Choix de portefeuille de grande taille et mesures de risque pour preneurs de décision pessimistes

This  thesis consists of three chapters on the topics of  portfolio choice in a high-dimensional context, and risk measurement. The first chapter addresses the estimation error issue that arises when constructing large portfolios in the mean-variance framework. The second chapter investigates the relevance of currency risk for optimal domestic portfolios, evaluates their ability of to diversify away currency risk, and  study the links between portfolio weights stability and currency risk. Finally, under the assumption that decision makers are  pessimistic, the third chapter derives the risk premium, propose a measure of the degree of pessimism, and provide a statistical framework for their estimation.  The first chapter improves the performance of the optimal portfolio weig-hts obtained under the mean-variance framework of Markowitz (1952). Indeed, these weights give unsatisfactory results, when the mean and variance are replaced  by their sample counterparts (plug-in rules). This problem is amplified when the number of assets is large and the sample covariance is singular or nearly singular. The chapter investigates four regularization techniques to stabilizing the inverse of the covariance matrix: the ridge, spectral cut-off, Landweber-Fridman, and LARS Lasso. These four methods involve a tuning parameter that needs to be selected. The main contribution is to derive a data-based method for selecting the tuning parameter in an optimal way, i.e. in order to minimize the expected loss in utility of a mean-variance investor. The cross-validation type criterion derived is found to take a similar form for the four regularization methods. The resulting regularized rules are compared to the sample-based mean-variance portfolio and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio and expected loss in utility. The main finding is that regularization to covariance matrix significantly improves the performance of the mean-variance problem and outperforms the naive portfolio, especially in ill-posed cases, as suggested by our simulations and empirical studies.  In the second chapter, we investigate the extent to which optimal and stable portfolios of domestic assets  can reduce or eliminate currency risk. This is done using monthly returns on 48 U.S. industries, from 1976 to 2008. To tackle the instabilities inherent to large portfolios, we use the spectral cut-off regularization described in Chapter 1. This gives rise to a family of  stable global minimum portfolios that allows investors to select different percentages of principal components for portfolio construction.  Our empirical tests are based on a conditional International Asset Pricing Model (IAPM), augmented with the size and book-to-market factors of Fama and French (1993). Using two trade-weighted currency indices of industrialized countries currencies and  emerging markets currencies, we find that currency risk is priced and time-varying for global minimum portfolios. These strategies also lead to a significant reduction in the exposure to currency risk, while keeping the average premium contribution to total premium approximately the same. The global minimum weights considered are an alternative to market capitalization weights used in  the U.S. market index. Therefore, our findings complement the well established results that currency risk is significantly priced and economically meaningful at the industry and country level in most countries.  Finally, the third chapter derives a measure of the risk premium for rank-dependent preferences  and proposes a measure of the degree of pessimism, given a distortion function.  The introduced measures generalize the common risk measures derived in the expected utility theory framework, which is frequently violated in both experimental and real-life situations. These measures are derived in the neighborhood of a given random loss variable, using the notion of local utility function. A particular interest is devoted to the CVaR, which is now  widely used for asset allocation and has been advocated to complement the Value-at-risk (VaR) proposed since 1996 by the Basel Committee on Banking Supervision. We provide the statistical framework needed to conduct inference on the derived measures. Finally, the proposed estimators

Keyphrases: Portfolio selection, International asset pricing, Risk premium, Regularization, Estimation error, Mean-variance analysis, Currency risk, Model selection, Pessimism, Technique de regularization