The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

CHOOSING A PORTFOLIO OF RISKY ASSETS

Diversification in the manner suggested by Markowitz leads to the construction of portfolios that have the highest expected return for a given level of risk. Such portfolios are called efficient portfolios.

Constructing Efficient Portfolios

The technique of constructing efficient portfolios from large groups of stocks requires a massive number of calculations. In a portfolio of G securities, there are (G²–G)/2 unique covariances to estimate. Hence, for a portfolio of just 50 securities, there are 1,224 covariances that must be calculated. For 100 securities, there are 4,950. Furthermore, in order to solve for the portfolio that minimizes risk for each level of return, a mathematical technique called quadratic programming must be used. A discussion of this technique is beyond the scope of this chapter. However, it is possible to illustrate the general idea of the construction of efficient portfolios by referring again to the simple two-asset portfolio consisting of assets C and D.

Recall that for two assets, C and D, E(R_C) = 12%, SD(R_C) = 30%, E(R_D) = 18%, and SD(R_D) = 40%. We now further assume that cor(R_C,R_D) =–0.5. Exhibit 3.4 presents the expected portfolio return and standard deviation for five different portfolios made up of varying proportions of C and D.¹⁶

Feasible and Efficient Portfolios

A feasible portfolio is any portfolio that an investor can construct given the assets available. The five portfolios presented in Exhibit ...