Exchange traded funds: uma análise do desempenho de rastreamento e persistência

This study assesses the tracking performance and persistence of a set of Exchange Traded Funds (ETF) created to track a benchmark equity index. Starting from a selected sample of 11 international ETFs, it analyzes performance and performance persistence, tracking error and its persistence in the period between 2013 and 2020. The methodology consisted of calculating performance evaluation measures such as logarithmic profitability, standard deviation, tracking error, excess return and a set of indicators that includes Sharpe, Treynor, Sortino and Jensen's alpha ratios. Cross-sectional regressions are also performed to assess the persistence of performance and tracking error. Overall, the results suggest that most ETFs underperform their benchmark. Evidence shows that Jensen's ratio observes many negative and statistically significant alphas in most cases. The estimates of the Sharpe measure and the Treynor and Sortino ratios confirm an underperformance under the benchmark. Only in two of the eleven ETF funds analyzed did the performance surpass the respective benchmark. Evidence of performance persistence in the gross return of ETFs is found only between 2019 and 2020, but also in the context of the use of ratios, in several pairs of years. The analyzed ETFs present tracking errors in almost all periods, positive and significant beta coefficients showing temporal persistence. The magnitude of the tracking error appears to be low, although the t test indicates that this difference is statistically significant. The two funds that replicate the American indices have lower tracking error, with the opposite occurring in the ETF that tracks the Chinese stock market. Tracking accuracy tended to change over the years with no definite trend in replication discrepancies.Este estudo avalia o desempenho de rastreamento e a persistência de um conjunto de Exchange Traded Funds (ETF), criados para acompanhar um índice acionista de referência. Partindo de uma amostra selecionada de 11 ETF internacionais, analisa o desempenho e a persistência de desempenho, o tracking error e a sua persistência no período entre 1 de janeiro de 2013 e 31 de dezembro de 2020. A metodologia consistiu no cálculo de medidas de avaliação de desempenho como a rendibilidade logarítmica, o desvio padrão, o tracking error, o excess return e ainda um conjunto de indicadores que inclui os rácios de Sharpe, Treynor, Sortino e o alfa de Jensen. São também efetuadas regressões cross-sectional para aferir a persistência de desempenho e tracking error. Em termos gerais, os resultados sugerem que a maioria dos ETF apresenta um desempenho inferior ao seu benchmark. As evidências mostram que o rácio de Jensen observa muitos alfas negativos e estatisticamente significativos na maioria dos casos. As estimativas da medida de Sharpe e dos rácios de Treynor e Sortino confirmam um desempenho inferior ao índice de referência. Apenas em dois dos onze fundos ETF analisados o desempenho supera o respetivo benchmark. É encontrada prova de persistência de desempenho na rendibilidade bruta dos ETF apenas entre 2019 e 2020, mas também no contexto da utilização dos rácios, em vários pares de anos. Os ETF analisados apresentam tracking errors em quase todos os períodos, coeficientes beta positivos e significativos evidenciando persistência temporal. A magnitude do erro de rastreamento afigura-se baixa, embora o teste t indique que essa diferença é estatisticamente significativa. Os dois fundos que replicam os índices americanos apresentam erro de rastreamento mais baixo, verificando-se o oposto no ETF que rastreia o mercado acionista chinês. A precisão do rastreamento tendeu a alterar-se ao longo dos anos sem uma tendência definida nas discrepâncias na replicação

Portfolio optimisation models

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonIn this thesis we consider three different problems in the domain of portfolio optimisation. The first problem we consider is that of selecting an Absolute Return Portfolio (ARP). ARPs are usually seen as financial portfolios that aim to produce a good return regardless of how the underlying market performs, but our literature review shows that there is little agreement on what constitutes an ARP. We present a clear definition via a three-stage mixed-integer zero-one program for the problem of selecting an ARP. The second problem considered is that of designing a Market Neutral Portfolio (MNP). MNPs are generally defined as financial portfolios that (ideally)exhibit performance independent from that of an underlying market, but, once again, the existing literature is very fragmented. We consider the problem of constructing a MNP as a mixed-integer non-linear program (MINLP) which minimises the absolute value of the correlation between portfolio return and underlying benchmark return. The third problem is related to Exchange-Traded Funds (ETFs). ETFs are funds traded on the open market which typically have their performance tied to a benchmark index. They are composed of a basket of assets; most attempt to reproduce the returns of an index, but a growing number try to achieve a multiple of the benchmark return, such as two times or the negative of the return. We present a detailed performance study of the current ETF market and we find, among other conclusions, constant underperformance among ETFs that aim to do more than simply track an index. We present a MINLP for the problem of selecting the basket of assets that compose an ETF, which, to the best of our knowledge, is the first in the literature. For all three models we present extensive computational results for portfolios derived from universes defined by S&P international equity indices with up to 1200 stocks. We use CPLEX to solve the ARP problem and the software package Minotaur for both our MINLPs for MNP and an ETF

Essays in Financial Engineering

This thesis consists of three essays in financial engineering. In particular we study problems in option pricing, stochastic control and risk management. In the first essay, we develop an accurate and efficient pricing approach for options on leveraged ETFs (LETFs). Our approach allows us to price these options quickly and in a manner that is consistent with the underlying ETF price dynamics. The numerical results also demonstrate that LETF option prices have model-dependency particularly in high-volatility environments. In the second essay, we extend a linear programming (LP) technique for approximately solving high-dimensional control problems in a diffusion setting. The original LP technique applies to finite horizon problems with an exponentially-distributed horizon, T. We extend the approach to fixed horizon problems. We then apply these techniques to dynamic portfolio optimization problems and evaluate their performance using convex duality methods. The numerical results suggest that the LP approach is a very promising one for tackling high-dimensional control problems. In the final essay, we propose a factor model-based approach for performing scenario analysis in a risk management context. We argue that our approach addresses some important drawbacks to a standard scenario analysis and, in a preliminary numerical investigation with option portfolios, we show that it produces superior results as well

Financial Portfolio Risk Management: Model Risk, Robustness and Rebalancing Error

Risk management has always been in key component of portfolio management. While more and more complicated models are proposed and implemented as research advances, they all inevitably rely on imperfect assumptions and estimates. This dissertation aims to investigate the gap between complicated theoretical modelling and practice. We mainly focus on two directions: model risk and reblancing error. In the first part of the thesis, we develop a framework for quantifying the impact of model error and for measuring and minimizing risk in a way that is robust to model error. This robust approach starts from a baseline model and finds the worst-case error in risk measurement that would be incurred through a deviation from the baseline model, given a precise constraint on the plausibility of the deviation. Using relative entropy to constrain model distance leads to an explicit characterization of worst-case model errors; this characterization lends itself to Monte Carlo simulation, allowing straightforward calculation of bounds on model error with very little computational effort beyond that required to evaluate performance under the baseline nominal model. This approach goes well beyond the effect of errors in parameter estimates to consider errors in the underlying stochastic assumptions of the model and to characterize the greatest vulnerabilities to error in a model. We apply this approach to problems of portfolio risk measurement, credit risk, delta hedging, and counterparty risk measured through credit valuation adjustment. In the second part, we apply this robust approach to a dynamic portfolio control problem. The sources of model error include the evolution of market factors and the influence of these factors on asset returns. We analyze both finite- and infinite-horizon problems in a model in which returns are driven by factors that evolve stochastically. The model incorporates transaction costs and leads to simple and tractable optimal robust controls for multiple assets. We illustrate the performance of the controls on historical data. Robustness does improve performance in out-of-sample tests in which the model is estimated on a rolling window of data and then applied over a subsequent time period. By acknowledging uncertainty in the estimated model, the robust rules lead to less aggressive trading and are less sensitive to sharp moves in underlying prices. In the last part, we analyze the error between a discretely rebalanced portfolio and its continuously rebalanced counterpart in the presence of jumps or mean-reversion in the underlying asset dynamics. With discrete rebalancing, the portfolio's composition is restored to a set of fixed target weights at discrete intervals; with continuous rebalancing, the target weights are maintained at all times. We examine the difference between the two portfolios as the number of discrete rebalancing dates increases. We derive the limiting variance of the relative error between the two portfolios for both the mean-reverting and jump-diffusion cases. For both cases, we derive ``volatility adjustments'' to improve the approximation of the discretely rebalanced portfolio by the continuously rebalanced portfolio, based on on the limiting covariance between the relative rebalancing error and the level of the continuously rebalanced portfolio. These results are based on strong approximation results for jump-diffusion processes