Dollars and Jens
Tuesday, December 09, 2014

I started my adult life in physics, and have now come to economics by way of finance; one of the differences between how economics is practiced and how physics is practiced is that economics frequently suppresses "units"; especially in introductory economics, supply and demand curves are frequently specified with quantity and price in some implicit units and coefficients of e.g. "5" where a physicist would say "5 $/widget2". In practical contexts, this is most pervasive in economic and financial contexts when the implicit unit is time; "year" frequently is 1. Otherwise smart people seem occasionally to forget that interest rates have an implicit time unit in them; bonds are yielding 3%per year.

This brings me to the term "basis point". You can go to websites (or at least comments sections of blogs) about linguistics and watch people fight about what words really mean, or which uses are inappropriate; finance specialists will have that argument about the term "basis point" perhaps more than any other term, but the permitted uses seem to be "nested", in that you won't usually encounter two people where one says A is acceptable and B isn't while the other allows for B but not A; when two people disagree about the proper use, usually one has a strictly narrower use than the other. The basic definition, though, is that a basis point is the reciprocal of 10,000 years, i.e. .01% per year.

The term "basis" is frequently used in finance to refer to a difference between two things, especially two things that are similar or related; the "basis" is then the extent to which they are different. If you buy oil futures because you need to buy jet fuel in the future and you want to hedge your risk, "basis risk" is the risk that the price of oil and the price of jet fuel don't actually move in lockstep. The term "basis point" was originally used in the context of different interest rates; an interest rate of 3.43% per year is 1bp less than an interest rate of 3.44% per year. There are some people who insist that any use of "basis point" other than in referring to differences or change in interest rates is wrong. Some people are willing to use it for anything related to interest rates, convenience yields, or other interest-rate-like objects. Any use of "basis point" that satisfies the definition I gave seems fine to me; if you want to talk about the growth rate of GDP in terms of basis points, that seems entirely cromulent to me.

The point at which I start to object is where the units are changed, which is mostly to say when people start multiplying it by "year" without telling you that. The employment-to-population ratio, for example, was .5923 in October and .5919 in November, according to the latest BLS report; there are people who would tell you that it dropped by 4 basis points. Note that, in this context, even if one were attempting to specify a rate, this is a change from one month to the next; to say that it dropped at a "rate of 50bp" is more in tune with the initial definition, and more likely to confuse people.

This morning I see in Matt Levine's linkwrap that Vanguard is looking to launch an advisory service

for a fee of 30 basis points per year instead of "an industry average of more than 1 per cent"

where I would contend "per year" should be moved from its current location to the end of the blockquote; they seek a fee of 30bp, as compared to 1 per cent per year.

I should perhaps note here that, as far as I know, I am the only person who has a problem with "basis point" meaning 1/100 of one percentage point but is fine with using it to express growth rates. If there are others, I wouldn't be surprised if they got into finance through physics, or some other field that uses a lot of dimensional analysis; it is, from my background, simply "obvious" that one system of usage is self-consistent and the other is not.

Allow me to move on from "basis point" but not from picking on Matt Levine who, as far as I've been able to tell, has adopted from FDIC regulators the practice of referring to a regulatory rule about "leveraged loans" as applying to loans to companies with debt that is "at least six times EBITDA". (I suspect Levine has no problem with this, but he doesn't seem to have originated it.) EBITDA is a flow, and debt is a stock; the ratio of debt to EBITDA again has units of time. What they all mean is "six years' worth of EBITDA"; if you have quarterly* EBITDA, multiply by 24 to get the debt limit. The national debt/GDP ratio is almost always given in years, but with the "years" unspoken; one often sees an outsized importance given to "100%", i.e. debt equal to one year's GDP, and while some of the people who see that as an important milestone may simply see that as a psychologically significant number in a broad plausibly economically relevant range, I read some commentary that seems to think it's important because, come on, all of your GDP is debt, or something — which loses even its superficial coherence if you change units.

This, ultimately, is where it matters — when it screws up people's conceptual understanding of what's going on. If you're attentive to which numbers are stock and which are flows, and you make sure to annualize anything that needs annualizing and develop an intuition around annualized numbers, various semantic conventions that seem unnecessarily confusing to me are just language, and probably is a perfectly good choice among ultimately arbitrary coding rules.

* "Quarter", of course, is a unit of time equal to a quarter of a year, in the same pattern of "year=1".

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