A Category Theory of Financial Instruments and Financial Institutions -  A Fundamental Ontology of Law and Finance

-Draft Abstract-

In an early paper examining the regulation of private placement memorandum (PPM) regulation, we found that there are in general two approaches to financial regulations: (1) the regulation of the behaviours of the financial institution; and (2) regulation of the financial instruments.  PPMs are interesting financial instruments since they sit in-between two extremes of financial regulatory types: (1) purely private form of financial intermediation (that is, at the extreme, we have bilateral financial contracts) and (2) highly ritualized guidance on what can be communicated in the raising of capital (that is, prospectus-type regulations) stemming from the Securities Act of 1933 and Securities Exchange At of 1934.  The unnatural divide between the regulation of financial institutions and the regulation of financial instruments has played itself out in terms regulations which aim at adjusting the incentives relating to particular types of businesses within a financial institutional framework.  In general, the play out has been a border conflict between banking regulations and capital market regulations.  This is not to say that any particular jurisdiction uses one type of financial regulation exclusively to the exclusion of the other, but rather there is a combination or admixture of financial regulations, that in total, ascribe to one general tendency or the other.  Recall the legal theorists who attempted to justify financial regulations on the basis that “Law Matters”, stating in particular that law matters in that it set outs the initial permit or license to practice a certain form of business.  As we shall see, if we apply certain fundamental risk and return models, which the financial industry itself uses to measure its own financial instruments, we can distinguish different sorts of businesses according to these risk and return financial instrument components.  Thus, from an extreme financial institutional perspective, which applies financial theory to its own institutional design, behaviours and assessment of behaviours, financial instrument theory applies laws to accomplish the institution’s particular objectives and the discipline and guidance therefore are simple financial theory models of risk and return, which captures the market definition of money.  From the institutional perspective apply financial theory, an institution is simply a financial instrument with certain risk and return characteristics.  Thus, financial institutions regarding themselves as financial instruments are constrained by the “rules of the game” of finance, which are basically arbitrage (“the law of one price”) which forever use laws such as contracts, and every other sort of law and regulation, as merely instrumental.  There are researchers who assert that there should be a legal theory of finance and use legal ideas to promote the logical priority of law to finance. There is no argument with this thesis if we add the distinction that law is the context in which finance exists.  However, it is not entirely plausible to say that finance exists because of law, nor is it plausible to assert that law is absolutely necessary for finance to exist in the world.  In any case, the purpose of this paper is not to adjust or determine where the horse and carriage can become one or the other—we believe that is actually an obvious distinction--but rather to understand if possible the system, model or ecology in which law and finance co-exist.  As a theoretical approach, we shall combine the financial instrument view and the financial institutional view into one totality, and call that totality, a law and finance ontology.  Our view, which is slightly complicated because of the distinctness of disciplines and variety of sub-disciplines involved in law and finance, is to start with the simplest ideal financial instrument and then to ask ourselves what would happen to that financial instrument in the real world of law and finance.

This model of moving from a well-defined financial instrument (which is the particular in the Aristotelian sense of a genus-specie category or more modernly, the event) to how this financial instrument operates in the real world (the generalized reality of abstract continuity) is in effect a study of the reality of finance given a legal context in the form of a mapping or under a mapping technology.