TY - JOUR
T1 - Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model
AU - Kim, Young Shin
AU - Giacometti, Rosella
AU - Rachev, Svetlozar T.
AU - Fabozzi, Frank J.
AU - Mignacca, Domenico
PY - 2012/12
Y1 - 2012/12
N2 - In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.
AB - In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts that have been observed for asset distributions: fat-tails and an asymmetric dependence structure. Assuming infinitely divisible distributions, we derive closed-form solutions for two important measures used by portfolio managers in portfolio construction: the marginal VaR and the marginal AVaR. We illustrate the proposed model using stocks comprising the Dow Jones Industrial Average, first statistically validating the model based on goodness-of-fit tests and then demonstrating how the marginal VaR and marginal AVaR can be used for portfolio optimization using the model. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a more tractable method for portfolio optimization.
KW - Fat-tailed distribution
KW - Marginal contribution
KW - Multivariate normal tempered stable distribution
KW - Portfolio budgeting
KW - Portfolio optimization
KW - Portfolio risk
UR - http://www.scopus.com/inward/record.url?scp=84870511854&partnerID=8YFLogxK
U2 - 10.1007/s10479-012-1229-8
DO - 10.1007/s10479-012-1229-8
M3 - Article
AN - SCOPUS:84870511854
VL - 201
SP - 325
EP - 343
JO - Annals of Operations Research
JF - Annals of Operations Research
SN - 0254-5330
IS - 1
ER -