Causal Uncertainty in Capital Markets: A Robust Noisy-Or Framework for Portfolio Management

Abstract

Understanding the causal relations that drive markets is integral to both explaining past events and predicting future developments. Although there are various theories of economic causality, there has not yet been a wide adoption of machine learning–inspired causal frameworks within economics and finance. Causal networks are among the latter and provide one of the most transparent and practical models for representing the relationships between economic causes and effects that are relevant for making investment decisions. Among the various approaches to causal networks, the noisy-or model stands out because it provides the formal means to simplify the calculation of the cumulative impact of more than one cause on an effect. One of the implicit assumptions of the noisy-or model is that the causal probability values posited by model builders are completely reliable. This assumption is unrealistic, however, especially in financial applications in which beliefs about market events are generally supported by significantly less data relative to beliefs about natural phenomena. Moreover, aside from the need to evaluate the reliability of individual beliefs, portfolio managers presumably also need to assess the investment processes that produce those beliefs. To address the foregoing challenges, in this article, a formal, logic-based framework to produce robust, uncertainty-adjusted causal probability assignments within the noisy-or model is proposed. The robust noisy-or framework described provides both a technical enhancement of the basic noisy-or model and a practical solution for addressing the challenge posed by the varying quality of evidence that supports most investment decisions.

TOPICS: Big data/machine learning, quantitative methods, statistical methods

Key Findings

• ▪ Causal networks provide an efficient framework for assisting with investment decisions that are supported by both quantitative and qualitative evidence.

• ▪ Within the formal setting of causal networks, the noisy-or model simplifies the processing of large sets of evidence that support investment views. It does this by assuming that causes act independently of one another in terms of their ability to influence the actualization of effects.

• ▪ Evidence-based subjective logic is a many-valued logic that provides a way for investors to precisely account for model uncertainty, with regard to both the reliability of their individual causal probability assignments and their overall conviction in their investment process. The logic also provides the means to combine different causal probability assignments on a single belief, each driven by a distinct set of evidential support.