Robust portfolio optimization and dimensional analysis in finance

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Dissertation, Universität Wien, 2018

This thesis consists of two parts. The first one is devoted to robust portfolio optimization. We review tractable reformulations of the mean-risk portfolio selection problem under model ambiguity. In particular, we study the portfolio selection problem when all probability distributions contained in a Wasserstein-neighborhood of some reference model are taken into account. It is then an original contribution of this dissertation that we introduce the portfolio selection problem under dependence uncertainty. We assume the marginal return distributions of the individual assets are known and that the model ambiguity lies solely in the dependence structure between the assets. We show theoretically and empirically that under high model ambiguity (in the respective sense) the two approaches have diametrically opposed implications: Portfolio diversification is optimal under high ambiguity with respect to the joint distribution, whereas portfolio concentration is optimal under high dependence uncertainty. In the second part of this dissertation, we use dimensional analysis to study relations between financial quantities. Firstly, we apply this concept, which is well known in physics, to derive the following remarkable fact. If the market impact of a meta-order only depends on four well-defined and financially meaningful variables, then there is only one possible functional form of this dependence. In particular, the market impact is proportional to the square-root of the size of the meta-order. This result is based on three scaling invariances with respect to the units in which the considered quantities are measured as well as on the assumption of leverage neutrality. The latter is a restrictive assumption on the behavior of the considered quantities when the corresponding stock is paying dividends. Secondly, we apply the same line of argument in the context of trading activity. Different combinations of the relevant explanatory variables result in different proportionality relations, which have been proposed in the literature. Hence, the question which of the derived relations describe the reality boils down to which set of variables indeed fully explains the variables of interest - in our case the number of trades. Hence, we perform an empirical analysis to examine the fit of the considered relations to data from the stock market.

Enthält 3 Beiträge

Zusammenfassung in deutscher Sprache

10.25365/thesis.53052 [DOI]

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