Portfolio optimization models for project valuation

Abstract

This dissertation presents (i) a framework for selecting and managing a portfolio of risky multi-period projects, called Contingent Portfolio Programming (CPP), and (ii) an inverse optimization procedure that uses this framework to compute the value of a single project. The dissertation specifically examines a setting where the investor can invest both in private projects and securities in financial markets, but where the replication of project cash flows with securities is not necessarily possible. This setting is called a mixed asset portfolio selection (MAPS) setting. The valuation procedure is based on the concepts of breakeven selling and buying prices, which are obtained by first solving an optimization problem and then an inverse optimization problem.

In the theoretical part of the dissertation, it is shown that breakeven prices are consistent valuation measures, exhibiting sequential consistency, consistency with contingent claims analysis (CCA), and sequential additivity. Due to consistency with CCA, the present approach can be regarded as a generalization of CCA to incomplete markets. It is also shown that, in some special cases, it is possible to derive simple calculation formulas for breakeven prices which do not require the use of inverse optimization. Further, it is proven that breakeven prices for a mean-variance investor converge towards the prices given by the Capital Asset Pricing Model (CAPM) as the investor's risk tolerance goes to infinity. The numerical experiments show that CPP is computationally feasible for relatively large portfolios both in terms of projects and states, and illustrate the basic phenomena that can be observed in a MAPS setting.