Finance people are good people. Economics needs finance people. Some of my best friends are finance people. But (you heard that "but" coming), finance people (though there are of course honourable exceptions) just don't seem to get money.
I can hear the reply now: "Yeah, and money people don't get finance either!". And I think you are right, but only half right, about that. I think that money people do get simple basic finance; it's the more complicated stuff we don't get. But finance people, it seems to me, often don't get the simple basic stuff about money.
And that's not because money people are smarter than finance people (though we are better-looking). It's because money is weird. Money is not like other assets. So when you take simple basic finance theory, that works OK for other assets, and apply it to money, you can get in a mess.
I watched a finance person on Twitter ask the question: what determines the market value of a zero-coupon perpetuity, like currency? That's a very good question to ask, but you won't get a sensible answer if you do a standard Present Value calculation of a perpetual stream of zeros. Why isn't it zero??
Let's do this Present Value calculation very slowly. (And please excuse my cruddy math, which I always get wrong.) Start with a perpetuity that has a fixed annual coupon C, a market price P(t) at time t, where people are willing to own it at a discount rate r(t). We know that:
P(0) = C + P(1)/(1+r(0))
and since P(1) = C + P(2)/(1+r(1), we get
P(0) = C + C/(1+r(0) + P(2)/[(1+r(0))(1+r(1)]
Wash, rinse, and repeat, for a horizon of T periods, and we get:
P(0) = PV[C] + PV[P(T)] where "PV[.]" stands for Present Value of, and you know the formula better than I do.
Now we want to take the limit of that equation as T approaches infinity. And it is very tempting to say that the second term PV[P(T)] approaches zero in the limit as T goes to infinity, unless there's some sort of bubble, so we can re-write that equation as
P(0) = PV[C]
Or, in the simple case where r(t) is a constant over time:
P(0) = C/r + lim[P(T)/(1+r)T] as T goes to infinity
and the denominator in the second term goes to infinity if r > 0, so the second term must go to zero if the price is always finite.
So if currency is a zero-coupon perpetuity, it is very tempting to say it must have a fundamental value of zero. But since (obviously) currency does not have zero value, there's gotta be something funny going on.
Here's a different way to think about it, that you might find useful:
You know that liquidity matters. Other things equal, people prefer holding a more liquid asset than a less liquid asset. They will own a more liquid asset even when it has a lower rate of return than competing less liquid assets. The discount rate we should be using in the Present Value calculation should reflect the liquidity of that particular asset, and should be the rate at which people will just be willing to own that particular asset.
Now suppose there were some very liquid asset that people would just be willing to own at a zero rate of return?
If we stick r(t) = 0% for all t in the Present Value calculation above, we can't get rid of the second term PV[P(T)]=P(T)/(1+r)T. Because the denominator stays at one, and does not approach infinity in the limit as T goes to infinity.
That really messes up the Present Value calculation. We can no longer say that the fundamental value of a zero-coupon perpetuity is zero, if it's very liquid so people are just willing to own it at a 0% rate of return. But what the hell is it? What is 0 divided by 0?
Here's the standard way that money people have answered that question:
Suppose the demand curve for liquidity slopes down, but is also an increasing function of Nominal GDP. So the rate of return at which people would be just willing to own a particular very liquid asset, at the margin, for a given set of rates of return on other less liquid assets, is an increasing function of the Market Capitalisation of that particular asset as a ratio of NGDP. So the r(t) we use in our Present Value calculation for this particular asset is an increasing function of M(t).P(t)/NGDP(t), where M(t) is the number of "shares". And the r(t) will go negative if the market capitalisation is small enough.
So, in the simple case where everything is constant over time, it's easy to reconcile the formula P(0) = C/r with a zero-coupon perpetuity like currency. Just use the liquidity demand function (we call it a "money demand function") to figure out the P(0) at which the ratio of market capitalisation to NGDP gives us an r=0%. Done.
Come to think of it though, shouldn't all finance be done a bit like this? Is it really plausible that the rate of return at which people are just willing to hold a particular asset, at the margin, is always strictly exogenous with respect to the price and hence market capitalisation of that asset? Sure, that might be an OK simplification for some partial equilibrium work in very competitive markets, but it won't be generally true.
Oh, and money is special because it's the unit of account, so its price is normally written as 1/P(t), where P(t) is the price of everything else in terms of money, and so its market capitalisation is M(t)/P(t). And the ratio of market cap to NGDP becomes M(t)/P(t).RGDP(t) where RGDP is real GDP.
And the reason money is so very liquid (in fact the most liquid) asset is because everything else is bought and sold for money (it's the medium of exchange), but getting properly into that issue is beyond the scope of this post.