Single-Period Problems

Abstract

In the single-period portfolio choice problem, the investor is assumed to make allocation decisions once and for all at the beginning of a given period (e.g. one quarter or one year), based on estimated prospects for the risk and return relationships of a universe of N investable assets over the horizon. Once made, the allocation decisions are not allowed to change until the end of the period; the impact of decisions arising in subsequent periods is not considered in this case, and for this reason, single-period problems lead to so-called myopic policies. Markowitz (1952) introduced the basic formulation, including expressions for the expected portfolio return and variance in terms of the portfolio weights and expected returns, variances and covariances of individual assets. He also introduced the efficient frontier and its depiction on the mean-variance plane. Since the original formulation uses the asset variances (and covariances) as the risk measure, the methodology is often called mean–variance allocation.