Taniguchi Masanobu et al. Statistical Portfolio Estimation

CRC Press, 2018. — 389 p.The field of financial engineering has developed as a huge integration of economics, probability theory, statistics, etc., for some decades. The composition of portfolios is one of the most fundamental and important methods of financial engineering to control the risk of investments. This book provides a comprehensive development of statistical inference for portfolios and its applications. Historically, Markowitz (1952) contributed to the advancement of modern portfolio theory by laying the foundation for the diversification of investment portfolios. His approach is called the mean variance portfolio, which maximizes the mean of portfolio return with reducing its variance (risk of portfolio). Actually, the mean-variance portfolio coefficients are expressed as a function of the mean and variance matrix of the return process. Optimal portfolio coefficients based on the mean and variance matrix of return have been derived by various criteria. Assuming that the return process is i.i.d. Gaussian, Jobson and Korkie (1980) proposed a portfolio coefficient estimator of the optimal portfolio by making the sample version of the mean-variance portfolio. However, empirical studies show that observed stretches of financial return are often are non-Gaussian dependent. In this situation, it is shown that portfolio estimators of the mean-variance type are not asymptotically efficient generally even if the return process is Gaussian, which gives a strong warning for use of the usual portfolio estimators. We also provide a necessary and sufficient condition for the estimators to be asymptotically efficient in terms of the spectral density matrix of the return. This motivates the fundamental important issue of the book. Hence we will provide modern statistical techniques for the problems of portfolio estimation, grasping them as optimal statistical inference for various return processes.