Portfolio Selection to achieve a target beta

Abstract

Suppose an investor wishes to construct a portfolio of size k securities from a population of n securities (k≤n) such that a particular portfolio or target beta (β p ) is achieved. Since β p is a random variable, there will be some difference between a portfolio’s realized beta and the target beta. We investigate the problem of finding the combination of k securities that minimizes the variance of β p , or equivalently, minimizes the probability of a particular difference in target and realized beta. We also seek answers to a number of related questions. These are concerned with the effect on the variance of β p of naive selection of securities, of the choice of k, and of the presence of a risk-free asset. We also examine the characteristics of securities included in the optimal portfolio.