Optimising portfolio diversification and dimensionality

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree. The latter arises naturally due to our requirement that diversification measures should be leverage invariant. We introduce this new framework and argue the benefits relative to existing measures of diversification in the literature, before addressing the question of optimizing diversification or, equivalently, dimensionality. Maximising portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex and potentially have multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size and more akin to asset allocation problems, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate analytically and through numerical experiments that the framework reflects the desired properties often discussed in the literature

MAD risk parity portfolios

In this paper, we investigate the features and the performance of the risk parity (RP) portfolios using the mean absolute deviation (MAD) as a risk measure. The RP model is a recent strategy for asset allocation that aims at equally sharing the global portfolio risk among all the assets of an investment universe. We discuss here some existing and new results about the properties of MAD that are useful for the RP approach. We propose several formulations for finding MAD-RP portfolios computationally, and compare them in terms of accuracy and efficiency. Furthermore, we provide extensive empirical analysis based on three real-world datasets, showing that the performances of the RP approaches generally tend to place both in terms of risk and profitability between those obtained from the minimum risk and the Equally Weighted strategies

Tactical choices with smart beta approaches: an alternative to cap-weighted allocation

In this thesis is performed an analysis of smart beta indices. The main purpose is to assess tactical choices with smart beta approaches in comparison to cap wrichted approac

Commodities and portfolio diversification : myth of fact?

Mestrado em FinançasEste estudo pretende analisar se as matérias-primas apresentam potencial de diversificação para portefólios de ações de investidores com aversão às perdas. A recente financialização do mercado das matérias-primas pode estar a afetar a vida de milhões de famílias a nível global, uma vez que determina o custo de vida. Alargamos a abordagem de Bessler & Wolff (2015) com o uso de indicadores de desempenho com o principal foco no risco de queda. A análise empírica considera a perspetiva das finanças comportamentais na avaliação dos benefícios de diversificação de 16 contratos futuros individuais e um índice de matérias-primas. Este estudo confirma a elevada sensibilidade das matérias-primas às condições económicas do mercado. O sector energético de matérias-primas tem um melhor desempenho durante períodos de expansão económica. Os metais preciosos apresentam benefícios de diversificação tanto em períodos de expansão como de recessão, enquanto as matérias-primas do sector da pecuária apresentam um grande potencial de diversificação durante recessões. No geral concluímos que continuamos a observar benefícios de diversificação, mas estes dependem do período em análise, e têm vindo a decrescer ao longo do tempo.This study aims to investigate whether commodities yield diversification benefits to stock portfolios for loss-averse investors. The recent financialization of the commodity market increased correlations with stocks and thus may be hurting millions of households around the world, as it determines the cost of living. We extend the framework of Bessler & Wolff (2015) by using alternative performance measures mainly related to the downside risk. The empirical analysis accounts for a behavioral finance perspective in the assessment of diversification benefits from 16 individual future contracts and one index future on commodities. Our study confirms the high sensitivity of commodities to market economic conditions. The energy sector performs better under economic expansion periods. Precious metals yield diversification benefits both in expansion and recession periods, while livestock commodities display a high potential to reduce risk especially during recessions. Overall, our findings yield that there is still a diversification benefit, but it is time-dependent and the benefits have been decreasing over time.info:eu-repo/semantics/publishedVersio

Aspects of exchange rate determination : empirical evidence

The presence of a risk premium in foreign exchange markets for the floating exchange rate period has been examined by some researchers and the results obtained were not successful. In this thesis, we analyse a number of exchange rate models and assess their empirical performance. Using the data from the Group-S members in the post Bretton Woods period, we investigate the presence of the risk premium among different models. Our results are remarkably satisfactory.A 'new' random walk model is tested. It has been found that the null hypothesis of a unit coefficient with or without a constant cannot be rejected for several pairs of the countries. The statistically non-zero constant indicates the existence of the risk premium and/or transaction costs in the foreign exchange markets. Results of testing long run Real Interest Parity (RIP) show that such a condition holds in several cases, and this is explained by the existence of capital and exchange rate controls, and thus by the risk premium, rather than PPP and UIP conditions.One way to detect the existence of the risk premium is to test the significance of the semi-elasticity of bond supplies in a portfolio balance model. It has been shown that such a premium does exist in many cases. Thus the results support the view that the exchange rate is mainly determinated by investors' portfolio behaviour.Finally, a synthesis of monetary and portfolio balance models is also studied. We have been able to uncover evidence in support of the long run model of exchange rate determination for the floating exchange rate period. The evidence supports the synthesis model and a policy reaction function that manages the exchange rate by fully or partially offsetting systematic fluctuations in interest rate differentials

Evaluating Value-at-Risk Models via Quantile Regressions

We propose an alternative backtest to evaluate the performance of Value-at-Risk (VaR) models. The presented methodology allows us to directly test the performance of many competing VaR models, as well as identify periods of an increased risk exposure based on a quantile regression model (Koenker & Xiao, 2002). Quantile regressions provide us an appropriate environment to investigate VaR models, since they can naturally be viewed as a conditional quantile function of a given return series. A Monte Carlo simulation is presented, revealing that our proposed test might exhibit more power in comparison to other backtests presented in the literature. Finally, an empirical exercise is conducted for daily S&P500 return series in order to explore the practical relevance of our methodology by evaluating five competing VaRs through four different backtests.

Optimal portfolio strategies of cointegrated assets

Statistical arbitrage, as a quantitative method of speculation, has been increasingly prevalent along with the evolution of computational nance. One of the most popular statistical arbitrage strategies is called pairs trading, which is widely used by hedge funds and investment banks since the mid-1980s. Pairs trading strategy exploits price spread between paired assets by taking long-short positions. If price spread is temporary according to past price information, a trading opportunity arises and pro ts can be made from price correction process. To capture these opportunities, we focus on assets sharing cointegration relations. This long-term relationship implies that paired assets are exposed to common fundamentals, and hence it guarantees price convergence to the equilibrium level. Therefore, this thesis applies cointegration technique to capture short-term market anomalies and exploits these inefficiencies using pairs trading in order to build optimal portfolio strategies. The thesis consists of three chapters. The first chapter presents an equilibrium framework based on equity commonality explicitly adapted to describe the dynamics of pairs trading. Our methodology, built on the price discovery model of Figuerola-Ferretti and Gonzalo (Journal of Econometrics 2010) exploits price leadership for portfolio replication purposes and shows how pairs trading profitability is linked to the speed of equilibrium reversion. A persistence-dependent trading trigger is introduced to impose higher thresholds on pairs with slower mean reversion. Our model demonstrates that equilibrium price convergence guarantees positive abnormal pro tability. Applied to STOXX Europe 600 traded equities our strategy delivers Sharpe ratios that outperform benchmark rules used in the literature. Portfolio performance is enhanced after firm fundamental factor restrictions are imposed. The second chapter proposes a VECM representation for cointegrated assets in the continuous time framework. This model implies a simple method to check for cointegration based on the speed of equilibrium reversion. A pair of cointegrated assets is then identified to derive a dynamically optimal pairs trading portfolio with a risk-free bond. This involves maximizing the portfolio value at terminal time without the requirement of a functional form for investor´s preferences. To this end, we connect the derived optimal portfolio with European-type spread options and in consequence the optimal investment policies can be modeled using the spread option's resulting delta hedging strategies. Our framework is tested empirically using pairs identi ed from the Dow Jones Industrial Average. This analysis requires maximum likelihood estimates on continuous VECM parameters, compared to the benchmark Johansen methodology. We nd that the proposed optimal strategy delivers consistent profitability in terms of Sharpe ratio and cumulative returns. This supports the usefulness of introducing spread option's deltas as the optimal investment policies for pairs portfolio construction. In addition, our model-implied selection algorithm outperforms the Johansen (1991) methodology commonly applied in the previous literature. Finally, the third chapter examines the performance of pair trading portfolios when sorted by the level of cointegration of their constituents. The supercointegrated portfolio, that is formed by pairs at 1% confidence level of cointegration tests, exhibits a superior out-ofsample performance than simple buy-and-hold and passive investments in terms of Sharpe ratio. We find that the degree of performance of pairs strategy is positively related to the level of cointegration among pairs. These evidence are also documented in an international context, from the analysis on the European stock market. The time-varying risk of the pairs strategy is linked to aggregate market volatility. A positive risk-return relationship of the strategy is also found.Programa Oficial de Doctorado en Empresa y Finanzas / Business and FinancePresidente: Federico Zapatero; Secretario: Ángel León; Vocal: Genaro Sucarra