Intertemporal Mean-Variance Efficiency with a Markovian State Price Density

This paper extends Merton’s continuous time (instantaneous) mean-varianceanalysis and the mutual fund separation theory. Given the existence of a Marko-vian state price density process, the optimal portfolios from concave utility max-imization are instantaneously mean-variance efficient independent of the concaveutility function’s form. The Capital Asset Pricing Model holds with the marketportfolio induced by the growth optimal portfolio. The Markowitz-Tobin mutualfund separation is extended to include the lognormal assumption for asset pricesas a special case. Closed form solutions to the expected utility maximizationof terminal portfolio value are derived. We present an example in which thestate price processes are specified as a multivariate geometric Brownian motionand the asset prices follow a multivariate diffusion process with relatively generalparameters.