Principles of Portfolio Choice

Principles of Portfolio Choice: An Information-Theoretic, Likelihood-Based Perspective develops a scenario-level theory of portfolio selection. Its starting point is simple but powerful: market prices assign values to future scenarios, and once normalized these state prices define a market-implied probability measure. An investor who disagrees with the market is therefore not merely choosing portfolio weights; she is choosing a different likelihood model over the same scenarios.

The book's central translation is that a budget-normalized nonnegative payoff is a likelihood ratio. It compares the probability measure implied by a portfolio with the probability measure implied by market prices. Thus a portfolio is not only a financial object but also a statistical object: it expresses a scenario distribution. Conversely, a desired scenario distribution determines the payoff that would implement it, whenever that payoff can be replicated.

From this perspective, portfolio choice becomes a form of likelihood-model selection under market constraints. The investor first specifies the scenario probabilities she wishes to express; the financial problem is then to find the attainable payoff whose implied distribution best matches that view.

This scenario-by-scenario viewpoint connects portfolio theory to statistics and information theory. At the Kelly optimum, expected log return becomes relative entropy. Realized wealth becomes a likelihood score. Long-run performance becomes accumulated statistical evidence. Constrained portfolio selection becomes the problem of choosing a desired scenario distribution and finding the closest attainable market payoff.

The book translates Kelly growth, utility maximization, mean-variance analysis, martingale pricing, option payoffs, hedging, Bayesian averaging, and model selection into this likelihood-based language. It shows that many classical methods can be understood as approximations, transformations, or constrained versions of a single payoff-measure dictionary.

Written for quantitative analysts, portfolio managers, researchers, and graduate students, the book offers a new foundation for thinking about prices, beliefs, payoffs, and evidence in financial markets.

Features

• Presents portfolio choice at the level of individual market scenarios.
• Shows that normalized payoffs are likelihood ratios between portfolio-implied and market-implied probability measures.
• Interprets portfolio choice as the selection of likelihood models over future scenarios.
• Interprets returns as likelihood scores and Kelly growth as relative entropy.
• Translates classical portfolio methods into the language of statistics and information theory.
• Develops applications to option-induced densities, Gaussian mixtures, hedging, Bayesian averaging, and adaptive portfolios.
• Includes exercises designed to test and enhance understanding of the topics.