  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.
