Francois Gadenne

The roots of (i) expected value optimization, (ii) client-centric planning, and (iii) growth optimal selection twist-and-turn around one another over a centuries-long research history. This paper traces each strand chronologically. It also highlights their interconnections. Its goal is to connect what practitioners already know with Ergodicity Economics, because it is the next wave of product development and client advice.

We cannot individually experience ensemble averages, thus using Expected Value as the default investment decision criterion has created a large catalog of empirical puzzles, paradoxes, and anomalies. Financial Economics uses mathematics as a language to define the structure of investment problems. Ergodicity Economics (EE) restores mathematics as a method of skepticism to question the structure of economic and investment problems. This change has created a growing catalog of solutions to the traditional list of empirical puzzles, paradoxes, and anomalies.

The formalization of embedding randomness in Time by Ole Peters in 2011, as an alternative to embedding randomness in the Ensemble, is a critical development for the financial industry. At a personal level, it clarified the conceptual meaning of a path through three start-ups over three decades. This path went from expected value portfolio optimization, to client-centric retirement planning, and now growth optimal product selection.

Following EE’s example, the rapidly growing number of research papers becomes more manageable when one starts with the foundational papers. Thus, this narrated conceptual chronology starts each conceptual entry with the earliest research papers available, and lists the matching entries in ascending chronological order.

This narrated conceptual chronology proved to be a helpful exercise to connect the dots between Financial Economics and Ergodicity Economics. It also proved to be a productive platform for the development of additional content: Identifying and rank-ordering the empirical puzzles, paradoxes, and anomalies of Financial Economics that matter the most for practitioners, and that could benefit from solutions based on Ergodicity Economics.

This paper presents an overview of Ergodicity Economics (EE) in plain English.

Ergodicity Economics (EE) applies a modern mathematical formalization to familiar financial concepts to reveal implications, and consequences that were previously unseen.

EE provides a clear distinction between:

• methods of averaging (arithmetic means vs. geometric means),
• meanings of averaging (ensemble expectation vs. time average), and
• reasons for the different meanings (additive vs. multiplicative growth dynamics).

These are distinctions with a difference because the average experience of an ensemble over many trajectories may not be the average experience of an individual over a single life history. Using ensemble expectations inappropriately - i.e. for non-ergodic observables – misleads individuals because it implies a physical system of counterfactuals that cannot exist in a single life trajectory.

EE quantifies the differences and the trade-offs between the collective meaning and the individual meaning of financial methods. EE’s perspective opens up previously unseen distinctions for evidence-based recommendations. These distinctions enable the creation of previously unavailable recommendations for the explicit benefit of individual clients. This differentiating impact on economic theory, asset valuation, product development, and advisory best practices is developing rapidly.