Complex relationships among firm risk, asymmetric volatility, volatility skew, and the leverage effect

In finance, the asymmetric volatility phenomenon (AVP) and volatility skew are two well-known topics related to firm risk. In early research, the AVP was documented by Black (Proc 1976 Meetings Business Econ Stat Sect 1976, 177–181), who proposed two possible explanations. The veracity of one such explanation, the “leverage effect,” has long remained controversial. The volatility skew is considered to represent collective phenomena caused by heterogeneous beliefs regarding firm risk among investors. Although the relationship between leverage and firm size has been investigated, the investigations have yielded inconsistent conclusions. All related empirical evidence indicates that the relationships among firm risk, asymmetric volatility, volatility skew, and the leverage effect are complex. Regarding accounting principles, Ryan (Account Horizons 1997, 11, 85–95) proposed two concepts for describing firm risk. One of those concepts, “sources of operating risk versus leverage,” revealed the key to linking firm risk to leverage. Among the multidisciplinary methodologies, cybernetics plays a crucial role in complex systems research. The causal nets and feedback loop analysis of cybernetics offer accurate descriptions of realities in terms of causality, nonlinearity, and temporality. This study uses cybernetics to connect the accounting risk concept in microlevel analysis to volatility changes in macrolevel phenomena. This not only validates interdisciplinary analysis with different evidence but also enables the development of a managerial interpretation of different states of firm risk. This study contributes a novel approach that involves the application of a microlevel concept to macrolevel analysis and evidences the “less is more” art of modeling complex phenomena (Schuster, Complexity 2005, 11, 11–13).