On Negative Rates

Negative interest rates – weird, right?

In the five thousand years that interest rates have been recorded, they’ve never hit zero before.  Today, there’s some $15 trillion in negative-yielding bonds — admittedly down from $17 trillion last year, but still a very substantial fraction of the global bond market outside the US. At first it was only shorter bonds that were negative, but today German bunds are negative all the way out to 30 years. What’s going on? Does this mean it would be profitable to bulldoze the Rockies for farmland? Will it cause the extinction of the banking system? And more fundamentally, if the interest rate reflects the cost of a good today in terms of the same good next year, why would it ever be negative? Why would people place a higher value on stuff in the future than on stuff today?

Personally, I don’t think they’re so weird. And the reason I think that is that interest rates are not, in fact, the price of goods today in terms of goods tomorrow. It is, rather, the price of a financial asset that promises a certain schedule of money payments. Negative rates are only a puzzle in the real-exchange perspective that dominates economics, where we can safely abstract from money when discussing interest rates. In the money view, where interest transactions are swap of assets, or of a stream of money payments, nothing particularly strange about them. 

(I should say up front that this post is an attempt to clarify my own thinking. I think what I’m writing here is right, but I’m open to hearing why it’s wrong, or incomplete. It’s not a finished or settled position, and it’s not backed up by any larger body of work. At best, like most of what I wrote, it is informed by reading a lot of Keynes.)

The starting point for thinking about negative rates is to remember that these are market prices. Government is not setting a negative yield by decree, someone is voluntarily holding all those negative-yielding bonds. Or more precisely, someone is buying a bond at a price high enough, relative to the payments it promises, to imply a negative yield. 

Take the simplest example — a government bond that promises a payment of $100 at some date in the future, with no other payments in between. (A zero-coupon bond, in other words.) If the bond sells today for less than $100, the interest rate on it is positive. If the bond sells today for more than $100, the interest rate is negative. Negative yields exist insofar market participants value such a bond at greater than $100. 

So now we have to ask, what are the sources of demand for government bonds?

A lot of confusion is created, I think, by asking this question the wrong way. People think about saving, and about trading off spending today against spending tomorrow. This after all is the way an economics training encourages you to think about interest rates — as a shorthand for any exchange between present and future. Any transaction that involves getting less today in return for more tomorrow incorporates the interest rate as part of the price — at a high enough level of abstraction, they’re all the same thing. The college wage premium, say, is just as much an interest rate from this perspective as the yield on the bond. 

If we insist on thinking of interest rates this way, we would have to explain negative yields in terms of a society-wide desire to defer spending, and/or the absence of any store of wealth that even maintains its value, let alone increases it. Either of those would indeed be pretty weird!

(Or, it would be the equivalent of people paying more for a college education than the total additional wages they could expect to earn from it, or people paying more for a house than the total cost of renting an identical one for the rest of their lives. Which are both things that might happen! But also, that would be generally seen as something going wrong in the economic system.)

Since economists (and economics-influenced people) are so used to thinking of interest as reflecting a tradeoff between present and future, a kind of inter-temporal exchange rate, it’s worth an example to clarify why it isn’t. Imagine a typical household credit transaction, a car loan. The household acquires means to pay for the acquisition of a car, and commits to a schedule of payments to the bank; the bank gets the opposite positions. Is the household giving up future consumption in order to consume now? No. At every period, the value the household gets from the use of the car will exceed the payments the household is making for it — otherwise, they wouldn’t be doing it. If anything, since the typical term of a car loan is six or seven years while a new car should remain in service for a decade or more, the increased consumption comes in the future, when the car is paid off and still delivering transport services. Credit, in general, finances assets, not consumption. The reason car loans are needed is not to shift consumption from the future to the present, but because use of the transportation services provided by the car are tightly bound up with ownership of the car itself.

Nor, of course, is the lender shifting present consumption to the future. The lender itself, being a bank, does not consume. And no one else needs to forego or defer consumption for the banks to make the auto loan either. No one needs to deposit savings in a bank before it makes a loan; the lent money is endogenous, created by banks in the course of lending it. Whatever factors limit the willingness of the bank to extend additional auto loans — risk; liquidity; capital; regulation; transaction costs — a preference for current consumption is not among them. 

The intertemporal-exchange way of looking at government bonds would make sense if the only way to acquire one was to forego an equal amount of consumption, so that bond purchases were equivalent to saving in an economic sense. Then understanding the demand for government bonds, would be the same as understanding the desire to save, or defer consumption. But of course government bonds are not part of some kind of economy-wide savings equilibrium like that. First of all, the purchasers of bonds are not households, but banks and other financial actors. Second, the purchase of the bond does not entail a reduction in current spending, but a swap of assets. And third, the owners of bonds do not hold them in order to finance some intended real expenditure in the future, but rather for some combination of benefits from owning them (liquidity, safety, regulation) and an expectation of monetary profit. 

From the real-exchange perspective, there is one intertemporal price — the interest rate —  just as there is one exchange rate between any given pair of countries. From the money view perspective, there are many different interest rates, corresponding to the different prices of different assets promising future payments. Many of the strong paradoxes people describe from negative rates only exist if rates are negative across the board. But in reality, rates do not move in lockstep. We will set aside for now the question of how strong the arbitrage link between different assets actually is.

We can pass over these questions because, again, government bonds are not held for income. They are not held by households or the generic private sector. They are overwhelmingly held by banks and bank-like entities for some combination of risk, liquidity and regulatory motives, or by a broader set of financial institutions for return. Note for later: Return is not the same as income!

Let’s take the first set of motivations first. 

If you are a bank, you may want to hold some fraction of your assets as government bonds in order to reduce the chance your income will be very different from what you expected; reduce the chance that you will find yourself unable to make payments that you need or want to make (since it’s easy to sell the bonds as needed); and/or to reduce the chance that you’ll fall afoul of regulation  (which presumably is there because you otherwise might neglect the previous two goals).

The key point here is that these are benefits of holding bonds that are in addition to whatever return those bonds may offer. And if the ownership of government bonds provides substantial benefits for financial institutions, it’s not surprising they would be willing to pay for those services.

This may be clearer if we think about checking accounts. Scare stories about negative rates often ask what happens when households have to pay for the privilege of lending money to the bank. Will they withdraw it all as cash and keep it under the mattress? But of course, paying the bank to lend it money is the situation most people have always been in. Even before the era of negative rates, lots of people held money in checking accounts that carried substantial fees (explicit and otherwise) and paid no interest, or less than the cost of the fees. And of course unbanked people have long paid exorbitant amounts to be able to make electronic payments. In general, banks have no problem getting people to hold negative-yield assets. And why would they? The payments services offered by banks are valuable. The negative yield just reflects people’s willingness to pay for them.

In the national accounts, the difference between the interest that bank depositors actually receive and a benchmark rate that they in some sense should receive is added to their income as “imputed interest”, which reflects the value of the services they are getting from their low- or no- or negative-interest bank accounts. In 2019, this imputed interest came to about $250 billion for households and another $300 billion for non financial corporations. These nonexistent interest payments are, to be honest, an odd and somewhat misleading thing to include in the national accounts. But their presence reflects the genuine fact that people hold negative and more broadly below-market yield assets in large quantities because of other benefits they provide. 

Turned around this way, the puzzle is why government debt ever has a positive yield. The fundamental form of a bond sale is the creating of pair of offsetting assets and liabilities. The government acquires an asset in the form of a deposit, which is the liability of the bank; and the bank acquires an asset in the form of a bond, which is the liability of the government. Holding the bond has substantial benefits for the bank, while holding the deposit has negligible benefits for the government. So why shouldn’t the bank be the one that pays to make the transaction happen?

One possible answer is the cost of financing the holding. But, it is normally assumed that the interest rate paid by banks follows the policy rate. There’s no obvious reason for the downward shift in rates to affect spread between bank deposits and government bonds.  Of course some bank liabilities will carry higher rates, but again, that was true In the past too.

Another possible answer is the opportunity cost of not holding positive-yield asset. Again, this assumes that other yields don’t move down too. More fundamentally, it assumes a fixed size of bank balance sheets, so that holding more of one asset means less of another. In a world with with a fixed or exogenous money stock, or where regulations and monetary policy create the simulacrum of one, there is a cost to the bank of holding government debt, namely the income from whatever other asset it might have held instead. Many people still have this kind of mental model in thinking about government debt. (It’s implicit in any analysis of interest rates in terms of saving.) But in a world of endogenous credit money, holding more government debt doesn’t reduce a bank’s ability to acquire other assets. Banks’ ability to expand their balance sheets isn’t unlimited, but what limits it is concerns about risk or liquidity, or regulatory constraints. All of these may be relaxed by government debt holdings, so holding more government bonds may increase the amount of other assets banks can hold, not reduce it. In this case the opportunity cost would be negative. 

So why aren’t interest rates on government debt usually negative? As a historical matter, I suppose the reasons we haven’t seen negative yields in the past are, first, that under the gold standard, government bonds were not at the top of the hierarchy of money and credit, and governments had to pay to access higher-level money; in some contexts government debt may have been lower in the hierarchy than bank money as well. Second, in the postwar era the use of the interest rate for demand control has required central banks to ensure positive rates on public  as well as private debt. And third, the safety, liquidity and regulatory benefits of government debt holdings for the financial system weren’t as large or as salient before the great financial crisis of 2007-2009. 

Even if negative yields aren’t such a puzzle when we think about the sources of bank demand for government debt, we still have the question of how low they can go. Analytically, we would have to ask, how much demand is there for the liquidity, safety and regulatory-compliance services provided by sovereign debt holdings, and to what extent are there substitute sources for them?

But wait, you may be saying, this isn’t the whole story. Bonds are held as assets, not just as reserves for banks and bank-like entities. Are there no bond funds, are there no bond traders?

These investors are the second source of demand for government bonds. For them, return does matter. The goal of making a profit from holding the bond is the second motivation mentioned earlier.

The key point to recognize here is that return and yield are two different things. Yield is one component of return. The other is capital gains. The market price of a bond changes if interest rates change during the life of the bond, which means that the overall return on a negative-yielding bond can be positive. This would be irrelevant if bonds were held to maturity for income, but of course that is not bond investment works. 

For foreign holders, return also includes gains or losses from exchange rate changes, but we can ignore that here. Most foreign holders presumably hold government bonds as foreign exchange reserves, which is a subset of the safety/liquidity/regularity benefits discussed above. 

To understand how negative yielding bonds could offer positive returns, we have to keep in mind what is actually going on with bond prices, including negative rates. The borrower promises one or more payments of specified amounts at specified dates in the future. The purchaser then offers a payment today in exchange for that stream of future payments. What we call an interest rate is a description of the relationship between the promised payments and the immediate payment. We normally think of interest as something paid over a period of time, but strictly speaking the interest rate is a price today for a contract today. So unlike in the checking account case, the normal negative-rates situation is not the lender paying the borrower. 

Here’s an example. Suppose I offer to pay you $100 30 years from now. This is, formally, a zero-coupon 30-year bond. How much will you pay for this promse today? 

If you will pay me $41 for the promise, that is the same as saying the interest rate on the loan is 3 percent. (41 * 1.03 ^ 30 = 100). So an interest rate of 3 percent is just another way of saying that the current market price of a promise of $100 30 years from now is $41. 

If you will pay me $55 for the promise, that’s the same as an interest rate of 2 percent. If you’ll pay me $74, that’s the same as an interest rate of 1 percent.

If you’ll pay me $100 for the promise, that is of course equivalent to an interest rate of 0. And if you’ll pay me $135 for the promise of $100 30 years from now, that’s the equivalent of an interest of -1 percent. 

When we look at things this way, there is nothing special about negative rates. There is just continuous range of prices for an asset. Negative rates refer to the upper part of the range but nothing in particular changes at the boundary between them. Nothing magical or even noticeable happens when the price of an asset (in this case that promise of $100) goes from $99 to $101, any different from when it went from $97 to $99. The creditor is still paying the borrower today, the borrower is still paying the creditor in the future.

Now the next step: Think about what happens when interest rates change. 

Suppose I paid $135 for a promise of $100 thirty years from now, as in the example above. Again, this equivalent to an interest rate of -1 percent. Now it’s a year later, so I have a promise of $100 29 years from now. At an interest rate of -1 percent, that is worth $133.50. (The fact that the value of the bond declines over time is another way of seeing that it’s a negative interest rate.) But now suppose that, in the meantime, market interest rates have fallen to -2 percent. That means a promise of $100 29 years from now is now worth $178. (178 * 0.98 ^ 29 = 100.) So my bond has increased in value from $135 to $178, a capital gain of one-third! So if I think it is even modestly more likely that interest rates will fall than that they’ll rise over the next year, the expected return on that negative-yield bond is actually positive.

Suppose that it comes to be accepted that the normal, usual yield on say, German 10-year bunds is -1 percent. (Maybe people come to agree that the liquidity, risk and regulatory benefits of holding them are worth the payment of 1 percent of their value a year. That seems reasonable!) Now, suppose that the yield starts to move toward positive territory – for concreteness, say the current yield reaches 0, while people still expect the normal yield to be -1 percent. This implies that the rise to 0 is probably transitory. And if the ten-year bund returns to a yield of -1 percent, that implies a capital gain on the order of 10 percent for anyone who bought them at zero. This means that as soon as the price begins to rise toward zero, demand will rise rapidly. And the bidding-up of the price of the bund that happens in response to the expected capital gains, will ensure that the yield never in fact reaches zero, but stops rising before gets much above -1 percent. 

Bond pricing is a technical field, which I have absolutely no expertise in. But this fundamental logic has to be an important factor in decisions by investors (as opposed to financial institutions) who hold negative-yielding bonds in their portfolios. The lower you expect bond yields to be in the future, the higher the expected return on a bond with a given yield today. If a given yield gets accepted as usual or normal, then expected capital gains will rise rapidly when the yield rises above that — a dynamic that will ensure that the actual yield does not in fact depart far from the normal one. Capital gains are a bigger part of the return the lower the current yield is. So while high-yielding bonds can see price moves in response to fundamentals (or at least beliefs about them), these self-confirming expectations (or conventions) are likely to dominate once yields fall to near zero. 

These dynamics disappear when you think in terms of an intertemporal equilibrium where future yields are known and assets are held to maturity. When we think of trading off consumption today for consumption tomorrow, we are implicitly imagining something equivalent to holding bond to maturity. And of course if you have a model with interest rates determined by some kind of fundamentals by a process known to the agents in the model — what is called model-consistent or rational expectations — than it makes to sense to say that people could believe the normal or “correct” level of interest rates is anything other than what it is. So speculation is excluded by assumption.

Keynes understand all this clearly, and the fact that the long-term interest rate is conventionally determined in this way is quite important to his theory. But he seems never to have considered the possibility of negative yields. As a result he saw the possibility of capital gains as disappearing as interest rates got close to zero. This meant that for him, the conventional valuation was not symmetrical, but operated mainly as a floor. But once we allow the possibility of negative rates, conventional expectations can prevent a rise in interest rates just as easily as a fall. 

In short, negative yields are a puzzle and a problem in the real exchange paradigm that dominates economic conversation, in which the “interest rate” is the terms on which goods today exchange for goods in the future. But from the money view, where the interest rate is the (inverse of) the price of an asset yielding a flow of money payments, there is nothing especially puzzling about negative rates. It just implies greater demand for the relevant assets. A corollary is that while there should be a single exchange rate between now and later, the prices of different assets may behave quite differently. So while many of the paradoxes people pose around negative rates assume that all rates go negative together, in the real world the average rate on US credit cards, for example, is still about 15 percent — the same as it was 20 years ago. 

In the future, the question people may ask is not how interest rates could be negative, but why was it that the government for so long paid the banks for the valuable services its bonds offered them?