Optimal Use of Posterior Information in Portfolio Construction and the Separation Theorem

Abstract

Abstract. The notion of efficient portfolios is re-stated in terms of data-measurable investment rates as well as a modified definition of the risk, in which the risk is evaluated by the unconditional mean of the squared deviation of the total return from its conditional mean. An optimization problem is mathematically solved to find the efficient portfolio that attains maximum expected return with the risk constrained to an arbitrarily given level. In addition, there is found a result similar to Tobin's one-fund theorem.