Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for a Quadratic Utility Function

In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.Comment: 38 pages, 9 figures, 3 tables, changes: VAR(1)-CCC-GARCH(1,1) process dynamics and the analysis of increasing horizon are included in the simulation study, under revision in Annals of Operations Researc

Statistical inference of the efficient frontier for dependent asset returns

Asset allocation, Mean–variance efficient frontier, Optimal portfolios, Asymptotic normality,

Comparison of different estimation techniques for portfolio selection

Portfolio analysis, Mean-variance analysis, Estimation of portfolio weights, Shrinkage estimation,

Algorithmic Need for Subcopulas

One of the efficient ways to describe the dependence between random variables is by describing the corresponding copula. For continuous distributions, the copula is uniquely determined by the corresponding distribution. However, when the distributions are not continuous, the copula is no longer unique, what is unique is a subcopula, a function C(u,v) that has values only for some pairs (u,v). From the purely mathematical viewpoint, it may seem like subcopulas are not needed, since every subcopula can be extended to a copula. In this paper, we prove, however, that from the algorithmic viewpoint, it is, in general, not possible to always generate a copula. Thus, from the algorithmic viewpoint, subcopulas are needed