Asset Prices Under Knightian Uncertainty

We extend Lucas’s classic asset-price model by opening the stochastic process driving dividends to Knightian uncertainty arising from unforeseeable change. Implementing Muth’s hypothesis, we represent participants’ expectations as being consistent with our model’s predictions and formalize their ambiguity-averse decisions with maximization of intertemporal multiple-priors utility. We characterize the asset-price function with a stochastic Euler equation and derive a novel prediction that the relationship between prices and dividends undergoes unforeseeable change. Our approach accords participants’ expectations, driven by both fundamental and psychological factors, an autonomous role in driving the asset price over time, without presuming that participants are irrational.

Expectations Concordance and Stock Market Volatility: Knightian Uncertainty in the Year of the Pandemic

This study introduces a novel index based on expectations concordance for explaining stock-price volatility when novel events that are each somewhat unique cause unforeseeable change and Knightian uncertainty in the process driving outcomes. Expectations concordance measures the degree to which KU events are associated with directionally similar expectations of future returns. Narrative analytics of daily news reports allow for the assessment of bullish versus bearish views in the stock market. Increases in expectations concordance across all KU events results in reinforcing effects and an increase in stock market volatility. Lower expectations concordance produces a stabilizing effect wherein the offsetting views reduce market volatility. The empirical findings hold for ex post and ex ante measures of volatility and for OLS and GARCH estimates.

Ambiguity and the Tradeoff Theory of Capital Structure

We examine the impact of ambiguity, or Knightian uncertainty, on the capital structure decision, using a static tradeoff theory model in which agents are both ambiguity and risk averse. The model confirms the well-known result that greater risk—the uncertainty over outcomes—leads firms to decrease leverage. Conversely, the model indicates that greater ambiguity—the uncertainty over the probabilities associated with the outcomes—leads firms to increase leverage. Using a theoretically based measure of ambiguity, our empirical analysis presents evidence consistent with these notions, showing that ambiguity has an important and distinct impact on capital structure. This paper was accepted by Gustavo Manso, finance.

Expectations Concordance and Stock Market Volatility: Knightian Uncertainty in the Year of the Pandemic

This study introduces a novel index based on expectations concordance for explaining stock-price volatility when historically unique events cause unforeseeable change and Knightian uncertainty in the process driving outcomes. Expectations concordance measures the degree to which nonrepetitive events are associated with directionally similar expectations of future returns. Narrative analytics of daily news reports allow for assessment of bullish versus bearish views in the stock market. Increases in expectations concordance across all KU events leads to reinforcing effects and an increase in stock market volatility. Lower expectations concordance produces a stabilizing effect wherein the offsetting views reduce market volatility. The empirical findings hold for ex post and ex ante measures of volatility and for OLS and GARCH estimates.

Entrepreneurial Beliefs and Agency under Knightian Uncertainty

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later.

Institutions, uncertainty, and entrepreneurial judgment

Entrepreneurial action takes place in a context of Knightian uncertainty. In order to overcome this uncertainty, entrepreneurs engage in a process of judgment resulting in a decision about the course of action. Institutions arise mainly to reduce economic friction by providing structure to human interaction and thus reducing uncertainty. However, institutions may also introduce further uncertainty and thus disrupt the judgment process preceding entrepreneurial action. The present paper builds upon recent efforts to integrate the concepts of uncertainty and institutions within the entrepreneurial context. Drawing on Frank H. Knight's seminal insight, the judgment-based view of entrepreneurship, and relevant concepts of entrepreneurial outcomes, the main contribution of the paper lies in the development of a model offering a coherent description of the way institutions affect uncertainty and the entrepreneurial process.

A class of solvable multidimensional stopping problems in the presence of Knightian uncertainty

We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity-averse decision-maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends on either a linear combination of the factors or the radial part of the driving factor dynamics. We present a general characterization of the value of the optimal timing policy and the worst-case measure in terms of a family of explicitly identified excessive functions generating an appropriate class of supermartingales. In line with previous findings based on linear diffusions, we find that ambiguity accelerates timing in comparison with the unambiguous setting. Somewhat surprisingly, we find that ambiguity may lead to stationarity in models which typically do not possess stationary behavior. In this way, our results indicate that ambiguity may act as a stabilizing mechanism.