Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk

TL;DR

This paper introduces a new market model capturing fat-tails and asymmetry in asset returns, extending portfolio optimization to include asymmetry and providing practical solutions for risk management.

Contribution

It proposes a novel portfolio optimization method considering reward, dispersion, and asymmetry, with closed-form solutions for marginal VaR and CVaR, applicable to real stock data.

Findings

The model captures fat-tails and asymmetry in asset returns.

Extended efficient frontier in three dimensions of reward, dispersion, and asymmetry.

Closed-form solutions for marginal VaR and CVaR.

Abstract

In this paper, we propose a market model with returns assumed to follow a multivariate normal tempered stable distribution defined by a mixture of the multivariate normal distribution and the tempered stable subordinator. This distribution is able to capture two stylized facts: fat-tails and asymmetry, that have been empirically observed for asset return distributions. On the new market model, we discuss a new portfolio optimization method, which is an extension of Markowitz's mean-variance optimization. The new optimization method considers not only reward and dispersion but also asymmetry. The efficient frontier is also extended to a curved surface on three-dimensional space of reward, dispersion, and asymmetry. We also propose a new performance measure which is an extension of the Sharpe Ratio. Moreover, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal Value-at-Risk (VaR) and the marginal Conditional VaR (CVaR). We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average. First, perform the new portfolio optimization and then demonstrating how the marginal VaR and marginal CVaR can be used for portfolio optimization under the model. Based on the empirical evidence presented in this paper, our framework offers realistic portfolio optimization and tractable methods for portfolio risk management.