ABSTRACT
Chapter 5 segues into the problem of portfolio selection, wherein one can select to hold continuous amounts long or short in many different assets, under the objective of maximizing the signal-noise ratio. The Markowitz portfolio, which solves the basic portfolio optimization problem, is introduced. The problem is then generalized to include subspace constraints, and hedging constraints, with solutions given for each. The conditional expectation model is introduced, wherein expected returns are linear in some observable “features”, while covariance is independent of those features. Under this formulation, the optimal portfolio linear in the features is found. An alternative solution is pursued via “flattening”, wherein the covariance of returns may also vary with the features. This problem is generalized to the case where expected first and second moments of returns are general functions of the features. The solution to this problem is couched in terms of a linear problem.
