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SPEPS Preprint

Author(s): Yonggan Zhao, Nanyang Technological University, Singapore
William T. Ziemba, University of British Columbia, Vancouver
Title: Intertemporal mean-variance efficiency with a Markovian state price density
Date of Acceptance: 30.09.2003
Submission Date: 27.07.2003
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint: pdf (urn:nbn:de:kobv:11-10059197)
Keywords (eng): Mean-Variance Efficiency, Mutual Fund Separation, Utility Maximization, Equilibrium, Intertemporal CAPM, Markovian State Price Density
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Abstract (eng):
This paper extends Merton's continuous time (instantaneous) mean-variance analysis and the mutual fund separation theory. Given the existence of a Markovian state price density process, the optimal portfolios from concave utility maximization are instantaneously mean-variance efficient independent of the concave utility function's form. The Capital Asset Pricing Model holds with the market portfolio induced by the growth optimal portfolio. The Markowitz-Tobin mutual fund separation is extended to include the lognormal assumption for asset prices as a special case. Closed form solutions to the expected utility maximization of terminal portfolio value are derived. We present an example in which the state price processes are specified as a multivariate geometric Brownian motion and the asset prices follow a multivariate diffusion process with relatively general parameters.
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