In November 2011, the Financial Stability Board, in collaboration with the International Monetary Fund, published a list of 29 "systemically important financial institutions" (SIFIs, now referred to as "globally systemically important banks" or G-SIBs), institutions whose failure, by virtue of "their size, complexity, and systemic interconnectedness", could have dramatic negative consequences for the global financial system. While "size" and "interconnectedness" have been the subject of much quantitative analysis, less attention has been paid to measuring "complexity." Yet without a consistent way to measure complexity, there is little guarantee that the designated SIFIs capture the complexity that the FSB is concerned about, and little hope of mitigating the consequences that the FSB warns of. In this paper we propose the structure of an individual firm's majority-control hierarchy as a proxy for institutional complexity. We demonstrate as a proof-of-concept how this method might be used by bank supervisors, particularly the Federal Reserve under its authority as consolidated supervisor, using a data set containing information on the majority-control hierarchies of many of the designated SIFIs. Our mathematical intrafirm network representation (and various associated metrics we propose) provides a uniform way to compare firms with often very disparate organizational structures – one that is distinct from a simple size comparison.

We study an equilibrium risk and return model to explore the effects of the coronavirus crisis and associated skewness on the market price of risk. We derive the moment and equilibrium equations, specifying skewness price of risk as an additive component of the effect of variance on mean expected return. We estimate our model using the flexible skewed generalized error distribution, for which we derive the distribution of returns and the likelihood function. Using S&P 500 Index returns from January 1980 to mid-October 2020, our results show that the coronavirus crisis generated a deeply negative reaction in the skewness and total market price of risk, more negative even than the subprime and the October 1987 crises.