertain conditions

Motion Planning for Autonomous Vehicles in Partially Observable Environments

Unsicherheiten, welche aus Sensorrauschen oder nicht beobachtbaren Manöverintentionen anderer Verkehrsteilnehmer resultieren, akkumulieren sich in der Datenverarbeitungskette eines autonomen Fahrzeugs und führen zu einer unvollständigen oder fehlinterpretierten Umfeldrepräsentation. Dadurch weisen Bewegungsplaner in vielen Fällen ein konservatives Verhalten auf. Diese Dissertation entwickelt zwei Bewegungsplaner, welche die Defizite der vorgelagerten Verarbeitungsmodule durch Ausnutzung der Reaktionsfähigkeit des Fahrzeugs kompensieren. Diese Arbeit präsentiert zuerst eine ausgiebige Analyse über die Ursachen und Klassifikation der Unsicherheiten und zeigt die Eigenschaften eines idealen Bewegungsplaners auf. Anschließend befasst sie sich mit der mathematischen Modellierung der Fahrziele sowie den Randbedingungen, welche die Sicherheit gewährleisten. Das resultierende Planungsproblem wird mit zwei unterschiedlichen Methoden in Echtzeit gelöst: Zuerst mit nichtlinearer Optimierung und danach, indem es als teilweise beobachtbarer Markov-Entscheidungsprozess (POMDP) formuliert und die Lösung mit Stichproben angenähert wird. Der auf nichtlinearer Optimierung basierende Planer betrachtet mehrere Manöveroptionen mit individuellen Auftrittswahrscheinlichkeiten und berechnet daraus ein Bewegungsprofil. Er garantiert Sicherheit, indem er die Realisierbarkeit einer zufallsbeschränkten Rückfalloption gewährleistet. Der Beitrag zum POMDP-Framework konzentriert sich auf die Verbesserung der Stichprobeneffizienz in der Monte-Carlo-Planung. Erstens werden Informationsbelohnungen definiert, welche die Stichproben zu Aktionen führen, die eine höhere Belohnung ergeben. Dabei wird die Auswahl der Stichproben für das reward-shaped Problem durch die Verwendung einer allgemeinen Heuristik verbessert. Zweitens wird die Kontinuität in der Reward-Struktur für die Aktionsauswahl ausgenutzt und dadurch signifikante Leistungsverbesserungen erzielt. Evaluierungen zeigen, dass mit diesen Planern große Erfolge in Fahrversuchen und Simulationsstudien mit komplexen Interaktionsmodellen erreicht werden

Essays on risk management in portfolio optimization and gas supply networks

This work focuses on developing algorithms and methodologies to solve problems dealing with uncertainty in portfolio optimization and industrial gas networks. First, we study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio\u27s Net-Present Value (NPV) and the reward is measured by the portfolio\u27s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from thePSPLIB library of project scheduling problems. Both approaches are empirically shown to be effective and outperforming the default benchmark MIQP solver to find near-optimal solutions for the selected instances of the MSVP problem.Second, we present an algorithm to compute near-optimal Value-at-Risk (VaR) portfolios. It is known to be difficult to compute optimal VaR portfolios; that is, an optimal risk-reward portfolio allocation using VaR as the risk measure. This is due to VaR being non-convex and of combinatorial nature. In particular, it is well-known that the VaR portfolio problem can be formulated as a mixed-integer linear program (MILP) that is difficult to solve with current MILP solvers for medium to large-scale instances of the problem. The proposed algorithm addresses the shortcomings of the MILP formulation in terms of solution time. To illustrate the efficiency of the presented algorithm, numerical results are presented using historical asset returns from the US financial market. Empirical results suggest that the developed algorithm obtaining a lower bound for VaR outperforms the recently proposed algorithms from the literature. Additionally, we also show that the developed algorithms are able to obtain and guarantee near-optimal solutions for large scale instances of VaR portfolio optimization problem more efficiently than the off the shelf commercial solvers within 1% accuracy.Third, we analyze the impact of the sensor reading errors on parameters that affect the production costs of a leading US industrial gas supply company. For this purpose, a systematic methodology is applied first to determine the relationship between the system output and input parameters, and second to identify the assigned input sensors whose readings need to be improved in a prioritized manner based on the strength of those input-output relationships. The two main criteria used to prioritize these sensors are the decrease in production costs and the decrease in production costs’ volatility obtained when the selected sensor’s precision is improved. To illustrate the effectiveness of the proposed approach, we first apply it to a simplified version of the real supply network model where the results can be readily validated with the simulated data. Then, we apply and test the proposed approach in the real supply network model with historical data. The experiments suggest that we are able to obtain a significant decrease in production costs and in production costs’ volatility by prioritizing the sensors\u27 maintenance subject to a limited budget.Finally, we analyze the performance of portfolio allocation strategies using clustering techniques based on financial asset\u27s correlation matrices. The Markowitz\u27s mean-variance framework uses first and second order sample moment estimators which are highly subject to estimation errors. The estimation error on the moments could be very significant and it may offset the benefits obtained from the diversification of the portfolio. There are a number of methodologies proposed in the literature to reduce the effect of the estimation error on the moment estimators. A group of these are based on the clustering approaches using sample correlation coefficients as the similarity measure. The idea is to obtain a hierarchical structure between the financial assets and then to use this information to filter the underlying true representative economic information between the assets and to reflect it in a modified correlation matrix. The objective of this study is to replicate and verify some of the published work comparing different allocation strategies and also incorporating recently published hierarchical clustering based portfolio selection strategies into out of sample performance evaluation across different datasets. Initial findings suggest that the difference between the performance of the classical strategies and the recently developed clustering based methodologies are not statistically significant from each other when only positive weights are allowed in the portfolios