Statistical inference for the EU portfolio in high dimensions

In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the asymptotic behavior of the proposed test statistic under the high-dimensional asymptotic regime, namely when the number of assets $p$ increases at the same rate as the sample size $n$ such that their ratio $p/n$ approaches a positive constant $c\in(0,1)$ as $n\to\infty$. We provide an extensive simulation study where the power function and receiver operating characteristic curves of the test are analyzed. In the empirical study, the methodology is applied to the returns of S\&P 500 constituents.Comment: 27 pages, 5 figures, 2 table

Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

Improved Portfolio Choice using Second-Order Stochastic Dominance

We examine the use of second-order stochastic dominance as both a way to measure performance and also as a technique for constructing portfolios. Using in-sample data, we construct portfolios such that their second-order stochastic dominance over a typical pension fund benchmark is most probable. The empirical results based on 21 years of daily data suggest that this portfolio choice technique significantly outperforms the benchmark portfolio out-of-sample. As a preference-free technique it will also suit any risk-averse investor in e.g. a pension fund. Moreover, its out-of-sample performance across eight different measures is superior to widely discussed portfolio choice approaches such as equal weights, mean variance, and minimum-variance methods.second-order stochastic dominance, portfolio choice, portfolio measurement

A blocking and regularization approach to high dimensional realized covariance estimation

We introduce a regularization and blocking estimator for well-conditioned high-dimensional daily covariances using high-frequency data. Using the Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008a) kernel estimator, we estimate the covariance matrix block-wise and regularize it. A data-driven grouping of assets of similar trading frequency ensures the reduction of data loss due to refresh time sampling. In an extensive simulation study mimicking the empirical features of the S&P 1500 universe we show that the ’RnB’ estimator yields efficiency gains and outperforms competing kernel estimators for varying liquidity settings, noise-to-signal ratios, and dimensions. An empirical application of forecasting daily covariances of the S&P 500 index confirms the simulation results

The cost of sustainability on optimal portfolio choices

We examine the impact of sustainability criteria, as measured by the KLD scores, on optimal portfolio selection performed on an investment universe containing the equities in the S&P500 index and covering the period between 1993 and 2008. The optimizations are done according to the Markowitz mean-variance approach while sustainability constraints are introduced by eliminating from the investment pool those assets that do not comply to di®erent social responsibility criteria (screening). We compare the two efficient frontiers, i.e. the one without and the one with screening. A spanning test is performed to determine if the differences between the two types of efficient frontier are significant. We introduce a measure of how much an investor has to pay (through loss of return or through additional risk) in order to satisfy given sustainability criteria. The analysis is carried on separately on the three main dimensions of sustainability, namely Environmental, Social and Governance.Sustainability; Optimal portfolio

The merit of high-frequency data in portfolio allocation

This paper addresses the open debate about the usefulness of high-frequency (HF) data in large-scale portfolio allocation. Daily covariances are estimated based on HF data of the S&P 500 universe employing a blocked realized kernel estimator. We propose forecasting covariance matrices using a multi-scale spectral decomposition where volatilities, correlation eigenvalues and eigenvectors evolve on different frequencies. In an extensive out-of-sample forecasting study, we show that the proposed approach yields less risky and more diversified portfolio allocations as prevailing methods employing daily data. These performance gains hold over longer horizons than previous studies have shown

Efficient and robust estimation for financial returns: an approach based on q-entropy

We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvàt-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and effciency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.q-entropy; robust estimation; power-divergence; financial returns

Export Implicit Financial Performance: The Case of French Wine Companies

Noting the difficulties of measuring a company’s export performance and especially financial performance, we develop a new measurement approach grounded on modern portfolio theory. The export intensities and the global financial performance of exporting companies being known, this approach allows deducing the export margin ratio, export risk and correlation of domestic activities with export activities. Using a sampling from French companies in the wine industry from 2001-2005, these implicit financial export performance characteristics are estimated. Main results found: export activities permit a better global margin-risk relationship essentially due to diversification gains because export financial performance seems to be inferior to the domestic one for a great majority of companies.export, financial measures, performance, wine industry, Agricultural Finance, Financial Economics, Q10, Q14,

COVARIANCE MATRIX CONSTRUCTION AND ESTIMATION: CRITICAL ANALYSES AND EMPIRICAL CASES FOR PORTFOLIO APPLICATIONS

The thesis contributes to the financial econometrics literature by improving the estimation of the covariance matrix among financial time series. To such aim, existing econometrics tools have been investigated and improved, while new ones have been introduced in the field. The main goal is to improve portfolio construction for financial hedging, asset allocation and interest rates risk management. The empirical applicability of the proposed innovations has been tested trough several case studies, involving real and simulated datasets. The thesis is organised in three main chapters, each of those dealing with a specific financial challenge where the covariance matrix plays a central role. Chapter 2 tackles on the problem of hedging portfolios composed by energy commodities. Here, the underlying multivariate volatility among spot and futures securities is modelled with multivariate GARCH models. Under this specific framework, we propose two novel approaches to construct the covariance matrix among commodities, and hence the resulting long-short hedging portfolios. On the one hand, we propose to calculate the hedge ratio of each portfolio constituent to combine them later on in a unique hedged position. On the other hand, we propose to directly hedge the spot portfolio, incorporating in such way investor\u2019s risk and return preferences. Trough a comprehensive numerical case study, we assess the sensitivity of both approaches to volatility and correlation misspecification. Moreover, we empirically show how the two approaches should be implemented to hedge a crude oil portfolio. Chapter 3 focuses on the covariance matrix estimation when the underlying data show non\u2013Normality and High\u2013Dimensionality. To this extent, we introduce a novel estimator for the covariance matrix and its inverse \u2013 the Minimum Regularised Covariance Determinant estimator (MRCD) \u2013 from chemistry and criminology into our field. The aim is twofold: first, we improve the estimation of the Global Minimum Variance Portfolio by exploiting the MRCD closed form solution for the covariance matrix inverse. Trough an extensive Monte Carlo simulation study we check the effectiveness of the proposed approach in comparison to the sample estimator. Furthermore, we take on an empirical case study featuring five real investment universes characterised by different stylised facts and dimensions. Both simulation and empirical analysis clearly demonstrate the out\u2013of\u2013sample performance improvement while using the MRCD. Second, we turn our attention on modelling the relationships among interest rates, comparing five covariance matrix estimators. Here, we extract the principal components driving the yield curve volatility to give important insights on fixed income portfolio construction and risk management. An empirical application involving the US term structure illustrates the inferiority of the sample covariance matrix to deal with interest rates. In chapter 4, we improve the shrinkage estimator for four risk-based portfolios. In particular, we focus on the target matrix, investigating six different estimators. By the mean of an extensive numerical example, we check the sensitivity of each risk-based portfolio to volatility and correlation misspecification in the target matrix. Furthermore, trough a comprehensive Monte Carlo experiment, we offer a comparative study of the target estimators, testing their ability in reproducing the true portfolio weights. Controlling for the dataset dimensionality and the shrinkage intensity, we find out that the Identity and Variance Identity target estimators are the best targets towards which to shrink, always holding good statistical properties