## Doctoral Thesis

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#### Document Type

- Doctoral Thesis (1) (remove)

Economics of Downside Risk
(2019)

Ever since establishment of portfolio selection theory by Markowitz (1952), the use of Standard deviation as a measure of risk has heavily been criticized. The aim of this thesis is to refine classical portfolio selection and asset pricing theory by using a downside deviation risk measure. It is defined as below-target semideviation and referred to as downside risk.
Downside efficient portfolios maximize expected payoff given a prescribed upper bound for downside risk and, thus, are analogs to mean-variance efficient portfolios in the sense of Markowitz. The present thesis provides an alternative proof of existence of downside efficient portfolios and identifies a sufficient criterion for their uniqueness. A specific representation of their form brings structural similarity to mean-variance efficient portfolios to light. Eventually, a separation theorem for the existence and uniqueness of portfolios that maximize the trade-off between downside risk and return is established.
The notion of a downside risk asset market equilibrium (DRAME) in an asset market with finitely many investors is introduced. This thesis addresses the existence and uniqueness Problem of such equilibria and specifies a DRAME pricing formula. In contrast to prices obtained from the mean-variance CAPM pricing formula, DRAME prices are arbitrage-free and strictly positive.
The final part of this thesis addresses practical issues. An algorithm that allows for an effective computation of downside efficient portfolios from simulated or historical financial data is outlined. In a simulation study, it is revealed in which scenarios downside efficient portfolios
outperform mean-variance efficient portfolios.