Negative Rates: Zero is Just a Number

Byrne Hobart
Aug 9 · 19 min read

The German ten-year yields negative 0.56%, part of the world’s $15 trillion stock of negative-yielding debt, and that just sounds wrong. You give them your hard-earned money, and after a decade of waiting, you end up with… less than you started with. To anyone who grew up in the halcyon days of mostly positive interest rates, this just sounds weird. And yet, people do it: investors buy Bunds, JGBs, and Swiss government bonds despite negative yields.

Let’s talk about why.

Are Negative Rates Special?

Negative rates seem like they demand an explanation, but perhaps we’re all just slaves to our assumptions. There was a time when positive rates demanded an explanation. When the Czar told his secret police to write something really scurrilous, they plagiarized Dialogue in Hell Between Machiavelli and Montesquieu:

How are loans made? By the issue of bonds entailing on the Government the obligation to pay interest proportionate to the capital it has been paid. Thus, if a loan is at 5%, the State, after 20 years, has paid out a sum equal to the borrowed capital. When 40 years have expired it has paid double, after 60 years triple: yet it remains debtor for the entire capital sum.

In a certain cultural context, it makes perfect sense that interest rates were invented by someone bound for, or originally from, hell. Even today, I have friends — bright, educated people! — who can articulately argue that usury is a sin and should not be legal. I disagree with them, hence the “argue” part, but they do exist.

The intuition behind zero rates, or at least rates that only take into account the risk of repayment, is that the investor isn’t really taking any risk. Of course, they are: the risk you run when you lend money for ten years at X% is that, tomorrow, the rate of return on that loan will be higher than X%, meaning a) you missed an opportunity, and b) the present value of your bet is lower. In other words, opposition to usury can be characterized as “the risk premium for duration risk ought to be zero.”

There’s actually some interesting academic literature on why there is such a thing as duration risk. You can think of it as compensation for volatility in both interest rates and inflation. By making a loan now, you’re losing the opportunity to a) make a different loan later, and b) to spend those dollars on something tangible, if you’re worried that they’ll lose value.

Rates and Reality

Taking a step back, we red-blooded Americans do earn positive returns on our debt. Lend the government money for ten years, and you get a whole 1.7%. But that’s in dollars. The simple interpretation of ten-year treasuries yielding 1.7% while Bunds yield negative 0.56% is that over the next ten years, USD inflation will be about 2.3% higher, such that at the end of the period, your return in your chosen consumption basket is the same: you have more dollars, but they buy less housing, oil, cars, etc., than the German saver’s Euros.

That’s a good way to explain interest rate differentials, and when rates are positive, you can make sense of it without any effort. Two equivalently creditworthy borrowers — the US Treasury, the German Finance Agency, should pay equivalent real interest rates, and any difference in nominal rates is just due to different inflation expectations.

Still, it’s weird. There seems to be a relative-value trade here: if you’re a natural buyer of German bonds, replace that position with a bunch of cash under a mattress. You earn a risk-free 56 basis points per year. Nice!

We’re Gonna Need a Bigger Mattress

Or not so nice. Have you ever actually slept on a mattress stuffed with money?

I have not, but I can imagine it’s not so pleasant. Maybe a couple thousand Euros would be fine, even tens of thousands, but what about millions? Billions? The EU’s M2 is around 12 trillion Euros. At 337m Euro per cubic meter, that’s 35,600 meters. A queen-size mattress is, conveniently, roughly one cubic meter in volume, so it’s about 35,600 queen-sized mattresses. Nontrivial.

Cash has a non-zero cost of storage. Storing a lot of it is dangerous, and the only people who do it are very dangerous people — a while ago, it occurred to me that in general, a neighborhood where people park nice cars in front of their houses is safer than a neighborhood where they park old and beat-up cars in front of their houses. But the most dangerous neighborhoods are probably the ones where most of the cars are old and beat-up, but there are some really nice cars in pristine condition. People who can protect easily-stolen material goods, but don’t want to keep their money in the bank, are not the nicest of people.

The most extreme example of this is the story about Pablo Escobar’s brother, who used to do the cartel’s accounting. They kept their cash in the form of literal cash; bales and bales of bills. And they had an annual budget for spoilage: every year, about 10% of their cash would be damaged by water or eaten by rats.

That’s some negative carry. Pablo would have been happy to earn -58 basis points. The money launderer who got his cash into Bunds would have been earning 942bps/year of alpha, unlevered.

In fact, you can think of the stream of returns from a bond as both the coupon and the service of keeping the money safe. When rates are positive, your actual return on a 1%, $1,000 face-value bond might be $10 of interest and $10 for storage. It’s only at negative 1% interest that your actual nominal rate turns negative. (In this case, the slope of the yield curve represents the value of buying storage in bulk. Normally, you’d discount the value of future storage back to the present, but at near-zero rates, you don’t — so yield curves flatten as they get closer to zero and become more dominated by storage costs.)

All these cash-storage thoughts present some fun policy options. Kenneth Rogoff has written extensively about various schemes for implementing negative interest rates without prompting a flight to cash — such as banning cash, having an exchange rate between electronic and physical cash that slowly devalues paper money, etc. One option he hasn’t considered: decriminalize the theft of sufficiently large sums. It’s wrong to mug someone for $50, but if you break into someone’s house and find $500,000, you’ve probably done the world a favor. On that note, it’s truly unfortunate that Japan of all countries hit the zero lower bound first, since their lower crime rate and trusted financial institutions give them a higher lower bound.

So, negative rates can exist for prosaic logistical reasons, involving the lumpiness of cash-stuffed mattresses; the cost of climate control, armored cars, and guards who can be trusted around bearer instruments; and the relative cost of just earning negative carry. And negative rates in one currency can coexist with positive rates in another, so long as there’s a differential in inflation expectations.

But, even if they can exist, why do they?

Exogenous Synthetic Animal Spirits

If you want to look like Ronnie Coleman, you’re going to have to spend a lot of time in the gym.[1] But you’re also going to have to inject a bunch of synthetic hormones that signal to your body that it should produce enough muscle mass to make you look like a balloon animal. Central Banks have an analogous financial steroid for juicing the economy: they can lower the return of less risky behavior. But, as Ronnie says, that only works well if you put in the effort, too.

The two measures central banks can target are the slope of the yield curve and the absolute level of rates. The slope of the yield curve (i.e. the difference between short- and long-term rates) is, in effect, a measure of the extent to which banks are subsidized for borrowing short and lending long.

At the bottom of the 2003 rate-cutting cycle, the federal funds rate was 1%, while the 10-year paid 4.25%. Since many fixed-income assets are benchmarked to long bonds, this meant that the annual subsidy for lending money out rather than keeping it on hand was 325 basis points. So banks lent with alacrity — although heavily to people buying houses, unfortunately.[2]

Generally, short-term rates are set by central banks, while long-term rates are set by the market. But Central Banks have what Ben Bernanke correctly identified as “a technology, called a printing press, that allows it to produce as many dollars as it wishes at essentially no cost.” They can use it to, you know, print money and exchange it for other assets. And the easiest asset for them to buy — the one they can buy a lot of , with low transaction costs, while knowing exactly what they’re getting — is their own debt.

So, since the financial crisis (or since 2001 in Japan), banks have been printing up local currency and using it to buy longer-term government debt, in order to push interest long-term rates lower.

They’re in a tricky situation: buying long-term debt necessarily flattens the yield curve, reducing banks’ implicit subsidy for lending. But committing to buy, and to buy as much as necessary, has a different effect: it promises that investors will be paid to take duration risk — that if they own long-term fixed-income assets, those assets will appreciate.

So the goal of a properly-calibrated debt-monetization policy is to spend enough that:

  1. Rates are low enough that banks prefer to make risky loans rather than own risk assets,
  2. These loans stimulate the economy enough to make the loans less risky — i.e. they overcome the deflationary effect of a burst bubble, and the ongoing disinflationary effects of aging, but
  3. They don’t convince investors that an ongoing, arbitrarily high appetite for monetizing debt is the single most reliable force in the market, making levered positions in risk-free assets the best risk-adjusted trade. (If 10-year rates are -0.4%, and a central bank credibly signals that they’ll be -1.0% in a year, an investor who pays €1,041 for a bond now can expect to sell it for €1,094.7 in a year. A 5.2% return is modest, sure, but when rates are this low…)

Before rates went below zero, we talked about the “zero lower bound,” the fact that banks can cut rates to zero, but can’t cut rates below that. But now, we know they can, so we have to talk about something different: the Mad Max lower bound, the deposit rate at which it makes financial sense to withdraw your cash from a bank and buy a bunch of guns to keep it safe.

Of course, all this ignores the question of whether there are other ways to raise growth rates. There is another traditional approach: get some inflation. This is where Europe is having some problems. The natural way to raise inflation when you’ve exhausted the potential of monetary policy is to let governments run deficits.

Let’s check in on how that’s going. Right. Italy generated weeks of headlines as they negotiated their budget deficit down from 2.4% of GDP (violating EU rules against deficits in excess of 2% of GDP) to -2.04% (which is apparently within the rules, which allow for rounding. Given the EU’s love of policies that fall within the letter but not the spirit of procedural norms, I propose that during the next crisis they announce that the 2% rule stays, but they now round to the nearest 100% of GDP.) The Euro area overall ran a deficit of about 0.7% of GDP last year. The IMF says that’s a little high, but in the ballpark. Meanwhile, try as they might, they can’t get their inflation rate to 2%. Maybe another year of tiny deficits and an aging populace will do the trick.

For whatever reason, the EU is extremely reluctant to let member states run large deficits, even when their economies are performing below potential.

(Okay, we all know the real reason: Germany spent the first half of the twentieth century periodically trying to conquer Europe by unilaterally exporting large quantities of soldiers and artillery shells, and then spent the second half of the twentieth century doing it by accident by exporting cars and capital equipment. Now a global export power with a high savings rate sets policy for a continent of weaker exporters with lower propensities to save.)

Here in the US, we don’t have bland technocrats fighting over the last tenth of a percentage point of fiscal deficit. No, we elect people who promise to eliminate the national debt in eight years, and, of course, promptly set records.

Investors’ Incentives

Aside from central banks, who buys negative-yielding debt? The answer seems to be: banks, insurance companies, pensions, some retail investors, and some speculators.

The main reason financial institutions buy these bonds is that they have to; there are regulatory limits on risk assets, so they end up being buyers of risk-free assets at any price. For pension funds and life insurance companies, there’s another factor: duration, which we’ve talked about above.

You can think of duration in two senses: the literal timing of cash flows, and the theoretical exposure to changes in rates. In the literal sense, if a pension fund needs to make payments in ten years, they need their assets to have ten-year maturity. The way to get that is to buy something that matures in ten years. If they don’t, they face reinvestment risk: if a pension fund is fully funded now, and declines to buy bonds at a -40 bps yield, they’re underfunded in a world where short-term rates drop to -1% and stay there — but in that world, the long-term bond they eschewed does just fine.

It’s the second interpretation of duration — the sensitivity to interest rates — that encourages speculators to buy bonds as well. The convexity of bonds means that they’re more sensitive to rate changes as rates get lower, so a pessimist expecting lower rates gets more exposure the more right they are. Speculative investors might believe that current rates are artificially low, but they’ll still buy if they have to sell to a forced buyer in the near future.[3] When a country ages, any institution that makes promises in the future is naturally short duration. Under low inflation — the sort you get when your working-age population isn’t growing — stocks tend to have negative effective duration, so there’s a tendency for these institutions to prefer fixed-income for risk-management purposes even if equities have higher expected returns.

The combination of convexity and return-chasing has historically led to some wild swings in long bond prices. In the early 90s, hedge funds somehow convinced their prime brokers to let them lever up 100:1 in long treasury positions. This would have been fine if one fund did it, but the funds that did it made enough money that other funds piled into the trade, until the marginal price-setter in the treasury market was a group of extremely levered people with hair-trigger loss-cutting discipline. Inevitably, this blew up in a big way, leading to Bill Clinton’s infamous question: “You mean to tell me that the success of the economic program and my re-election hinges on the Federal Reserve and a bunch of fucking bond traders?”

Can This Keep Going?

There are a few models you can use to explain the proliferation of negative rates:

  1. Maybe everyone has just gone crazy. They’re discounting the possibility of inflation, and just copying everyone else. That may be true, but “everyone is crazy” always has equivalent explanatory value. Also, crazy people tend to rationalize their beliefs. They don’t think they’re crazy — one extended description of a psychotic break includes the author’s observation that he actually felt completely rational the entire time, and could articulate his logic at length to anyone who asked. John Nash similarly noted that his delusions were compelling because they felt as logical as his proofs.
  2. The “excess savings” argument holds that there are more investors looking for savings than there are risk assets to absorb their savings, so negative yields are a matter of supply and demand. If you factor in the cost-of-storage argument above, nominal yields are probably still positive, albeit barely.
  3. The technology-and-demographics theory, a more specific version of the above. It’s not a coincidence that Japan is one of the oldest countries in the world, and its yields went negative first. Europe is aging, and its yields are also negative. The US is young for a developing country, and has higher yields, and the developing world is very young indeed and has countries sporting mid-single digit real yields. If there were profitable new investments to buy, savers would buy them, but opportunities are limited.

What’s scary about the demographics-and-technology story is that it’s self-perpetuating. While there are late-bloomers in every field, scientific discoveries tend to peak at a young age — early 20s in math and physics, a little later in other topics, much later in fields like history where the half-life of knowledge is long and insights thus accrue slowly.

Investing, with its combination of rapid response time and pattern-matching, is paradoxically a field in which we’d expect people to have unusually long periods of peak productivity: someone who was incredibly quick-witted as a trader at 25 has read a lot more balance sheets and seen a lot more charts by the time they’re 75, so as long as they accept a style drift away from rapid-fire trading — necessary if they’re good, because they accumulate more assets — they can continue to produce good returns for decades.

A further reason this problem can compound: interest rates also represent the cost of dawdling. If you’re paying 12% for your capital, a month’s delay on a project costs you 1%. If you’re paying 1% for your capital, you’d barely notice. It’s striking that one of the big innovations in container shipping recently is going slower to save on fuel. And if you look at the industries that grew by issuing high-yield debt in the 70s and 80s, they didn’t mess around, either.

This may be one of the hidden advantages of startups. Since they’re so risky, investors demand a high risk premium, and that risk premium translates into a higher cost of time. One of the cheapest ways to get the most out of a day is to spend the entire day hard at work. Your burn rate doesn’t drop just because you’re sleeping. So sleep less.

It might also apply to highly seasonal businesses. Natural gas, e-commerce, scooter rental — nothing concentrates the mind like knowing that if you miss your launch deadline by a week you’ll have to push it back a year.

These micro-incentives may not matter much in the aggregate, but they certainly make a difference on the margin. Is it a coincidence that the Big Dig was proposed during a time of high rates but implemented — very slowly — when rates were much lower? How much of America’s infrastructure delays — or Germany’s airport disaster — can we attribute to the declining cost of letting the schedule slip?

Persistently low rates can push countries into a lower-growth trap, where ports, airports, power plants, LNG facilities, and other giant projects don’t get built, and the incremental businesses they’d enable don’t get founded.

Balance Sheet Recessions and Negative Rate Contagion

The economist Richard Koo has been a longtime advocate of another theory of zero interest rates: the balance-sheet recession. During the Japanese bubble, he argues that many companies borrowed to buy land at insane valuations, and ended up with negative net worths but positive cash flows. Even at low rates, they preferred to pay down debt rather than expand. This theory holds that the reason quantitative easing doesn’t lead to runaway inflation is that there’s no demand for loans, so the incremental supply of cash just sits in the banking system.

It’s an interesting scenario, and Koo concedes that it’s quite rare — he points to Germany in the early 2000s and the US in the1930s as earlier case studies. For this dynamic to work, you need tight cooperation between banks and borrowers: banks don’t want to admit that their loans were bad, borrowers don’t want to admit that they’re nearly insolvent, but everyone is relieved when the loans get paid down.

For this opacity to persist, you need high trust among elites. I’m not familiar with German business culture, but the US in the 1920s certainly had that — both big companies and banks were heavily dominated by WASP elites. “Really? You won’t roll over a loan for a fellow Yale Man? It’s as if our shared experience in the Skull & Bones coffin means nothing to you.” In Japan, there seems to have been a similar dynamic, with extremely long-term relationships between banks, borrowers, and regulators.

Koo argues that Japan’s fiscal stimulus after the bubble was the only way to prevent a colossal, 1930s-style recession. But there’s another framing: a balance sheet recession is just the world’s saddest corporate debt bubble. Borrowers are paying back loans at face value instead of restructuring — i.e. they’re overpaying for corporate credit (their own, but still). Banks are rolling over loans they should call in; they, too, are overpaying. It’s all the pathological malinvestment of a bubble, with none of the champagne.

Perhaps Japan would have a higher GDP per capita today if they’d had a fierce, record-setting depression that eliminated the least efficient 20% of their companies, recapitalized the now-insolvent banks, and freed up the rest of the economy to keep expanding.

Balance sheet recessions tend to happen in countries that generate a trade surplus, and investor risk aversion is stickier than actual risk levels. This creates a contagious dynamic: when rates are low in one country, risk-averse investors seek out low-risk assets in other countries.

This makes balance sheet recessions gradually contagious: Japanese investors dissatisfied with the yields on Yen-denominated debt might try earning dollars or Euros instead. As their corporate sector deleverages, net savings rise, and tend to go elsewhere. Thus we end up with weird cases like Taiwanese insurance companies owning 4% of all US investment-grade corporate bonds and 14% of long-term corporate bonds. (Taiwan may end up like Japan, with occasional accidental reverse-currency crises where locals sell foreign assets and cause a short squeeze in their own currency.)

Labor Globalization vs Convergence: Where the Money Won’t Go

It’s hard to apply the balance sheet recession framing to the present situation. The timing doesn’t work. We did have a giant bonfire of writedowns in 2007–9, but long-term rates went down well after that. And as companies have globalized their workforces and funding sources, the cozy homogeneity is disappearing. In theory, globalization could just push rates down everywhere, but in practice it seems that the low-rate contagion just shows up between rich countries.

Globalization actually exerts an interesting negative force on one escape from low rates: faster growth outside developed countries. Right now, by far the smartest thing for a talented person in a poor country to do is move, as quickly as possible, to a rich country. American and European multinationals are happy to hire talent wherever they can find it, and American universities attract a lot of it.

This puts poor countries in a bind: they need the talent locally, both to build companies and to regulate them. But they can’t compete with Goldman and McKinsey’s pay scales. So the only regulators they can hire are either crooks or patriots — and any crook with a modicum of talent can easily fake patriotism. Corruption can accelerate growth in the short term by providing a workaround for bad regulations, but in the long term it introduces variability — embezzlement, for example, is a form of money-creation (both the thief and the victim spend as if they have the money), leading to opaque crises. A little corruption gets around bad rules, but pervasive regulation encourages the creation of rules that exist specifically to expedite bribes.

China is an odd exception to this, both because it’s a good place to get rich and because of the structure of bureaucratic compensation. Formally, bureaucrats are not paid very well, but in practice when they send their kids to Harvard they tend to send along a very expensive car, too. The de facto comp plan for a local bureaucrat in China is to take a cut of a) local governments’ land sales to private companies, and b) loans from state-run or state-influenced banks.

In a way, China has backed into hiring a competent, well-compensated bureaucracy, funded by a Georgist taxation scheme coupled with a Tobin Tax on bank loans. This was not by design, but was probably a result of the beneficiaries getting too well-entrenched for the central government to evict them. It’s certainly not a sustainable model: they’ll run out of land to sell, and their banking system is already stretched past its limits. But it does help to explain why China has been converging while much of the rest of the developing world still isn’t.

That lack of convergence creates an increasingly bimodal world: countries with growth opportunities can’t credibly take advantage of them, while countries with capital can’t find a good place to put it.

Sustained low rates lead to a two-sided trap: in rich countries, the low cost of delays means we’re slow to complete the sorts of big infrastructure and research projects that could lead to a step-function acceleration in growth. The ongoing short squeeze in duration, coupled with equities’ negative duration, draws money away from risk assets even at good prices. The brutal math of negative equity duration under low inflation further compounds the problem, by forcing pension funds and life insurers to reduce their equity exposure lest rates get even lower. Meanwhile, we end up draining a lot of the talent from poorer countries where people could produce higher growth in wealth, albeit off a lower base.

There’s no particular reason to expect either of these trends to reverse any time soon. To the extent that deeply negative long-term rates are a bubble, it might pop, leading to higher rates that are still low by historical standards, but the fundamental problem remains.

Don’t freak out because negative rates “don’t make sense.” Freak out because they do.


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[1] As Ronnie himself put it: “Everyone wants to be a bodybuilder, but nobody wants to lift no heavy-ass weights.”

[2] Interestingly enough, the spread between the 10-year and the Federal Funds rate is strongly inversely correlated with trailing loan growth, and even with forward business loan growth, probably because the Fed reacts to the business cycle faster than banks admit they’ve made bad loans.

[3] I hate with a passion the use of the term “front-running” to describe trading with the expectation that someone else will make the same trade. Front-running is a useful term of art: it means misappropriating the knowledge that someone else will trade. If you’re a broker, and your client says “I think Berkshire is overpriced, and I’m selling all my shares today,” and your client’s name is Warren Buffett, it is absolutely wrong to short some BRK before you execute the trade. But if you sell something because you expect someone else to want to buy it back from you later at a more favorable price, you’re… just doing what every active investor does. That’s literally the point of the whole endeavor. It’s not front-running. Stop saying that.

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