High-dimensional Dantzig dynamic minimum variance portfolio

Abstract

In financial markets, there are important common features that are mainly contributing to market situations, and they have their own time series. These time series structures generate stylized market dynamics structures, such as volatility clustering. Portfolio managers need to develop time-dependent dynamic volatility models that capture such market dynamic structures and intend to update small parts of the portfolio every day according to slight changes in daily market dynamics. In this paper, we develop a new portfolio model which is called the Dantzig dynamic minimum variance portfolio, based on the market dynamics volatility model and dynamic portfolio rebalancing method. For the large dynamic volatility matrix, we assume a latent factor model on returns and employ a multivariate GARCH time series model on the factor volatility. We optimize every sparse daily portfolio differences through the $l_1$ norm minimization under a risk constraint in the $l_\infty$ norm sense. Both the simulation study and the empirical study with the recent S&P 1500 index data emphasize that it achieves enough lower risk similar to several static portfolios with considerably smaller daily weight changes.