An Introduction to Financial Markets

Chapter Eight Mean–Variance Efficient Portfolios

This chapter is fairly technical and is meant to be a bridge between the general framework of mean–risk models, which we introduced in Section 7.4, and Chapters 9 and 10, where we describe factor and equilibrium models. Here, we adopt standard deviation as a risk measure, momentarily setting aside the critical remarks that we made in Section 7.4.1, in order to develop the theory of mean–variance efficient portfolios, which is the foundation of a body of knowledge broadly known as modern portfolio theory (MPT). In portfolio optimization, variance is typically used, rather than standard deviation, but this is just a matter of computational convenience. Despite its deceptive simplicity and the limitation of symmetric risk measures, MPT provides us with useful insights. Everything hinges on the determination of an efficient frontier of risky portfolios and the selection of an optimal portfolio mixing risky assets with a risk-free asset. The risk-free asset may be thought as a safe zero-coupon bond with maturity corresponding to the portfolio holding period, or a safe bank account offering a constant interest rate.

The theory, in its basic form, only deals with a single-period decision problem. To fix ideas, we will essentially consider equity portfolios, even though, in principle, any asset would do, since we may consider the holding period return from whatever asset, including a bonds and commodities. A further limitation of our ...