What's in a rate?

Have you ever looked inside a rate?  In this post I'll try to do so, giving some ideas about how you might slice up a rate in terms of economic forces or financial forces in markets.    Remember, first and foremost a rate is just a fraction of some reference amount.  In other words it describes a unit or quantity in terms of its size relative to some reference quantity.

Let's talk money.  A money rate describes some amount of money with respect to some other reference amount of money.  In the vast majority of cases in fixed income finance, the reference amount of money represents either a starting amount or a closing amount.  Usually the rate summarises some kind of financial promise you're involved in or it represents a post hoc analysis of some investment you made in a security or portfolio of securities.

These rates are also known as returns, yields, and interest.  Return is a nice expression, conjuring up an image of the return of invested capital, with some extra capital too.  Yield is quite an agricultural sounding variant - think of it as expressing the size of a crop with respect to the size of the field.  Interest (interesse) was originally a late payment penalty built into the contracts for loans, which then morphed into contract structures where failure was built in.  This allowed the contracts to side-step Christian usury laws.  Muslims perform a similar piece of arithmetical/contractual engineering in their dealings with returns.

The clearest security with a return is probably a loan by a lender to a borrower for a fixed term, with no intervening days of reckoning, where accumulated interest is rolled into the current capital embedded in the security (compounding).  That is, in cases with just two days of reckoning - at the start day and on the last day - the day of termination of the loan.  The slightly more general case is where the rate as expressed fits into a compound growth formula, as described in another posting.  This implies all such rates must have associated with them implicitly recipes for how they are used.  These recipes are called the rate's time basis, compounding frequency, day count convention.  They flesh out how to operate with the rate.  As noted, again in a previous post, they're all fully interchangeable, so we shouldn't look here to find out what's inside a rate.

 In the next posting I'll explain why I think it is good to categorise of the constituents of a rate as follows: inflation, the market, participant profiles, this deal.  I think of this as a slow zoom camera, first of all, picking up macroeconomic effects, then market (and close-market) effects, then evaluating the states and preferences of the contract participants, before finally looking at the terms of the contract.