Portfolio Optimization

Chapter 9

Sharpe Ratios under

Constraints, and Kinks

Practical po r t folio optimization requires constraint s. These may be

lower bound constraints to contro l short selling and upper bound con-

straints to ensure that reoptimized portfolios do not move too far

from the original portfolio. Practitioners may use linear inequality con-

straints to model various aspects of the theory they are implementing.

In any case, linear inequality constraints are essential to realistic port-

folio optimization.

In this chapter, we will generalize many of the results of Sections

4.2 and 4.3 (Sharpe ratios and implied risk free returns) to problems

having general linear inequality constraints. We assume throughout this

chapter that the covariance matrix Σ is positiv ...