Topics in Statistics and Financial Econometrics: Penalized Estimators and Stochastic Discount Factors

Diplôme Thèse Topics in Statistics and Financial Econometrics: Penalized Estimators and Stochastic Discount Factors eng 2021-12-13 author Quaini Alberto 0000-0002-1251-0599 805819 director Trojani Fabio 788164 Recherche et enseignement GSEM (RESEM) collaborator Korsaye Sofonias Alemu 886112 10.13097/archive-ouverte/unige:158890 urn:nbn:ch:unige-1588902 GSEM 106 This thesis is composed of two parts. The first part is based on a paper co-authored with Fabio Trojani, entitled ”A Unifying Convex Analysis Framework for Penalized Least Squares”. In this paper, we establish a framework for studying the statistical properties of Penalized Least Squares Estimators (PLSEs)with con- vex penalties, which is applicable both under a regular and a singular design. Our approach borrows from a reinterpretation of PLSEs as proximity operators and Moreau's decomposition of these operators. This allows for a general characterization of the asymp- totic properties of PLSEs, which only depends on suit- able functional transformations of the PLSE limit penalty. Exploiting our approach, we propose convenient Oracle PLSEs for singular designs exhibiting the grouping effect, and valid bootstrap approximations for the associated asymptotic distributions. The second part consists in a paper co-authored with Sofonias Kor- saye and Fabio Trojani, entitled ”Smart Stochastic Discount Factors”, which proposes a novel no-arbitrage framework exploiting convex asset pricing constraints to study investors' marginal utility of wealth or, more generally, Stochastic Discount Factors (SDFs). We establish a duality between minimum dispersion SDFs and penalized portfolio selection problems, building the foundation for characteriz- ing the feasible trade- offs between a SDF's pricing accuracy and its comovement with systematic risks. Empirically, a minimum variance CAPM–SDF produces a Pareto optimal tradeoff. This SDF only depends on two distinct risk fac- tors: A traded mar- ket factor and a minimum variance excess return that bounds the mispricing of risks unspanned by market shocks. Dewey 650 Dewey 310 116 Geneva Finance Research Institute S4 117 Research Center for Statistics S5 false 4b954bc0-f4bb-404d-a971-e1a466b1c0d7 Thesis Public thesis.pdf 3869947 application/pdf openAccess Faculté d'économie et de management / Geneva Finance Research Institute Faculté d'économie et de management / Research Center for Statistics

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