Efficient Portfolios

TL;DR

This paper discusses the concept of efficient portfolios in finance, highlighting that the CAPM formula applies to realized returns as random variables, not just their expected values, based on a one-period investment model.

Contribution

It demonstrates that the CAPM formula holds for realized returns as random variables, extending its applicability beyond expected returns.

Findings

CAPM applies to realized returns as random variables

Efficient portfolios minimize variance for given expected return

One-period investment model supports the main observation

Abstract

Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz and Roy introduced the following criterion for risk vs. return in portfolio selection: if two portfolios have the same expected realized return then prefer the one with smaller variance. An efficient portfolio has the least variance among all portfolios having the same expected realized return. The primary contribution of this short note is observation that the CAPM formula holds for realized returns as random variables, not just their expectations. This follows directly from writing down a mathematical model for one period investments.