Financial Theory with Python

Chapter 4. Optimality and Equilibrium

Much of economic theory is based on the premise: given two alternatives, an agent can, and will if able, choose a preferred one.

Darrell Duffie (1988)

A portfolio analysis starts with information concerning individual securities. It ends with conclusions concerning portfolios as a whole. The purpose of the analysis is to find portfolios which best meet the objectives of the investor.

Harry Markowitz (1959)

This chapter is about the modeling of agents and their optimization problems. It presents some of the fundamental building blocks of microeconomic theory (see Varian (1992)) and financial economics (see Eichberger and Harper (1997)). At the core of this chapter is the expected utility maximization paradigm, which is the dominant way of modeling an agent’s preferences in financial economics. Based on this paradigm, two central topics are discussed.

First, we discuss how an agent chooses an optimal investment portfolio given their preferences and the initial wealth. This type of problem is typically called optimal portfolio choice. The approach presented here does not rely on any form of simplification as seen with the mean-variance portfolio (MVP) approach and the Capital Asset Pricing Model (CAPM) that, for example, reduce the problem of choosing investment portfolios to the first and second moments of the return distributions of financial assets as well as their covariance.

Second, while prices for financial assets in the previous two ...