Academic literature on the topic 'Optimal trading portfolio'

Portfolio optimization is the main concern for portfolio managers. Financial securities are placed within the portfolio based on the investor’s risk tolerance. The study measures the risk-reward relationship when the number of stocks in the portfolio increases. Six diverse portfolios have been created with a different number of stocks, such as portfolios with 47 stocks, 95 stocks, 142 stocks, 190 stocks, 239 stocks, and 287 stocks. Stock prices and trading volume were collected on a weekly basis from the six largest European stock exchanges (FTSE100, CAC40, FTSE MIB, IBEX35, DAX, and MDAX). Markowitz’s (1952) diversification formula has been used to measure the risk level of the individual portfolios. The results of the study show that the diversification risk constantly decreases when we move from the portfolios with 47 stocks to the portfolios with 287 stocks. The weighted average returns increase on the portfolios with a higher number of stocks, which is contrary to the standard portfolio theories. The results of the study indicate managerial implications for financial investors that are focused exclusively on the largest European stock exchanges.

Over the past decade, there has been a significant rise in assets managed under passive and systematic strategies. Such strategies hold and trade portfolios in a coordinated manner, often concentrating trading around the end of the trading session. Simultaneously, there has been a rise in activity from market participants that act as liquidity providers, themselves trading along portfolio directions. In “Cross-Sectional Variation of Intraday Liquidity, cross-impact, and Their Effect on Portfolio Execution,” Min, Maglaras, and Moallemi investigate the implications of these two observations, specifically exploring how the phenomenon of portfolio liquidity provision leads to cross-security impact and influences the optimal execution schedules of risk-neutral traders that seek to minimize their expected execution costs. They show that the optimized schedules deviate from the naïve approach that trades each security separately and instead, couple the trading intensity across stocks so as to benefit from the liquidity provided along attractive portfolio trading directions. Empirical analysis demonstrates that coupled optimized schedules could lower costs by as much as 15% relative to the naïve approach.

Purpose – The purpose of this paper is to present an alternative approach to equity trading that is based on cointegration. If there are long-run equilibria among financial assets, a cointegration-based trading strategy can exploit profitable opportunities by capturing mean-reverting short-run deviations. Design/methodology/approach – First, the author introduces an equity indexing technique to form cointegration tracking portfolios that are able to replicate an index effectively. The author later enhances this tracking methodology in order to construct more complex portfolio-trading strategies that can be approximately market neutral. The author monitors the performance of a wide range of trading strategies under different specifications, and conducts an in-depth sensitivity analysis of the factors that affect the optimal portfolio construction. Several statistical-arbitrage tests are also carried out in order to examine whether the profitability of the cointegration-based trading strategies could indicate a market inefficiency. Findings – The author shows that under certain parameter specifications, an efficient tracking portfolio is able to produce similar patterns in terms of returns and volatility with the market. The author also finds that a successful long-short strategy of two cointegration portfolios can yield an annualized return of more than 8 percent, outperforming the benchmark and also demonstrating insignificant correlation with the market. Even though some cointegration-based pairs-trading strategies can consistently generate significant cumulative profits, yet they do not seem to converge to risk-less arbitrages, and thus the hypothesis of market efficiency cannot be rejected. Originality/value – The primary contribution of the research lies within the detailed analysis of the factors that affect the tracking-portfolio performance, thus revealing the optimal conditions that can lead to enhanced returns. Results indicate that cointegration can provide the means to successfully reproducing the risk-return profile of a benchmark and to implementing market-neutral strategies with consistent profitability. By testing for statistical arbitrage, the author also provides new evidence regarding the connection between the profit accumulation of cointegration-based pairs-trading strategies and market efficiency.

Purpose The purpose of this paper is to investigate the impact of factor-based trading strategies on pricing and volume. Design/methodology/approach The authors employ a regression discontinuity approach to identify abnormalities in volume or pricing around expected portfolio changes. In addition, the authors characterize more granular effects on pricing and volume as a result of portfolio re-classification through Fama and Macbeth (1973) regressions. Findings The authors find that firms which are predicted to transfer among the factor portfolios of Fama and French (1993) exhibit strong and statistically significant short-term variation in stock price and volume. Short-term returns around the cutoff values comprising SMB and HML tend to be temporarily high if the firm is predicted to move into a long component of a factor-mimicking portfolio, and temporarily low if moving into a short component. Similar results are apparent when examining movement in and out of the 25 size and book-to-market sorted test asset portfolios. Practical implications The use of portfolio strategies formulated on the basis of sorting procedures, while once upon a time a niche market in the portfolio management industry, is now ubiquitous. The results of this study raise interesting methodological questions about the pricing implications arising from these common methodologies. Originality/value This study makes a number of contributions. First, it contributes to the idea that the publication or dissemination of trading strategies or – more generally – common portfolio sorting methods, leads to effects on pricing and volume through commonly motivated trading pressure. In other words, recipe-like discoveries of advantageous trading strategies lead to a synthetic creation of demand. Second, by noting that a lot of factor-focused trading activity begins around July and August of each year, the study relates to existing literature which documents seasonal variation in stock returns and volume. The findings raise questions about what guides institutional investors’ portfolio allocation decisions and whether these are optimal in aggregate.

In this paper, we propose a pairs trading model that incorporates a time-varying volatility of the constant elasticity of variance type. Our approach is based on stochastic control techniques; given a fixed time horizon and a portfolio of two cointegrated assets, we define the trading strategies as the portfolio weights maximizing the expected power utility from terminal wealth. We compute the optimal pairs strategies by using a finite difference method. Finally, we illustrate our results by conducting tests on historical market data at daily frequency. The parameters are estimated by the generalized method of moments.

Aim/purpose – The aim of the paper is to rank the optimal portfolios of shares of com- panies listed on the Warsaw Stock Exchange, taking into account the investor’s propen- sity to risk. Design/methodology/approach – Investment portfolios consisting of varied number of companies selected from WIG 20 index were built. Next, the weights of equity holdings of these companies in the entire portfolio were determined, maximizing portfolio’s expected (square) utility function, and then the obtained structures were compared between investors with various levels of risk propensity. Using Hellwig’s taxonomic development measure, a ranking of optimum stock portfolios depending on the inves- tor’s risk propensity was prepared. The research analyzed quotations from 248 trading sessions. Findings – The findings indicated that whilst there are differences in the weight struc- tures of equity holdings in the entire portfolio between the investor characterized by aversion to risk at the level of γ = 10 and the investor characterized by aversion to risk at the level of γ = 100, the rankings of the constructed optimum portfolios demonstrate strong similarity. The study validated, in conformity with the literature, that with the increase in the number of equity holdings in the portfolio, the portfolio risk initially decreases and then becomes stable at a certain level. Research implications/limitations – The study used data from the past as for which there is no guarantee that they will be adequate for the future. There is sensitivity to the selection of the period from which the historic data come. When changing the period of the analyzed historic data by a small time unit it may prove that the portfolio composi- tion will become totally different. Originality/value/contribution – The paper compares the composition of optimum stock portfolios depending on the investor’s propensity to risk. Their ranking was cre- ated using the taxonomic method for this purpose. Taking advantage of this method also additional variables can be taken into account, which describe and differentiate the port- folio and they can be assigned relevant significance depending on the investor’s prefer- ences. Keywords: optimal portfolio, expected rate of return on the portfolio, portfolio standard deviation, expected utility theory, multidimensional comparative analysis. JEL Classification: G10, G11.

As social insurance company of the Republic of Indonesia, PT ABC (Persero) has a captive market based on the provisions of Undang-undang in Indonesia. The company has managed funds from the government, and is one of the four insurance products in the company, into an investment portfolio. As one of the company’s revenue generator, PT ABC needs to put the fund into investment instruments that have higher returns to meet the needs of the company, one of which is through stock investment. The formation of stock portfolio is carried out through an optimum portfolio approach by using single index model method. This is a quantitative descriptive research using analysis tools and data processing by Microsoft Excel software. Portfolios are formed into several scenarios by considering the composition of the current portfolio in one of the company’s products and stock price movements in Indonesia. The data used in this study are historical data on daily stock movements for the five years of the 2014-2018 trading period and historical data on the investment portfolio for XYZ products in 2018. From this research, 2 strategic plans for forming company portfolios and 1 recommendation of stocks are produced that have good resilience during a pandemic. The results of the calculations are expected to be taken into consideration by the company in the formation of future company portfolios

This paper addresses the optimal rebalancing problem of a long–short portfolio with high net asset value under trading impact losses. The fund manager may employ leveraging as a tool to increase portfolio returns. However, to mitigate potential leverage risks, frequent rebalancing may become necessary, which leads to significant slippage losses that dampen portfolio performance ex post. We consider the problem in an integrated framework by incorporating trading impact and leverage restrictions ex ante within a mean–variance framework, where leverage control is imposed using a chance constraint. The resulting mean–variance–leverage optimization model (MVL) is non-convex, and we develop an efficient scheme to obtain the optimal portfolio. We investigate how portfolio leverage modifies the MV efficient frontier in the presence of trading impact, and highlight the significant outperformance of the proposed model relative to the standard mean–variance model. Increased target means require less restrictions on leverage, which result in higher rates of slippage losses. Our analysis supports the notion that leverage restrictions contribute to choosing high beta assets, even in the presence of trading impact.

This paper presents of model of market closure in the management of international portfolios. We consider an investor holding a portfolio of domestic stocks and foreign stocks who faces market closure in the management of his portfolio. The investor's portfolio is affected by the exchange rate risk and different dynamics of the underlying assets during the period of trading and non-trading. The investor must determine the optimal proportions of his wealth to allocate to domestic stocks and foreign stocks during the market open and close periods. The paper investigates the effects of opening and closing on transactions demand of domestic and foreign stocks. The transactions demand at open and close periods in the securities markets are studied in the presence of information costs using the main concepts in Merton's (1987) model of capital market equilibrium with incomplete information. Using optimal control theory, we provide a solution in the general case and propose analytic solutions for the constant relative aversion utility functions. The model can be applied to solve several problems in financial economics in the presence of market closure.

This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naïve portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process.

The two main questions arising from the problem of optimal bond portfolio management concern the formulation of an optimal trading rule and the specification of an appropriate dynamic risk measure in which to express portfolio objectives. We study these questions in two related essays: (l) a theoretical study of optimal trading policies in view of, as yet unspecified, portfolio objectives when trading is costly; and (2) an empirical, comparative study of several bond risk measures, proposed in the literature or in use by practitioners, for the government or default-free bond market. The theoretical study considers a delegated portfolio management setting, in which the manager optimizes a cumulative reward over a finite time period and where the reward rate increases with portfolio value and decreases with deviations from the given risk objectives. Trading is then often not worthwhile, as the possible gains from smaller objective deviations are offset by losses on account of transactions costs. This setting obviates the need for separate ex post performance evaluation. The trading problem is formulated as one of optimal impulse control in the framework of stochastic dynamic programming; this formulation improves upon prior results in the literature using continuous control theory. A myopic optimal trading rule is characterized, which is also applicable to time-homogeneous problems and more general preferences. An algorithm for its use in applications is derived. The empirical study applies the usual methods of stock market tests to the returns of constant risk bond portfolios. These portfolios are artificial constructs composed, at varying risk levels, of traded bonds on the basis of six different one or two dimensional risk measures. These risk measures are selected in order to obtain a cross-section of term structure variabilities; they include duration, short interest rate risk, long (13-year) interest rate risk, combined short and consol rate risks, duration combined with convexity, and average time-to-maturity. The sample period is the 1970s decade, for which parameter estimates for the risk measures— where necessary—are available from source papers. This period is known to be one with wide-ranging term structure movements and is therefore ideally suited for the tests of this paper. Portfolios are formed at two levels of diversification: bullet and ladder selection. We confirm that all of these risk measures are reasonably effective in capturing relevant bond market risk: the state space of bond returns has in all cases a low dimension (two or three), with only a single factor significantly priced. Best fit is found for portfolios selected by duration, the 13-year spot yield risk, and the two-dimensional short/consol rate risk, all of which consist predominantly of "long" rate risk. The short rate-based risk measure does not explain portfolio returns as well: it has difficulty discriminating between portfolios with long remaining times-to-maturity. Convexity, furthermore, adds nothing to the explanatory power of duration. Average time-to-maturity compares reasonably well with the above risk measures, provided the portfolios are well-diversified across the maturity spectrum; this lends some support to the use of yield curves. A strong diversification effect has also been found, to the extent that the returns on ladder portfolios are practically linear combinations of two or three of the portfolios, typically the lowest and highest risk portfolios in the one dimensional risk cases, with an intermediate portfolio added in the two-dimensional cases. Provided that diversified portfolios are used, the comparatively easy to implement duration measure is as good as any of the risk measures tested.
Business, Sauder School of
Finance, Division of
Graduate

Актуальність теми: на даний момент не існує жодного сервісу, який дозволяє користувачу швидко дізнатися оптимальне співвідношення між активами в торговому портфелі, не дивлячись на те, що математично проблема давно вирішена. Окрім цього, великою проблемою трейдерів-початківців є вибір активів, які входять до портфелю. На сьогоднішній день жоден з аналітичних сервісів ринку іноземних валют не надає користувачеві простого, і головне математично обгрунтованого способу для вибору активів до складу свого портфелю. Мета дослідження: Основною метою є дослідження та розробка архітектури програмного забезпечення для зменшення витрат часу користувача на створення портфелю активів шляхом поєднання в одному застосунку алгоритмів кластеризації та оптимізації. Для реалізації поставленої мети сформульовані наступні завдання: – налагодження ETL процесу в системі; – програмна реалізація алгоритмів; – дослідження і порівняння швидкодії реалізованих алгоритмів; – побудова гнучкої архітектури десктопного застосунку; – створення програмних інтерфейсів для передачі результатів роботи алгоритму стороннім джерелам. Об’єкт дослідження: процес розробки програмного забезпечення формування оптимального портфелю на ринку іноземних валют. Предмет дослідження: алгоритми кластеризації та методи оптимізації, програмні бібліотеки алгоритмів оптимізації та кластеризації, шляхи поєднання кластеризації та математичної оптимізації в межах одного програмного застосунку. Наукова новизна результатів магістерської дисертації полягає в тому, що запропоновано архітектурне рішення для побудови програмного забезпечення для створення торгового портфелю, яке на відміну від інших надає користувачеві очікуваний результат при мінімальних затратах часу та кількості необхідних дій для початку роботи. Результат досягнутий шляхом розробки модернізованого алгоритму оптимізації. Практичне значення отриманих результатів полягає в тому, що реалізовані методи поєднані в межах одного застосунку і максимально прості у використанні для користувача. Також реалізовано АРІ-інтерфейс, за допомогою якого результати роботи алгоритмів можуть з легкістю отримувати і застосовувати сторонні сервіси. Зв’язок з науковими програмами, планами, темами: робота виконувалась на кафедрі автоматизованих систем обробки інформації і управління Національного технічного університету України "Київський політехнічний інститут імені Ігоря Сікорського". Публікації: Наукові положення дисертації опубліковані в Ясенова А.В. Застосування алгоритмів кластеризації на ринку іноземних валют/ А.В. Ясенова, О.А. Халус // Матеріали V всеукраїнської науково-практичної конференції молодих вчених та студентів «Інформаційні системи та технології управління» (ІСТУ-2020) – м. Київ: НТУУ «КПІ ім. Ігоря Сікорського», 26-27 листопада 2020 р.
Topicality: today there is no service which allows quickly find out optimal weights for trading portfolio components, despite the fact that mathematically the problem has long been solved. It is also very difficult for novice traders to choose the assets that are part of the portfolio. Today, none of the analytical services of the foreign exchange market provides the user with a simple and, most importantly, mathematically reliable way to compose trading portfolio. The aim of the study: the main target is to research and develop software architecture for decreasing the time spent on the portfolio creation by combining in one application clustering and optimization algorithms. To achieve this goal, the following tasks were formulated: – debug the ETL process; – implementation of algorithms; – compare efficiency of implemented algorithms; – build flexible infrastructure; – create API interfaces to transfer results of work to internal sources. – create interfaces for receiving results of work of algorithms. Object of research: the process of developing software for composing the optimal portfolio in the foreign exchange market. Subject of research: clustering algorithms and optimization methods, software libraries of optimization and clustering algorithms, ways to combine clustering and mathematical optimization within one software application. The scientific novelty of the results of the master's dissertation is that for the first time proposed architecture decision for building software for composing a trading portfolio, which, unlike others, provides the user with the expected result with minimal time and the number of necessary actions to get started. The result was achieved by developing an upgraded optimization algorithm. The practical value of the obtained results is that the implemented methods are combined within one application and are as easy to use for the user. Also implemented API-interface, through which the results of the algorithms can easily receive and use third-party services. Relationship with working with scientific programs, plans, topics: work was performed at the Department of Automated Information Processing and Management Systems of the National Technical University of Ukraine «Kyiv Polytechnic Institute. Igor Sikorsky». Publications: Scientific provisions of the dissertation published in Yasenova A.V. The application of clustering methods on the foreign exchange market / A.V.Yasenova, O.A. Khalus // Proceedings of the Fifth All-Ukrainian Scientific and Practical Conference of Young Scientists and Students "Information Systems and Management Technologies" (ISTU- 2020) - Kyiv: NTUU “KPI them. Igor Sikorsky”, November 26-27, 2020.

In this thesis we study the utility maximization problem for assets whose prices are cointegrated, which arises from the investment practice of convergence trading and its special forms, pairs trading and spread trading. The major theme in the first two chapters of the thesis, is to investigate the assumption of market-neutrality of the optimal convergence trading strategies, which is a ubiquitous assumption taken by practitioners and academics alike. This assumption lacks a theoretical justification and, to the best of our knowledge, the only relevant study is Liu and Timmermann (2013) which implies that the optimal convergence strategies are, in general, not market-neutral. We start by considering a minimalistic pairs-trading scenario with two cointegrated stocks and solve the Merton investment problem with power and logarithmic utilities. We pay special attention to when/if the stochastic control problem is well-posed, which is overlooked in the study done by Liu and Timmermann (2013). In particular, we show that the problem is ill-posed if and only if the agent’s risk-aversion is less than a constant which is an explicit function of the market parameters. This condition, in turn, yields the necessary and sufficient condition for well-posedness of the Merton problem for all possible values of agent’s risk-aversion. The resulting well-posedness condition is surprisingly strict and, in particular, is equivalent to assuming the optimal investment strategy in the stocks to be market-neutral. Furthermore, it is shown that the well-posedness condition is equivalent to applying Novikov’s condition to the market-price of risk, which is a ubiquitous sufficient condition for imposing absence of arbitrage. To the best of our knowledge, these are the only theoretical results for supporting the assumption of market-neutrality of convergence trading strategies. We then generalise the results to the more realistic setting of multiple cointegrated assets, assuming risk factors that effects the asset returns, and general utility functions for investor’s preference. In the process of generalising the bivariate results, we also obtained some well-posedness conditions for matrix Riccati differential equations which are, to the best of our knowledge, new. In the last chapter, we set up and justify a Merton problem that is related to spread-trading with two futures assets and assuming proportional transaction costs. The model possesses three characteristics whose combination makes it different from the existing literature on proportional transaction costs: 1) finite time horizon, 2) Multiple risky assets 3) stochastic opportunity set. We introduce the HJB equation and provide rigorous arguments showing that the corresponding value function is the viscosity solution of the HJB equation. We end the chapter by devising a numerical scheme, based on the penalty method of Forsyth and Vetzal (2002), to approximate the viscosity solution of the HJB equation.

Since its’ invention at Morgan Stanley in 1987 pairs trading has grown to be one of the most common and most researched strategies for market neutral returns. The strategy identifies stocks, or other financial securities, that historically has co-moved and forms a trading pair. If the price relation is broken a short position is entered in the overperforming stock and a long in the underperforming. The positions are closed when the spread returns to the long-term relation. A pairs trading portfolio is formed by combining a number of pairs. To detect adequate pairs different types of data analysis has been used. The most common way has been to study historical price data with different statistical models such as the distance method. Gatev et al (2006) used this method and provided the most extensive research on the subject and this study will follow the standards set by that article and add new interesting factors. This is done through an investigation on how the analysis can be improved by using the stocks fundamental data, e.g. P/E, P/B, leverage, industry classification. This data is used to set up restrictions and Lasso models (type of regression) to optimize the trading portfolio and achieve higher returns. All models have been back-tested using S&P 500 stocks between 2001-04-01 and 2015-04-01 with portfolios changed every six months. The most important finding of the study is that restricting stocks to have close P/E-ratios combined with traditional price series analysis increases returns. The most conservative measure gives annual returns of 3.99% to 4.98% depending on the trading rules for this portfolio. The returns are significantly (5%-level) higher than those obtained by the traditional distance method. Considerable variations in return levels is shown to be created when capital commitments are changed and trading rules, transaction costs and restrictions on unique portfolio stocks are implemented. Further research regarding how analysis of P/E-ratios can improve pairs trading is suggested. The thesis has been written independently without an external client and studied an area that the author found interesting.

Le choix de portefeuille optimal d'actifs a été depuis longtemps et continue d'être un sujet d'intérêt majeur dans le domaine de la finance. L'objectif principal étant de trouver la meilleure façon d'allouer les ressources financières dans un ensemble d'actifs disponibles sur le marché financier afin de réduire les risques de fluctuation du portefeuille et d'atteindre des rendements élevés. Néanmoins, la littérature de choix de portefeuille a connu une avancée considérable à partir du 20ieme siècle avec l'apparition de nombreuses stratégies motivées essentiellement par le travail pionnier de Markowitz (1952) qui offre une base solide à l'analyse de portefeuille sur le marché financier. Cette thèse, divisée en trois chapitres, contribue à cette vaste littérature en proposant divers outils économétriques pour améliorer le processus de sélection de portefeuilles sur le marché financier afin d'aider les intervenants de ce marché. Le premier chapitre, qui est un papier joint avec Marine Carrasco, aborde un problème de sélection de portefeuille avec coûts de transaction sur le marché financier. Plus précisément, nous développons une procédure de test simple basée sur une estimation de type GMM pour évaluer l'effet des coûts de transaction dans l'économie, quelle que soit la forme présumée des coûts de transaction dans le modèle. En fait, la plupart des études dans la littérature sur l'effet des coûts de transaction dépendent largement de la forme supposée pour ces frictions dans le modèle comme cela a été montré à travers de nombreuses études (Dumas and Luciano (1991), Lynch and Balduzzi (1999), Lynch and Balduzzi (2000), Liu and Loewenstein (2002), Liu (2004), Lesmond et al. (2004), Buss et al. (2011), Gârleanu and Pedersen (2013), Heaton and Lucas (1996)). Ainsi, pour résoudre ce problème, nous développons une procédure statistique, dont le résultat est indépendant de la forme des coûts de transaction, pour tester la significativité de ces coûts dans le processus d'investissement sur le marché financier. Cette procédure de test repose sur l'hypothèse que le modèle estimé par la méthode des moments généralisés (GMM) est correctement spécifié. Un test commun utilisé pour évaluer cette hypothèse est le J-test proposé par Hansen (1982). Cependant, lorsque le paramètre d'intérêt se trouve au bord de l'espace paramétrique, le J-test standard souffre d'un rejet excessif. De ce fait, nous proposons une procédure en deux étapes pour tester la sur-identification lorsque le paramètre d'intérêt est au bord de l'espace paramétrique. Empiriquement, nous appliquons nos procédures de test à la classe des anomalies utilisées par Novy-Marx and Velikov (2016). Nous montrons que les coûts de transaction ont un effet significatif sur le comportement des investisseurs pour la plupart de ces anomalies. Par conséquent, les investisseurs améliorent considérablement les performances hors échantillon en tenant compte des coûts de transaction dans le processus d'investissement. Le deuxième chapitre aborde un problème dynamique de sélection de portefeuille de grande taille. Avec une fonction d'utilité exponentielle, la solution optimale se révèle être une fonction de l'inverse de la matrice de covariance des rendements des actifs. Cependant, lorsque le nombre d'actifs augmente, cet inverse devient peu fiable, générant ainsi une solution qui s'éloigne du portefeuille optimal avec de mauvaises performances. Nous proposons deux solutions à ce problème. Premièrement, nous pénalisons la norme des poids du portefeuille optimal dans le problème dynamique et montrons que la stratégie sélectionnée est asymptotiquement efficace. Cependant, cette méthode contrôle seulement en partie l'erreur d'estimation dans la solution optimale car elle ignore l'erreur d'estimation du rendement moyen des actifs, qui peut également être importante lorsque le nombre d'actifs sur le marché financier augmente considérablement. Nous proposons une méthode alternative qui consiste à pénaliser la norme de la différence de pondérations successives du portefeuille dans le problème dynamique pour garantir que la composition optimale du portefeuille ne fluctue pas énormément entre les périodes. Nous montrons que, sous des conditions de régularité appropriées, nous maîtrisons mieux l'erreur d'estimation dans le portefeuille optimal avec cette nouvelle procédure. Cette deuxième méthode aide les investisseurs à éviter des coûts de transaction élevés sur le marché financier en sélectionnant des stratégies stables dans le temps. Des simulations ainsi qu'une analyse empirique confirment que nos procédures améliorent considérablement la performance du portefeuille dynamique. Dans le troisième chapitre, nous utilisons différentes techniques de régularisation (ou stabilisation) empruntées à la littérature sur les problèmes inverses pour estimer le portefeuille diversifié tel que définie par Choueifaty (2011). En effet, le portefeuille diversifié dépend du vecteur de volatilité des actifs et de l'inverse de la matrice de covariance du rendement des actifs. En pratique, ces deux quantités doivent être remplacées par leurs contrepartie empirique. Cela génère une erreur d'estimation amplifiée par le fait que la matrice de covariance empirique est proche d'une matrice singulière pour un portefeuille de grande taille, dégradant ainsi les performances du portefeuille sélectionné. Pour résoudre ce problème, nous étudions trois techniques de régularisation, qui sont les plus utilisées : le rigde qui consiste à ajouter une matrice diagonale à la matrice de covariance, la coupure spectrale qui consiste à exclure les vecteurs propres associés aux plus petites valeurs propres, et Landweber Fridman qui est une méthode itérative, pour stabiliser l'inverse de matrice de covariance dans le processus d'estimation du portefeuille diversifié. Ces méthodes de régularisation impliquent un paramètre de régularisation qui doit être choisi. Nous proposons donc une méthode basée sur les données pour sélectionner le paramètre de stabilisation de manière optimale. Les solutions obtenues sont comparées à plusieurs stratégies telles que le portefeuille le plus diversifié, le portefeuille cible, le portefeuille de variance minimale et la stratégie naïve 1 / N à l'aide du ratio de Sharpe dans l'échantillon et hors échantillon.
The optimal portfolio selection problem has been and continues to be a subject of interest in finance. The main objective is to find the best way to allocate the financial resources in a set of assets available on the financial market in order to reduce the portfolio fluctuation risks and achieve high returns. Nonetheless, there has been a strong advance in the literature of the optimal allocation of financial resources since the 20th century with the proposal of several strategies for portfolio selection essentially motivated by the pioneering work of Markowitz (1952)which provides a solid basis for portfolio analysis on the financial market. This thesis, divided into three chapters, contributes to this vast literature by proposing various economic tools to improve the process of selecting portfolios on the financial market in order to help stakeholders in this market. The first chapter, a joint paper with Marine Carrasco, addresses a portfolio selection problem with trading costs on stock market. More precisely, we develop a simple GMM-based test procedure to test the significance of trading costs effect in the economy regardless of the form of the transaction cost. In fact, most of the studies in the literature about trading costs effect depend largely on the form of the frictions assumed in the model (Dumas and Luciano (1991), Lynch and Balduzzi (1999), Lynch and Balduzzi (2000), Liu and Loewenstein (2002), Liu (2004), Lesmond et al. (2004), Buss et al. (2011), Gârleanu and Pedersen (2013), Heaton and Lucas (1996)). To overcome this problem, we develop a simple test procedure which allows us to test the significance of trading costs effect on a given asset in the economy without any assumption about the form of these frictions. Our test procedure relies on the assumption that the model estimated by GMM is correctly specified. A common test used to evaluate this assumption is the standard J-test proposed by Hansen (1982). However, when the true parameter is close to the boundary of the parameter space, the standard J-test based on the chi2 critical value suffers from overrejection. To overcome this problem, we propose a two-step procedure to test overidentifying restrictions when the parameter of interest approaches the boundary of the parameter space. In an empirical analysis, we apply our test procedures to the class of anomalies used in Novy-Marx and Velikov (2016). We show that transaction costs have a significant effect on investors' behavior for most anomalies. In that case, investors significantly improve out-of-sample performance by accounting for trading costs. The second chapter addresses a multi-period portfolio selection problem when the number of assets in the financial market is large. Using an exponential utility function, the optimal solution is shown to be a function of the inverse of the covariance matrix of asset returns. Nonetheless, when the number of assets grows, this inverse becomes unreliable, yielding a selected portfolio that is far from the optimal one. We propose two solutions to this problem. First, we penalize the norm of the portfolio weights in the dynamic problem and show that the selected strategy is asymptotically efficient. However, this method partially controls the estimation error in the optimal solution because it ignores the estimation error in the expected return, which may also be important when the number of assets in the financial market increases considerably. We propose an alternative method that consists of penalizing the norm of the difference of successive portfolio weights in the dynamic problem to guarantee that the optimal portfolio composition does not fluctuate widely between periods. We show, under appropriate regularity conditions, that we better control the estimation error in the optimal portfolio with this new procedure. This second method helps investors to avoid high trading costs in the financial market by selecting stable strategies over time. Extensive simulations and empirical results confirm that our procedures considerably improve the performance of the dynamic portfolio. In the third chapter, we use various regularization (or stabilization) techniques borrowed from the literature on inverse problems to estimate the maximum diversification as defined by Choueifaty (2011). In fact, the maximum diversification portfolio depends on the vector of asset volatilities and the inverse of the covariance matrix of assets distribution. In practice, these two quantities need to be replaced by their sample counterparts. This results in estimation error which is amplified by the fact that the sample covariance matrix may be close to a singular matrix in a large financial market, yielding a selected portfolio far from the optimal one with very poor performance. To address this problem, we investigate three regularization techniques, such as the ridge, the spectral cut-off, and the Landweber-Fridman, to stabilize the inverse of the covariance matrix in the investment process. These regularization schemes involve a tuning parameter that needs to be chosen. So, we propose a data-driven method for selecting the tuning parameter in an optimal way. The resulting regularized rules are compared to several strategies such as the most diversified portfolio, the target portfolio, the global minimum variance portfolio, and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio.

AbstractEconomics encompasses two broad subjects: macroeconomics and microeconomics. Macroeconomics deals with an economy in aggregate and addresses issues such as inflation, unemployment, interest rates, and economic growth. We present a macroeconomic perspective in Chap. 10.1007/978-3-030-74817-3_3. Microeconomics, the focus of this chapter, operates, as its name indicates, on the micro level, addressing household consumption decisions and the production decisions of firms. In this chapter, we focus on the parallels (and a few differences) between a standard microeconomics formulation (a household’s selection of an optimal consumption bundle) and a standard finance model (an investor’s selection of a portfolio that optimally combines a riskless asset – cash – and a risky equity portfolio). The finance formulation is the Capital Asset Pricing Model (CAPM). CAPM is a keystone of what is known as modern portfolio theory, the originator of which is Harry Markowitz who was awarded a Nobel Memorial Prize in Economic Sciences in 1990 for having developed the theory of portfolio choice. We then introduce friction (trading costs) and show how CAPM’s frictionless market equilibrium is perturbed. The analysis provides a good lead-in to the next chapter on finance.

This chapter examines the performance of liquidity-adjusted risk modeling in obtaining optimum and coherent economic-capital structures, subject to meaningful operational and financial constraints as specified by the portfolio manager. Specifically, the chapter proposes a robust approach to optimum economic-capital allocation in a liquidity-adjusted value at risk (L-VaR) framework. This chapter expands previous approaches by explicitly modeling the liquidation of trading portfolios, over the holding period, with the aid of an appropriate scaling of the multiple-assets' L-VaR matrix along with GARCH-M technique to forecast conditional volatility and expected return. Moreover, in this chapter, the authors develop a dynamic nonlinear portfolio selection model and an optimization algorithm, which allocates both economic-capital and trading assets by minimizing L-VaR objective function. The empirical results strongly confirm the importance of enforcing financially and operationally meaningful nonlinear and dynamic constraints, when they are available, on the L-VaR optimization procedure.

The article deals with the problem of analysis of banking activity and modern methods of investment development of the bank based on pairs trading models. The essence of the pair trading method as one of the most popular and qualitative methods of investment paper quality analysis is disclosed. The basis of the pairing trading method is defined as the beta-neutral portfolio strategy, which consists of creating a portfolio with a beta coefficient equal to zero, and the main advantage of which is the complete independence of the final paper yield from the market yield, it is only dependent on the future ratio of the value of one security to another. For the successful introduction of this method in banking activity, a clear algorithm for the construction of a paired trading model based on economic-mathematical methods and models is proposed. The proposed algorithm contains three stages in which the following steps are to be taken: analysis and selection of securities; development of a pairing trading model; development and regulation of the selected strategy. The implementation of the proposed algorithm begins with the selection of statistical data on the prices of securities, provides for the verification of data on stationarity, as well as the identification of a system for combining series, and the analysis of coefficients of the matching between prices of securities. As a result of the steps taken, pairs of securities are selected that are more closely related and a full economic analysis of the pairs is made, and the parameters of co-integration equations to pairs of paper are selected, evaluated and analyzed then the errors of the co-integration model are checked for stationary. In the work models of pairs trading are constructed for the realization of an aggressive strategy of trade spreads. In order to build an effective strategy for pairing trading, data on prices of securities, which are the most attractive to Ukrainian banks, namely, US Treasury bonds, have been examined. The hypothesis being tested in the paper is that it is necessary to identify a pair of securities with a sufficiently strong dependency where one should have a rapid growth or decline relative to the other, after which the sale of the revalued security and the purchase of the undervalued security is mandatory. The study found that for each pair of Treasury bonds, the ratio was satisfactory. This indicates that the resultant securities pairs are suitable as an investment that, with a well-designed strategy, will allow the bank to obtain optimum returns. The final step of the algorithm is the analysis of the results obtained, which includes a comprehensive analysis of the conducted research and effective decision-making. The application of the proposed algorithm will allow banks to make informed decisions on the choice and regulation of the strategy in exchange market changes in order to obtain a low level of risk and a high level of profit.

CVaR-sensitive online portfolio selection (CS-OLPS) becomes increasingly important for investors because of its effectiveness to minimize conditional value at risk (CVaR) and control extreme losses. However, the non-stationary nature of financial markets makes it very difficult to address the CS-OLPS problem effectively. To address the CS-OLPS problem in non-stationary markets, we propose an effective news-driven method, named CAND, which adaptively exploits news to determine the adjustment tendency and adjustment scale for tracking the dynamic optimal portfolio with minimal CVaR in each trading round. In addition, we devise a filtering mechanism to reduce the errors caused by the noisy news for further improving CAND's effectiveness. We rigorously prove a sub-linear regret of CAND. Extensive experiments on three real-world datasets demonstrate CAND’s superiority over the state-of-the-art portfolio methods in terms of returns and risks.