Portfolio Selection with Heavy Tails

Abstract

Consider the portfolio problem of choosing the mix between stocks and bonds under a downside risk constraint. Typically stock returns exhibit fatter tails than bonds corresponding to their greater downside risk. Downside risk criteria like the safety …rst criterion therefore often select corner solutions in the sense of a bonds only portfolio. This is due to a focus on the asymptotically dominating …rst order Pareto term of the portfolio return distribution. We show that if second order terms are taken into account, a balanced solution emerges. The theory is applied to empirical examples from the literature.

The Cross-Section of Tail Risks in Stock Returns

“…We use the second-order approximation of the VaR of X = ωX 1 + (1 − ω)X 2 provided in Hyung and de Vries (2007). The approximation depends on the comparison between α 2 − α 1 and min{γ 1 , 1}.…”

Dependence structure of risk factors and diversification effects

“…In a series of papers by Hyung and de Vries (2002, 2005, 2007, the portfolio diversification problem is studied by assuming a specific dependence structure such as the single-index factor market model, the Capital Asset Pricing Model (CAPM). Hyung and de Vries (2002) confirm Fama and Miller's conclusion in a dependent setup with the specific dependence structure, the CAPM.…”

Asymptotic Multivariate Dominance: A Financial Application

“…Modern portfolio optimization methods also take into account the possible tail-weightiness of the returns' distribution. We may refer to the works of Hyung and De Vries (2007) and Jansen et al (2000), which are based on the safety-first criterion, in order to take into account the probability of big losses. Moreover, related papers (Ortobelli et al 2010;Ortobelli and Rachev 2001) also propose and discuss some stable Paretian models for optimal portfolio selection and for quantifying the risk of a given portfolio.…”