Bayes' rule is a fundamental principle that has been applied across multiple disciplines. However, few studies have addressed its origin as a cognitive strategy or the underlying basis for generalization from a small sample. Using a simple binary choice model subject to natural selection, we derive Bayesian inference as an adaptive behavior under certain stochastic environments. Such behavior emerges purely through the forces of evolution, despite the fact that our population consists of mindless individuals without any ability to reason, act strategically, or accurately encode or infer environmental states probabilistically. In addition, three specific environments favor the emergence of finite memory—those that are Markov, nonstationary, and environments where sampling contains too little or too much information about local conditions. These results provide an explanation for several known phenomena in human cognition, including deviations from the optimal Bayesian strategy and finite memory beyond resource constraints.

One of the longest debates in economics involves the existence of a rare Hominid “species” known as Homo economicus, the economic human. H. economicus is able to determine the optimal use of its resources to maximize its well-being as defined by the assumptions of neoclassical economics, leading to behavior that has come to be known as economic rationality. When interacting with other members of this species in market settings, such behavior leads to a magical outcome. The participants’ self-interested efforts to exploit their disparate pieces of information aggregates, distills, and compresses their information into a single number: the price. And because no piece of information is left unused or uninterpreted in the process of price discovery, this market is deemed “efficient.” Prices fully reflect all available information, as Eugene Fama concluded in his first articulation of the efficient markets hypothesis (1).

We construct an evolutionary model of a population consisting of two types of interacting individuals that reproduce under random environmental conditions. We show that not only does the evolutionarily dominant behavior maximize the number of offspring of each type, it also minimizes the correlation between the number of offspring of each type, driving it toward −1. We provide several examples that illustrate how correlation can be used to explain the evolution of cooperation.

We use a global survey of over 22,400 individual investors, 4,892 financial advisors, and 2,060 institutional investors between 2015 and 2017 to elicit their asset allocation behavior and risk preferences. We find substantially different behaviors among these three groups of market participants. Most institutional investors exhibit highly contrarian reactions to past returns in their equity allocations. Financial advisors are also mostly contrarian; a few of them demonstrate passive behavior. However, individual investors tend to extrapolate past performance. We use a clustering algorithm to partition individuals into five distinct types: passive investors, risk avoiders, extrapolators, contrarians, and optimistic investors. Across demographic categories, older investors tend to be more passive and risk averse.

One of the most enduring empirical regularities in equity markets is the inverse relationship between stock prices and volatility. Also known as the “leverage effect”, this relationship was first documented by Black (1976), who attributed it to the effects of financial or operating leverage. This paper documents that firms which had no debt (and thus no financial leverage) from January 1973 to December 2017 exhibit Black’s leverage effect. Moreover, it finds that the leverage effect of firms in this sample is not driven by operating leverage. On the contrary, in this sample the leverage effect is stronger for firms with low operating leverage as compared to those with high operating leverage. Interestingly, the firms with no debt from the lowest quintile of operating leverage exhibit the leverage effect that is on par with or stronger than that of debt-financed firms.

This two-volume set brings together a unique collection of key publications at the intersection of biology and economics, two disciplines that share a common subject: Homo sapiens. Beginning with Thomas Malthus–whose dire predictions of mass starvation due to population growth influenced Charles Darwin–economists have routinely used biological arguments in their models and methods. This collection summarizes the most important of these developments, including articles in sociobiology, evolutionary psychology, behavioral ecology, behavioral economics and finance, neuroeconomics, and behavioral genomics. Together with an original introduction by the editors, this important research collection will appeal to economists, biologists, and practitioners looking to develop a deeper understanding of the limits of Homo Economicus.

The information revolution has transformed everyday life for billions of people throughout the world. For example, according to mobile phone research group GSMA Intelligence, there are currently over 5 billion unique mobile phone subscribers, out of an estimated global population of 7.6 billion. This is the equivalent of a mobile phone for every person on the planet between the ages of 15 and 65.

Bacteria are easily characterizable model organisms with an impressively complicated set of abilities. Among them is quorum sensing, a cell-cell signaling system that may have a common evolutionary origin with eukaryotic cell-cell signaling. The two systems are behaviorally similar, but quorum sensing in bacteria is more easily studied in depth than cell-cell signaling in eukaryotes. Because of this comparative ease of study, bacterial dynamics are also more suited to direct interpretation than eukaryotic dynamics, e.g., those of the neuron. Here we review literature on neuron-like qualities of bacterial colonies and biofilms, including ion-based and hormonal signaling, and a phenomenon similar to the graded action potential. This suggests that bacteria could be used to help create more accurate and detailed biological models in neuroscientific research. More speculatively, bacterial systems may be considered an analog for neurons in biologically based computational research, allowing models to better harness the tremendous ability of biological organisms to process information and make decisions.

Half of all Americans have money in the stock market, yet economists can't agree on whether investors and markets are rational and efficient, as modern financial theory assumes, or irrational and inefficient, as behavioral economists believe—and as financial bubbles, crashes, and crises suggest. This is one of the biggest debates in economics and the value or futility of investment management and financial regulation hang on the outcome. In this groundbreaking book, Andrew Lo cuts through this debate with a new framework, the Adaptive Markets Hypothesis, in which rationality and irrationality coexist.

Drawing on psychology, evolutionary biology, neuroscience, artificial intelligence, and other fields, Adaptive Markets shows that the theory of market efficiency isn't wrong but merely incomplete. When markets are unstable, investors react instinctively, creating inefficiencies for others to exploit. Lo's new paradigm explains how evolution shapes behavior and markets at the speed of thought—a fact revealed by swings between stability and crisis, profit and loss, and innovation and regulation.

A fascinating intellectual journey filled with compelling stories, Adaptive Markets starts with the origins of market efficiency and its failures, turns to the foundations of investor behavior, and concludes with practical implications—including how hedge funds have become the Galápagos Islands of finance, what really happened in the 2008 meltdown, and how we might avoid future crises.

Ever since I was a graduate student in economics, I’ve been struggling with the uncomfortable observation that economic theories often don’t seem to work in practice. That goes for that most influential economic theory, the Efficient Markets Hypothesis, which holds that investors are rational decision makers and market prices fully reflect all available information, that is, the “wisdom of crowds.”

We propose an evolutionary framework for optimal portfolio growth theory in which investors subject to environmental pressures allocate their wealth between two assets. By considering both absolute wealth and relative wealth between investors, we show that different investor behaviors survive in different environments. When investors maximize their relative wealth, the Kelly criterion is optimal only under certain conditions, which are identified. The initial relative wealth plays a critical role in determining the deviation of optimal behavior from the Kelly criterion regardless of whether the investor is myopic across a single time period or maximizing wealth over an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.

Stop-loss strategies are commonly used by investors to reduce their holdings in risky assets if prices or total wealth breach certain pre- specified thresholds. We derive closed-form expressions for the impact of stop-loss strategies on asset returns that are serially correlated, regime switching, and subject to transaction costs. When applied to a large sample of individual U.S. stocks, we show that tight stop-loss strategies tend to under-perform the buy-and-hold policy in a mean-variance frame work due to excessive trading costs. Outperformance is possible for stocks with sufficiently high serial correlation in returns. Certain strategies succeed at reducing downside risk, but not substantially.