Why the discrepancy?

Vitalik Buterin had a thought-provoking tweet a few days back about interest rates.

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

Today's post explores what goes into determining interest rates, not blockchain stuff. So for those who don't follow the blockchain world, let me get you up to speed by decoding some of the technical-ese in Buterin's tweet.

DAI is a version of the U.S. dollar. There are many versions of the dollar. The Fed issues both a paper and an electronic version, Wells Fargo issues its own account-based version, and PayPal does too. But whereas Wells Fargo and PayPal dollars are digital entries in company databases, and Fed paper dollars are circulating bearer notes, DAI is encoded on the Ethereum blockchain.

Buterin points out that DAI owners can lend out their U.S. dollar lookalikes on Compound, a lending protocol based on Ethereum, for 11.5%. That's a fabulous interest rate, especially when traditional dollar owner can only lend their dollars out to the government—the U.S. Treasury—at a rate of 1.5%.

Why this difference, asks Buterin?

Interest rates are a lot of fun to puzzle through. I had to think this one over for a bit—so let's slowly work through some of the factors at play.

Let's begin by flipping Buterin's question around. When the U.S. Treasury borrows from the public, the bonds it issues are promises to pay back regular dollars (i.e. Federal Reserve dollars). But what if the U.S. Treasury decided to borrow DAI by issuing bonds promising to repay in DAI? What would the interest rate on these Treasury DAI bonds be? Would it be 11.5% or 1.5%? Perhaps somewhere in between?

Credit risk

First, there's the question of credit risk. The U.S. Treasury is a very reliable debtor. It won't welch. If it issues both types of bonds, it'll be just as likely to repay its DAI bond as it will its regular dollar bond. Since the market already requires 1.5% from the Treasury to compensate it for credit risk (and a few other risks), the Treasury's DAI bonds should probably yield 1.5% too. (I'll modify this later as I add some more layers).

Now let's look at Compound. A DAI loan made on Compound (for simplicity let's just call it a Compound DAI bond) is surely much riskier than our hypothetical Treasury DAI bond. Compound is a blockchain experiment. It could malfunction due to buggy code. Maybe every single Compound borrower goes bust. To compensate for this risk, a prospective bond buyer will require a higher return from Compound DAI bonds than they will U.S. Treasury DAI bonds.

So Compound credit risk (Buterin's third option) probably explains a big chunk of the huge gap between the 11.5% interest rate on Compound DAI bonds and our hypothetical 1.5% interest rate on the U.S. Treasury's DAI bonds. But not all of it.

Collapse risk

Buterin mentions a second risk: the chance that DAI, the entity that creates blockchain dollars, collapses. Like Compound, DAI is a new monetary experiment. The code could be buggy. It might get hacked. By comparison, conventional dollar issuers—say Wells Fargo or PayPal—are far less likely to malfunction.

How does DAI collapse risk get built into the price of a hypothetical Treasury DAI bonds

The average market participant (I'm not talking about crypto fans here, but large & smart institutional actors) should be genuinely worried about purchasing a Treasury DAI bond—not so much because the Treasury is unlikely to pay it back—but because the DAI tokens that the Treasury ends up repaying could, in the even of DAI breaking, be worth 99% less than their original value. Average bond buyers will expect some compensation for bearing this risk. How much? Say 5.5% (I'm just guessing here).

Earlier I said that a Treasury DAI bond would yield 1.5%. But if we add 5.5% worth of failure risk to 1.5% in basic risk, a Treasury DAI bond should yield 7.0% before the average investor is going to hold it.

Now let's go back and look at a Compound DAI bond. As Buterin pointed out, they yield 11.5%, which is much higher than the 7.0% yield on our hypothetical Treasury DAI bond. We've already assumed that DAI collapse risk works out to 5.5%. If we subtract collapse risk from a Compound DAI bond's 11.5% yield, the remaining 6% is accounted for by risks such as Compound failing (11.5% - 5.5%). Put differently, investors in Compound DAI bonds will require 5.5% and 6.0% to compensate for collapse risk and credit risk respectively, for a total of 11.5%. Again, these are hypothetical numbers. But they help us puzzle things out.

Two different blockchain dollars: USDC vs DAI

Interestingly, Compound doesn't just facilitate DAI loans. It also expedites loans in another blockchain dollar, USDC. We'll refer to these as Compound USDC bonds. As Buterin points out later on in the thread, the rate on Compound USDC bonds is 6.5%, quite a bit lower than Compound DAI bonds.

What might explain this discrepancy?

Not credit risk, since in both instances the same creditor—Compound—is responsible for creating the bonds. Which leaves varying levels of collapse risk as an explanation. USDC is a regulated stablecoin (i.e. it has the government's approval). DAI isn't. And USDC has genuine U.S. dollars backing it, whereas DAI is backed by highly volatile cryptocurrencies. So the odds of USDC collapsing are surely lower than DAI.

How much interest do USDC bond holders require to compensate them for collapse risk? Assuming that Compound's risk of failing is worth 5.5% of interest (as we already claimed), that leaves just 1% attributable to the risk of USDC failing (6.5%-5.5%). Put differently, investors in Compound USDC bonds will require 5.5% and 1.0% to compensate for credit risk and collapse risk respectively, for a total of 6.5%.

Oddly, the yield on a Compound USCD bond is less than the hypothetical yield on our safe Treasury DAI bond (6.5% vs 7.0%). Why is that? Even though Compound is riskier to lend to than the Treasury, a DAI-linked return is riskier than a USDC return. Another way to think about this is that if the Treasury were to also issue USDC bonds, those bond would only yield 2.5%. To account for credit (and other) risks investors would require a base 1.5% with an extra 1.0% on top for the risk of USDC breaking.

The convenience yield

Let's bring in one last layer. Something called the convenience yield is lurking behind this.

When you lend me some tokens, you need to be compensated for more than just credit risk i.e. the risk that I won't pay back the tokens. You are also doing without the convenience of these tokens for a period of time. The replacement, my IOU, won't be very handy. For instance, the convenience of a dollar bill can be though of as the ability to mobilize it whenever you need to meet some pressing need. But if you've lent a $100 bill to me then you've given up all that bill's usefulness. Instead, you're stuck with my awkward $100 IOU. You need some compensation for this. (Unconvinced? Head over to Steve Randy Waldman's classic ode to the convenience yield).

So when we break down the components of the interest rate on DAI bonds, there must be some compensation required for forgoing the convenience of DAI, its convenience yield. Earlier I attributed the big gap between rates on Compound DAI and USDC bonds to varying odds of each scheme failing. However, the gap could also be explained by varying convenience yields. If the convenience yield of a DAI token is higher than that of a USDC token, we'd expect an issuer of a DAI bond to pay a higher rate than on a USDC bond, in order to compensate DAI holders for giving up on those superior conveniences. 

If DAI's convenience yield is higher than USDC's, what might explain this gap? DAI is completely decentralized and can't be monitored. USDC isn't. It is less censorship-resistant than DAI. So perhaps USDC just isn't as handy to have around.

So some of the 11.5% rate on Compound DAI bonds—say 2%—may be due to the convenience yield forgone on lent DAI. If DAI had the same features as USDC, and thus had a lower convenience yield, a Compound DAI bond might only yield 9.5% (11.5% - 2.0%). If so, the discrepancy between the Compound DAI and USDC bonds—9.5% vs 6.5%—wouldn't be as extreme.

Summing up, let's revisit Buterin's tweet:

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

If my line of thinking is right, the discrepancy is accounted for a messy mix of the higher risk of lending to Compound (3), the danger of DAI cracking (2), and whatever convenience yield one forgoes when one no longer has DAI on hand (4-other). And of course, Buterin's first option is right too. I'm assuming that people are rational and can easily buy and sell various assets. But the sorts of large institutional players who set market prices may not be operating in crypto markets.

Paying interest on cash

Freigeld, or stamp scrip, is designed to pay negative interest, but it can be re-purposed to pay positive interest.

Remember when global interest rates were plunging to zero and all everyone wanted to talk about was how to set a negative interest rate on cash? Now that interest rates around the world are rising again, here's that same idea in reverse: what about finally paying positive interest rates on cash? I'm going to explore three ways of doing this. As for why we'd want to pay interest on cash, I'll leave that question till the end.

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The first way to pay interest on cash is to use stamping. Each Friday, the owner of a bill—say a $50 note—can bring it in to a bank to be officially stamped. The stamp represents an interest payment due to the owner. When the owner is ready to collect his interest, he deposits the note at the bank. For example, say that 52 weeks have passed and 52 stamps are present on the $50 note. If the interest rate on cash is 5%, then the banknote owner is due to receive $2.50 in interest.

Alternatively the note owner can collect the interest by spending the $50 note, say at a local grocery store. The checkout clerk will count the number of stamps, or interest due, and tack that on to the face value of the note. With 52 stamps, the owner of a $50 note should be able to buy $52.50 worth of groceries, not $50. After all, the store has the right to bring the $50 note to its bank and collect the $2.50 in interest for itself.

Stamped currency seems like a pretty big hassle to me. The clerk behind the counter must count out the stamps on the note by hand, and the owner of the note has to trek back and forth to the bank each week to get the stamp affixed. Instead, imagine that each banknote has a magnetic strip that records how long the bill had been in circulation. This would remove some of these hassles. Weekly trips to the bank for stamping would no longer be necessary, and a note reader installed at a bank or retailer would automatically record how much interest was due, precluding painstaking counting of stamps.

"They use this magnetic strip to track you." says Byers to Agent Scully, The X-Files

Apart from stoking conspiracy theories, there's still a major problem with a magnetic strip scheme. Because each note has entered circulation at a different time, each is entitled to a varying amounts of interest. And this means that banknotes are no longer fungible. Fungibility—the ability to cleanly interchange all members of a population—is one of the features of money that makes it so easy to use. Remove it and money becomes complicated, each piece requiring a unique and costly effort to ascertain its value.

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Our second way of paying interest on money doesn't destroy the fungibility of banknotes. The central bank needs to sever the traditional 1:1 peg between deposit money and cash, and then have cash slowly appreciate in value relative to deposits.

For instance, a central bank might start by setting an exchange rate of $1 note = $1 deposit on January 1, but on January 2 it adjusts this rate so $1 note is equal to $1.0001 deposits, and on January 3 adjust this rate to $1:$1.0002, etc. So the cash in your wallet is benefiting from capital gains. By December 31, the exchange rate will be around $1 note to $1.0365. Anyone who has held a banknote for the full year can deposit it and will have earned 3.65 cents in interest, or 3.65%. 

The major drawback with this scheme is the calculational burden imposed on the population by breaking the convenient 1:1 peg between cash and deposits. Assuming that retailers price their wares in terms of deposits, anyone who wants to pay in cash will have to make a currency conversion using that day's exchange rate. For instance, if the central bank's peg is currently being set at $1 note = $1.50 in deposits, then a popsicle that is priced at $1 will require—hmmm... let me check my calculator—$0.667 in cash. Phones will make this exchange rate calculation easy, but it is still likely to be a bit of a nuisance.

There are other hassles too. Would a capital gains tax have to be paid on the appreciation of one's cash? How would existing long-term contracts deal with the divergence? For instance, if my employer is paying me $50,000 per year, obviously I'd prefer this sum be denominated in steadily appreciating cash rather than constant deposits, and she will prefer the latter. What becomes the standard unit of account?

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The last way to pay interest (at least as far as I know) is to run lotteries based on banknote serial numbers, an idea independently proposed by Hu McCulloch and Charles Goodhart back in 1986.

It's surprisingly easy to get banknotes to pay interest. Run a lottery based on note serial numbers. Hu McCulloch dreamt this scheme up in 1986, but no central bank has ever tried it. Source: https://t.co/pUUf1liuhH pic.twitter.com/5mil9B62FN

— JP Koning (@jp_koning) January 14, 2018

Central banks would periodically hold draws entitling the winning serial numbers to large cash prizes. For example, if there was $100 billion in banknotes in circulation, the central bank could set the interest rate on cash at 5% by offering prizes over the course of the year amounting to 5% of $100 billion, or $5 billion.

This technique of paying interest on cash solves the fungibility problem that plagues the earlier stamping technique. Every note has the same chance of winning the lottery, and non-fungible winners are immediately withdrawn. And unlike the crawling peg idea, banknotes and deposits remain equal to each other so burdensome exchange rate calculations don't need to me made.

However, it introduces the threat of bank runs. The day before the big lottery is set to occur, everyone will withdraw deposits for cash so that they can compete in the draw. To prevent a bank run, it may be necessary to randomize the date of the big lottery so that no one knows when to withdraw notes, an idea proposed by Tyler Cowen. Another way to preclude bank runs is to have a regular stream of small weekly lotteries rather than one or two big ones each year.

Another drawback to note lotteries is the cost that is imposed on society by having everyone constantly checking serial numbers. As Brian Romanchuk points out, employees who are working behind their employer's tills may be tempted to switch out winning notes with losers. Employers may protect themselves by setting up scanning hardware to read in serial numbers as banknotes enter the tills, maintaining their own internal database of cash inventories so that winners can quickly be isolated and returned. But all of that is costly. Would it be worth it?

Interestingly, there is some precedent for these sorts of lotteries. In Taiwan, receipts are eligible for a receipt lottery, a neat way to incentivize people to avoid under-the-table transactions (ht Gwern). Lotteries can also be useful in attracting depositors, as outlined in this Freakonomics podcast (ht Ryan). George Selgin and William Lastrapes have gone into the idea of lottery-linked money in some detail:

Though the suggestion may appear far fetched, in many countries lotteries are presently being used with considerable success to market bank deposits. According to Mauro Guillen and Adrian Tschoegl (2002), “lottery-linked” deposit accounts have been especially popular with poorer persons, including many who might otherwise remain “outside the banking system.” ... In two popular Argentine schemes, for instance, depositors receive one ticket or chance of winning for every $200 or $250 on deposit (ibid., p. 221). Lottery-linked banknotes, in contrast, would themselves serve as tickets, allowing persons to play for as little as the value of the lowest note denomination, and with no apparent cost to themselves save that of occasionally inspecting their note holdings.

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Some readers may recognize these three techniques for paying interest on cash as the inverse of the three go-to ways of applying negative interest rates to cash being discussed a few years ago. For instance, one of the most well-known ways of imposing negative interest rates on owners of cash is to apply a Silvio Gesell style stamp scheme (see picture at top), whereby a currency owner must buy a stamp and affix it to the note in order to renew the validity of their currency each month. (I once discussed Alberta's experiment with Gesell's "shrinking money" here). Without the appropriate number of stamps, the note is illegitimate. In my first example above, Gesell's stamp tax has been re-engineered into a stamp subsidy. As for the magnetic strip modification, this is Marvin Goodfriend's 1999 update of Gesell, flipped around to award interest rather than docking it.

Miles Kimball has written extensively on escaping the zero lower bound to interest rates by setting a crawling peg on currency. But just as Kimball's crawling peg can impose a negative interest rate on banknotes, it can be used to pay interest, as I described above. Indeed, Miles (along with Ruchir Agarwal) frequently mention this possibility in his blog posts and papers (see this pdf).

Finally, remember Greg Mankiw's controversial 2009 article on imposing negative interest rates by serial number? He wrote:

Imagine that the Fed were to announce that, a year from today, it would pick a digit from zero to 9 out of a hat. All currency with a serial number ending in that digit would no longer be legal tender. Suddenly, the expected return to holding currency would become negative 10 percent.

Mankiw's idea is just the reverse of Goodhart and McCulloch's earlier lottery idea, the lottery replaced by with a demonetization.

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So why pay interest on currency? I can think of two reasons. One is based on fairness, the other on efficiency.

The decision to avoid paying the market rate of interest on currency amounts to a tax on currency users. Who pays this tax? Cash is often the only means for the poor, new immigrants, and unbanked to participate in the economy. So the tax falls on those who can least afford it. This hardly seems fair. By conducting note lotteries or stamping notes, those consigned to the cash economy can get at least the same return on banknotes as the well-off banked receive on deposits.

Now hold up JP, some you will be saying at this point. What about criminals? Yep, the other group of people who suffer from the lack of interest on banknotes are criminals and tax evaders. Rewarding them with interest hardly seems appropriate. One would hope that if central banks did adopt a mechanism for rewarding currency with interest, it would be capable of screening out bad actors. For instance, criminals may be leery of collecting their interest or lottery prize if making a claim at a bank means potentially being unmasked. Another way to set up the screen would be to pay interest or prizes on small denominations like $1-$10 notes, and not on $20s and above. Since criminal organizations prefer high denomination notes due to their compactness, they wouldn't benefit from interest.

As for the efficiency argument, this is nothing but the famous Friedman rule that I described in my previous post. All taxes impose a deadweight loss on society. When a good or service is taxed, people produce and consume less of it than the would otherwise choose, tax revenues not quite compensating for this loss. From a policy maker's perspective, the goal is to reduce deadweight loss as much as possible by selecting the best taxes.

In the case of cash, the deadweight loss comes from people holding less of it than they would otherwise prefer, incurring so-called shoe leather costs as they walk to the bank and back to avoid holding too much of the stuff. If a 0% return on cash is an inefficient form of taxation relative to other alternatives types of taxes, then it would be better for the government to just pay interest on the stuff and recoup the lost revenues elsewhere, say through consumption taxes or income taxes.

Is the Fed breaking the law by paying too much interest?

George Selgin had an interesting post describing how the Fed appears to be breaking the law by paying too much interest to reserve-holders. This is an idea that's cropped up on the blogosphere before, here is David Glasner, for instance.

I agree with George that the the letter of the law is being broken. That's unfortunate. As Section 19(b)(12)(A) of the Federal Reserve Act stipulates, the Fed can only pay interest "at a rate or rates not to exceed the general level of short-term interest rates." With three month treasury bills currently around 0.33% and the fed funds rate at 0.4%, the current interest rate on reserves (IOR) of 0.5% exceeds the legal maximum.

Unlike George, I don't think the Fed deserves criticism over this. If the letter of the law is being broken, the spirit of the law surely isn't.

If there is a spirit residing in the law governing IOR, it's the ghost of Milton Friedman. Since the Fed's inception in 1913, IOR had been effectively set at 0%, far below the general level of short term interest rates. This has acted as a tax on bankers. They have been forced to hold an asset—reserves—that provides a below-market return. Friedman's big idea was to remove this distortionary tax by bringing IOR up to the same level as other short term interest rates. Banks would now be earning the same rate as everyone else. The Fed would only get the authority to set a positive rate on reserves in 2008, long after most modern central banks like the Bank of Canada had implemented Friedman's idea.

Friedman wanted to remove the tax, but he didn't want to introduce a subsidy in its place. To prevent central bank subsidization of banks, the Federal Reserve Act is explicit that IOR should not exceed other short-term interest rates.

In practice, how might the Fed set IOR in a way that subsidizes banks? This is more complicated than it seems. If the Fed sets IOR at 1%, arbitrage dictates that all other short term rates will converge to that same level. After all, why would a financial institution buy a safe short term fixed income product for anything less than 1% if the central bank is fixing the yield of a competing product, reserves, at 1%?

Short-term yields won't converge exactly to IOR. Some will trade a hair above IOR, others a bit below. This is because each short-term fixed income product has its own set of peculiarities and these get built into their yield. For instance, buying federal funds is riskier than parking money at the Fed; in the latter transaction the Fed is your counterparty while in the former it's a bank, So the fed funds rate should trade a bit above IOR. But we wouldn't say that a higher fed funds rate is a sign of a below-market return on reserves, or that this spread represents an implicit tax on reserve owners. The fed funds rate exceeds IOR only because that is how the market has chosen to appraise the risk of owning fed funds.

Conversely, because a treasury bill is ofttimes less risky then parking money at the Fed, its yield should regularly dip below IOR. When it does, no one would say that the Fed is providing an unfair subsidy to reserve holders by paying IOR in excess of the treasury bill rate. The lower treasury bill rate is simply the free market's way of accounting for the superior risk profile of treasury bills relative to reserves.

Nowadays, with IOR at 0.5% and treasury bills yielding 0.33%, the Fed is clearly contradicting the wording of the Federal Reserve Act. IOR has been set at a rate that "exceeds the general level of short-term interest rates." But this by no means implies that the Fed is breaking the spirit of the law. The spirit of the law only tells the Fed not to pay subsidies to banks. As I explained above, the yield differential may simply reflect the market's assessment of the unique risks of various short-term fixed income products, not  a policy of paying subsidies.

To get the ghost of Milton Friedman rolling in his grave, here is how to structure IOR so that it offers a subsidy to banks. The Fed would have to set up a tiered reserve system where a bank's first tier of reserves earns a higher rate than the next tier. To begin with, assume that Fed officials deem that a 0.5% fed funds rate is consistent with a 2% inflation target. The Fed offers to pays interest of 100% on required reserves (I'm exaggerating to make my point) while offering just 0.5% on excess reserves. Banks will hold required reserves up to the maximum and reap an incredibly 100% yearly return. All reserves above that ceiling will either be parked at the Fed to earn 0.5% or lent out in the fed funds market.

Thanks to arbitrage, the 0.5% rate on excess reserves ripples through to other short term rates. Because a bank can always leave excess reserves at the Fed and earn an easy 0.5%, a borrower will have to bid up the fed funds rate and t-bill rates to at least 0.5% in order to coax the marginal lender away from the Fed.

And that's how the Fed would subsidize banks. The "general level" of rates as implied by the rate on fed funds and treasury bills hovers at 0.5% while banks are earning a stunning 100% on a portion of their reserve holdings. It's highway robbery! Milton Friedman would be furious; the distortionary tax he so disliked has been replaced with a distortionary subsidy.

By the way, if you really want to know what tiering and central bank subsidies to banks look like, this is the exact same mechanism the Bank of Japan and Swiss National Bank have introduced to help banks deal with negative interest rates. See here and here.  

So the bit of legalese that says that IOR should not exceed the "general level of short-term interest rates" is really just a poorly chosen set of words meant to describe a very specific idea, namely, a prohibition against setting a tiered reserve policy where the first tier, required reserves, earns more than the second, excess reserves, the ensuing subsidy flowing through to banks.

At the end of the day, what accounts for the current divergence between IOR and the other short term rates? Because the Fed has not set up a tiered reserve policy, there is simply no way that the divergence reflects a subsidization of banks. There is only one remaining explanation. Peculiar developments in the microstructure of the fed funds and t-bills markets have led traders to discount these rates relative to IOR.

So you can rest easy, Milton.

The peculiarities bedeviling the fed funds market are explained by Stephen Williamson here. There are several large entities, the GSEs, that can keep reserves at the Fed but are legally prevented from earning IOR. Anxious to get a better return, they invest in the fed funds market market, but only a limited number of banks have the balance sheet capacity to accept these funds. This oligopoly is able to extract a pound of flesh from the GSEs by lowballing the return they offer, the result being that the fed funds rate lies below IOR.

As for treasury bills, they are unique because, unlike reserves held at the Fed, they are accepted as collateral by a whole assortment of financial intermediaries. Put differently, treasury bills are a better money than reserves. Because the government is loath to issue too many of them, the supply of treasury bills has been kept artificially scarce so that they trade at a premium, a liquidity premium.

George ends his post by appealing to his readers to sue the Fed. I don't think think a lawsuit will bring much justice. If there are to be any legal battles to be fought, better to petition Congress to adjust the wording of the Federal Reserve Act so that it better fits the spirit of the law. We don't want the law to misidentify a situation involving IOR in excess of the "general level of interest rates" as necessarily implying subsidization when microstructure is actually at fault. While Milton Friedman had a lot of reasons to criticize the Fed, this probably wouldn't be one of them.

John Cochrane is too grumpy about negative rates

John Cochrane has written two posts that question the ability to implement negative interest rates given the wide range of 0%-yielding escape hatches available to investors. These escapes include gift cards, stamps, tax & utility prepayments, and more. In a recent post entitled However low interest rates might go, the IRS will never act like a bank, Miles Kimball and his brother rebut one of Cochrane's supposed exits; the Internal Revenues Service. I've responded to Cochrane's other schemes here.

Think of Cochrane's exits as arbitrage opportunities. As nominal rates plunge into negative territory, the public gets to harvest these outsized gains at the expense of institutions that issue 0% nominal liabilities. The Kimballs' point (and mine here) is that because these institutions will lose money if they continue to issue these liabilities, they will implement policies to plug the holes. Cochrane's multiple exits aren't the smoking gun he takes them to be.

In a new post, Cochrane tries to salvage his argument by making an appeal to symmetry. He points out that in the symmetrical case—a world with positive inflation and higher nominal rates—we don't actually observe people adopting the sort of behavior that Miles believes they would adopt in a negative rate world. So in practice, Cochrane doesn't believe that removing cash in order to implement negative interest rates will work.

This is a fair tactic to take. In general, people should demonstrate similar behavior whether nominal rates are positive or negative. However, is it true that in an environment with positive inflation and high nominal rates, institutions issuing liabilities (or those purchasing those liabilities) allow themselves to be systematically made the targets of arbitrage?

Take Cochrane's main example; gift cards. As I described here, once rates fall deep into negative territory, retailers will simply stop issuing gift cards since they won't care to earn a negative spread. Cochrane's appeal to symmetry implies that gift card issuers behave differently when rates are positive. Well let's imagine that rates are at 5%. An issuer of 0% gift cards is certainly not setting itself up to be arbitraged—in fact, given that it is funding itself at 0% in a 5% yield environment, it will be earning an excess return on each card issued. Nor will the liability-using public choose to subject itself to the money-losing obverse side of the trade. People can simply choose to avoid investing in 0% gift cards in favor of a 5% alternative. Likewise for the other liabilities that Cochrane mentions. Rather than prepaying taxes and earnings 0%, the public will pay at the last moment and harvest a 5% return until then. Instead of delaying the cashing of a check, they'll deposit it the day they receive it in order to earn interest.

So when interest rates are positive, people will try to avoid behaviour that allows them to be taken advantage of, whether they be an issuer or buyer or liability. Symmetrically, it follows that this same behaviour should prevail when rates are negative.

In his post, Cochrane seems to be changing the subject of the conversation from arbitrage to the indexing of contracts. His point is that during periods of positive inflation and high interest rates, nominal payments were not indexed to the nominal interest rate. His example is the IRS, which does not offer interest for early payment when market interest rates are high. Factually he is right. But this criticism is besides the point. The IRS doesn't offer interest to those who pay their taxes early because prepaid taxes aren't the government's main form of funding, treasury debt is. If the government's main form of financing *was* to offer savings accounts to tax payers, then you can be sure that those accounts would have to promise nominal payments that rise in line with the market's nominal interest rate—otherwise no one would open an account and the government would suffer a cash crunch. Nor would the government offer an excess nominal rate, since every American would exploit the situation and open an account—at the government's expense.

No one wants to be the dupe and end up on the wrong side of an arbitrage. If anyone is arguing for asymmetry, it is Cochrane. He needs to explain why liability issuers and users would exhibit such a degree of irrationality as to allow themselves to be exploited as rates fall into negative territory, but so rational as to avoid being exploited at positive rates.

The bond-stock conundrum

Here's a conundrum. Many commentators have been trying to puzzle out why stocks have been continually hitting new highs at the same time that bond yields have been hitting new lows. See here, here, here, and here. On the surface, equity markets and bond markets seem to be saying two different things about the future. Stronger equities indicate a bright future while rising bond prices (and falling yields) portend a bleak one. Since these two predictions can't both be right, either the bond market or the stock market is terribly wrong. It's the I'm with stupid theory of the bond and equity bull markets.

I hope to show in this post that investor stupidity isn't the only way to explain today's concurrent bull market pattern. Improvements in financial market liquidity and declining expectations surrounding the pace of consumer price inflation can both account for why stocks and equities are moving higher together. More on these two factors later.

1. I'm with stupid

The I'm with stupid view goes something like this...

If investors expect strong real growth for the next few decades, a new bond issue has to provide a competitive coupon in order to attract capital. Soon after the bond is issued, economic growth stagnates and the economy's expected real rate of return falls. The bond's coupon, originally rated for a much healthier economy, has become too good for the new slow-growth environment. The price of the bond has to rise relative to its face value (thus counterbalancing the juicy coupon with a guaranteed capital loss) so that its overall rate of return falls to a level commensurate with the economy's lower real rate of return. That's why rising bond prices are often a sign of a bleaker future.

As for equities, that same decline in the real rate of return will result in a fall in prices. A stock is a claim on whatever profits remain after interest, and lower real growth means a smaller remainder. No wonder then that a number of investment commentators believe that the modern rise of stock and bond prices requires one set of investors to be acting irrationally; after all, things can't be simultaneously better and worse off in the future. Either that or arbitrage between the two markets is simply impossible, say because large actors like the Fed are rigging the market. Whatever the case, concurrent bull markets implies a giant market inefficiency, as Diego Espinosa has described it.

Massive inefficiency isn't a very satisfying theory for the twin rises in bond and stock markets. Thankfully, we don't need to resort to changes in real growth rates to explain securities price changes. Let's explore two other factors that could be driving the concurrent bull market pattern:

2. Falling inflationary expectations and concurrent bull markets

Assume that the real growth rate is constant over time but inflation expectations decline. The real value of all flows of coupon payments from existing bonds are suddenly more valuable, causing a one-time jump in bond prices. If inflation expectations consistently fall over time, then a bull trend in bond prices will emerge. This is standard stuff.

And stocks? What many people don't realize is that those same declining inflation expectations will set off a bull market in equities as well. The general view is that a firm's bottom line waxes or wanes at the same pace as inflation, the result being that real stock returns are invariant to inflation. Corporate shares are supposed to be hedges against inflation.

This is (almost always) wrong, a point I've made before (here and here). Let me take another stab at it. In short, thanks to the interaction between historical cost accounting and the way taxes are collected, rising inflation expectations will boost a firm's real future tax burden, reducing real cash flows and therefore stock prices. Falling expectations about inflation act like a tax cut, increasing real cash flows and stock prices.

For folks who want to work through the logic, what follows is a numerical example. Take a very simple firm which incorporates itself, buys inventory and a machine with the cash raised, operates for four years, and dissolves itself. At the end of each year it pays out all the cash it has earned to its shareholders. At the outset, the company buys 40 unfinished widgets for $60 each. Over the course of its life, it expects to process 10 widgets a year and sell the finished product at a real price of $100. In order to process the unfinished widgets, it buys a widget upgrader for $500. The upgrader is used up, or depreciated, at a rate of $125 year so that it will be useless after year four. Since the company will have also depleted its inventory of unfinished widgets by that time, it has nothing left over after the fourth year.

The first table shows the anticipated cash flows that will be paid to shareholders after taxes have been rendered to the tax authority, assuming 0% inflation over the course of four years. The cash amounts to an even $876.25 a year.

Let's boost the expected inflation rate to 1% (see table below). The real value of cash flows starts out at $876.25 in year one but steadily declines, hitting $866.66 by year four. Shareholder get less real cash flows than they did in a stable inflation environment.

On the other hand, if we ratchet down expected inflation to -1%, the real value of cash flows starts out at $876.50 in the first year but climbs to $886.24 by the end of year four. Shareholders enjoy a larger real flow cash payments than they did in either the stable or the rising expected inflation environments. If cash dividends are immediately spent on consumption, this means that shareholders enjoy the greatest flow of consumption when inflation expectations are falling.

A reduction in expected inflation will cause a one-time jump in our company's share price. If these reductions in expected inflation occur consistently over time, we get a series of jumps in the company's share price, or a bull market.

The core intuition behind this result is that under historical cost accounting, a company's cost of goods sold and its depreciation expenses are both fixed in time. Cost of goods sold is valued on a first-in-first out basis, which means the price of the oldest good is used to value unit costs (in our case, $60), while depreciation is calculated as a fixed percentage of a machine's original purchase price. When inflation is stable, this is unimportant. But once expected inflation rises, the firm's costs grow stale and can no longer keep up with its anticipated revenues, the result being artificially higher pre-tax accounting profits and a larger tax bill. These bloated future tax bills drain cash from the firm, resulting in lower expected cash payouts to shareholders over the life of the firm.

When expected inflation falls, the firm's anticipated revenues shrink relative to its costs, the result being lower future pre-tax profits and a lighter tax bill. Less cash filters out of the firm, leaving more cash in the kitty for shareholders to enjoy at the end of each year.

The table below shows how our firm's real tax bill varies across each of these scenarios:

So a reduction in expected inflation is (almost always) good for equity prices as it amounts to a tax cut. Why have I inserted a caveat? When a company is indebted, lower-than-expected inflation will increase the real burden of that debt. If its debt load is heavy, the debt effect may outweigh the combined effects of cost of goods sold and depreciation. One reason why falling inflation expectations in Japan during the 1990s and 2000s didn't result in an equity boom is that Japanese companies tend to be far more indebted than companies in the rest of the world. (This may also explain why Japanese stocks outperformed U.S. stocks during the inflationary 1970s.) For most of the world's markets a reduction in expectations surrounding the rate of inflation is an ideal situation for equities.*

What do we know about the actual shape of inflation expectations? In general people have been marking their expectations downwards since the early 1980s, a trend that has been amplified since the credit crisis as central banks around the developed world have consistently undershot their inflation targets. We thus have the underpinnings for a concurrent bull market in stocks and bonds, driven by falling inflation expectations.

3. Liquidity and the concurrent bull market pattern

Let's move on to our second factor. Assuming that the real growth rate and expected inflation both stay constant, we can also generate concurrent bull markets in stocks and bonds by simultaneously improving their liquidity. Innovations in market infrastructure over the years have made it easier to buy and sell financial assets. Investors can increasingly use financial assets as media of exchange, swapping them directly for other financial assets rather than having to go through deposits as an intervening medium. Think buzz words like re-hypothecation and collateral chains.

As financial assets become more liquid, a larger portion of their overall return comes in the form of a non-pecuniary liquidity yield. All things staying the same, investors must cough up a larger premium in order to enjoy this liquidity-augmented return, resulting in a one time jump in asset prices. Consistent improvements to liquidity will result in a step-wise asset bull market.

I've written here about the ongoing liquidity enhancements in equity markets, and speculated here that thirty-year bull market is bonds is (partly) a function of improved bond liquidity. In the same vein, Frances Coppola once penned an article noting that when everything becomes highly liquid, the yield curve is flat, reducing returns across all classes of financial assets (a flattening of the yield curve implies a jump in the price of long term bonds).

While I think that liquidity-improving innovations in market technology and declining inflation expectations can explain a good chunk of the stock bull market, I don't think they can't quite explain as much of the secular rise in bond prices. After all, market interest rates haven't just plunged. In many cases both nominal and real bond interest rates have gone negative.

We can salvage this problem by resorting to another liquidity-based explanation for why bond investors are willing to accept negative returns. Government bonds provide a unique range of liquidity services in their role as a financial media of exchange, a role that cannot be replicated by central bank reserves or any other medium of exchange. Reserves, after all, can only be held by banks, and corporate bonds aren't safe enough to serve as universally-accepted collateral. However, governments have gone into austerity mode, reducing the flow rate of bonds coming onto the market. At the same time, central banks are buying up and removing government bonds from circulation. As a result, the supply of unique liquidity services provided by bonds is growing increasingly scarce, forcing investors to bid up the price of these services. Liquidity premia are high. So a negative real return on bonds may be a reflection of the the hidden fee that bond investors are willing to pay to own a government bond's flow of liquidity returns. I've written about this here.

In sum, the I'm with stupid theory, with its implication of massive inefficiencies, shouldn't be our only theory for concurrent bull markets. Asset prices move for many reasons, not just changes in expected real growth. Bond and equity investors may be reacting non-stupidly to shifting liquidity patterns and declining inflation expectations, the result being a steady bidding up of the prices of both assets.

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*If you are interested in the difference between Japan and the rest of the world, here are some papers worth investigating: 

The Taxation of Income from Capital in Japan, Kikutani and Tachibanaki (pdf)
The Cost of Capital in the U.S. and Japan: A Comparison, Ando and Auerbach (pdf)
Are Japanes Stock Prices to High. French and Poterba (pdf)

Hawk, Doves, and Canaries

Central bankers are usually classified as either hawks or doves. This post is devoted to a third and rare breed; today's monetary policy canaries. Having taken their respective deposit rates to -0.75%, deeper into negative territory than any other bank in history (save the Swedes), the Swiss National Bank and Denmark's Nationalbank are the canaries of the central banking world, plumbing depths that everyone assumes to be dangerous. Other central bankers, in particular the ECB's Mario Draghi, will no doubt be watching the Swiss and Danes quite closely. The information these two nations generate as they go deep into the bowels of negative rate territory will give a good indication of the level to which the others can safely reduce their own rates before hitting their respective effective lower bounds.

That there is an effective lower bound to rates stems from the fact that at some negative nominal interest rate, everyone will choose to convert deposits into cash, preferring to pay storage and handling costs on the underlying paper instrument than enduring a negative interest penalty on the electronic equivalent. Once this process starts, a central bank will be unwilling to push rates much lower given the possibility that the economy's entire deposit base gets converted into paper.

Last week Danish central banker Lars Rohde told the WSJ that while there is some lower bound for negative interest rates, "we haven't found it yet." What Rohde was basically saying is that the marginal storage costs of Danish cash are higher than -0.75%, Denmark's current monetary policy rate. If costs were lower, than Denmark's largest and most efficient cash hoarders, Danish banks, would have already rushed to convert their deposits held at the Nationalbank into banknotes—and Rohde would have found his as-yet inactive lower bound. Given his confident tone, Rohde must not be seeing much demand for banknotes. He would know. As his nation's central banker, he's privy to real time information on the quantity of cash that the central bank is being called upon to print up and provide to commercial banks.

We can get a rough feel for the data that Rohde is seeing. The chart below shows the year-over-year percent increase in end-of-month Danish cash and coin outstanding. The data is current to the end of February, eighteen days ago. Given that Denmark's deposit rate was initially reduced to -0.5% on January 29 and then to -0.75% on February 5, the data affords us an insight into the first thirty or so days of Danish cash demand at ultra low interest rates.

The chart shows that the yearly rate of growth in cash outstanding has accelerated slightly but is well within its normal range. What does this tell us about paper storage costs? Let's crunch some numbers. Danish banks currently have around 350 billion krone in funds on deposit at the Danish Nationalbanken in the form of certificates of deposit. This amounts to about US$50 billion. The central bank's -0.75% interest rate imposes yearly charges of around 2.5 billion krone, or US$375 million, on those deposits. In choosing to hold funds at the central bank, Danish banks are revealing that the cost of handling and storing paper cash must be somewhere above $375 million a year, else they'd have already started to convert into the cheaper alternative.

Keep in mind that this illustrates just thirty days with deep negative rates. With cash use in Denmark having been stagnant for a number of years (see chart here), vault space may have been re-purposed for other uses—maybe employees have been parking their commuter bikes in unused vaults or storing old bank documents in them. It could take time for vaults to be cleaned up. If so, a dash into cash could simply be delayed by a few weeks.

When Denmark hits its effective lower bound, what will the above chart look like? The 350 billion krone in deposits that banks currently keep at the central bank would quickly be converted into cash. Since Denmark currently has just 65 billion krone in notes and coin in circulation, we'd see a quintupling in cash outstanding. For comparison's sake, this would dwarf previous episodes of strong krone cash demand, like Y2K.

And what of our other canary, the SNB? The Swiss, so timely on matters of transport, don't think that up-to-date central banking data is important. The SNB's most recent data on cash outstanding is too stale to give a good idea how the Swiss have reacted so far to -0.75% rates. All we've got is anecdotes. This article reports that a Swiss pension fund attempted to withdraw a portion of its investments from its bank and hold it in a vault, thus saving 25,000 francs per 10 million francs after storage & handling costs, the implication being that these costs run around 0.5% a year. We'll have to wait for more data to come out of Switzerland before we can gauge whether it is at its effective lower bound.

What we do know is that Switzerland's bound will be much tighter than Denmark's. That's because while Denmark's largest denomination note is the 1000 krone note (worth about US$141), Switzerland's largest note is the 1000 franc note (worth about US$993.) That makes a US$1 million bundle of Danish notes seven times more bulky than that same bundle of Swiss notes, resulting in higher storage costs. This has important implications, since Mario Draghi's ECB, which issues a 500 euro note (worth US$530), likely has an effective lower bound that lies somewhere in between these two.

All of these data points may seem quite being arcane, but they have a very real policy significance. They're the difference between a central bank running out of interest rate ammunition, or buying itself an extra ten 10 basis point rate cuts.

Paul Krugman contemplates the lower bound

Paul Krugman has two posts discussing the effective lower bound to interest rates. The first I agree with, albeit with a caveat, and the other I don't.

In his first post Krugman takes Evan Soltas to task for including not only storage costs in his calculation of the effective lower bound, but also the extra convenience yield provided by deposits. Krugman's point is that once people are "saturated" with liquidity, as they seem to be now, then forgoing the liquidity of a short term marketable debt instrument (like a deposit) costs them nothing. If so, then the lower bound to nominal interest rates is solely a function of storage costs.

I agree with Krugman on this count. Take the 2 1/8% Nestle bond maturing May 29, which may be one of the first corporate bonds in history to trade at negative rates:

If it costs 0.50%/year to store and handle Swiss paper currency, then the rate on a Nestle bond can't fall below -0.50%. If it trades at -0.55%, an arbitrageur will contract to borrow the bond until it matures on May 29, sell it now, and convert the proceeds into 0% yielding SFr 1000 banknotes (these notes eventually being used to repay the bond lender). Our arbitrageur will incur 0.50%/year in storage costs while getting 0.55%/year from the bond lender, earning a risk-free return of 0.05%. Competition among arbitrageurs to harvest these gains will prevent Nestle's bond yield from falling much below storage costs.

However, here's the caveat. Krugman is assuming that liquidity is a homogeneous good. It could very well be that "different goods are differently liquid," as Steve Roth once eloquently said. The idea here is that the sort of conveniences provided by central bank reserves are different from the those provided by other liquid fixed income products like deposits, notes, and Nestle bonds. If so, then investors can be saturated with the sort of liquidity services provided by reserves (as they are now), but not saturated by the particular liquidity services provided by Nestle bonds and other fixed income products.

Assuming that  Nestle bonds are differently liquid than central bank francs, say because they play a special roll as collateral , then Soltas isn't out of line. Once investors have reached the saturation point in terms of central bank deposits, the effective lower bound to the Nestle bond isn't just a function of the cost of storing Swiss paper money, but also its unique conveniences.

This changes the arbitrage calculus. Our arbitrageur will now have to pay a fee to the lender of the Nestle bonds in order to compensate them for services forgone. Let's say the cost of borrowing the bond is 0.25%/year. Shorting the bond once it hits -0.55%, paying the borrowing cost of 0.25%, and storing the proceeds at a cost of 0.50% a year results in a loss of 0.20%. With the arbitrage being unprofitable, the Nestle bond can theoretically fall further than in our previous example before it hits the effective lower bound (specifically, its lower bound is now -0.75%).

How realistic is it that different goods are differently liquid? Since everybody seems to turn to Michael Woodford as the ultimate moderator of all questions monetary, here he is in his famous Jackson Hole paper [pdf] talking about the potential for different assets to have different types of convenience yields:

...one might suppose that Treasuries supply a convenience yield of a different sort than is provided by bank reserves, so that the fact that the liquidity premium for bank reserves has fallen to zero would not necessarily imply that there could not still be a positive safety premium for Treasuries.

Unfortunately, it's almost impossible to know for sure whether the liquidity services of a Nestle bond, or any other bond for that matter, are valued on the margin when people are already saturated in reserves. This is because there is no market for liquidity. If there was, then we could back out the specific price that investors are currently placing on a given bond's liquidity services, say by asking them to put a value on how much they need to be compensated if they are to forgo those services for a period of time. I've mentioned liquidity markets in many different posts. But I digress.

Krugman ends his first post saying that "I am pinching myself at the realization that this seemingly whimsical and arcane discussion is turning out to have real policy significance." But in his second post he backtracks, saying that a "minus x lower bound" isn't all that special in term of policy, implying that x (i.e. storage cost) is low and likely to diminish thanks to financial innovation. Here I disagree. Once a central bank has reduced rates to the point at which it is facing a run into paper storage, it can turn to a new tool to buy itself even more room to the downside for rate cuts: the manipulation of x, or the storage costs of cash.

To conclude, we've all found out by now that there isn't a zero lower bound. Instead it's a minus x lower bound. The next step is to realize that x isn't set in stone, it can itself be made into a tool of monetary policy.

Why so down?

If you've been reading Bill Gross's last few letters, you'll know that he's been a bit grumpy of late. It's that dang new trend that has hit bond markets, negative interest rates. Gross has been using words like incredible, surreal, and inconceivable to describe their arrival.Negative nominal bond rates certainly seem odd. Just look at the chart below, which illustrates what could very well be the two lowest-yielding bonds in the world, maybe all of history: the 3.75% Swiss government maturing in July 10, 2015 and the 4% Danish government bond maturing November 15, 2015. But is the idea of a negative rates really so strange?

Gross blames negative rates on central bankers who "continue to go too far in their misguided efforts to support future economic growth," in doing so "distorting" capitalism's rules. He's not alone; plenty of people claim that without autocratic price fixers like the SNB's Tommy Jordan and the Danmarks Nationalbank's Lars Rohde, rates would rapidly to rise to a more natural level like 1% or 2%.

Not necessarily. Even an economy without meddling central banks could be characterized by negative nominal rates from time to time, or, stealing from Tony Yates; "a negative rate doesn't distort capitalism, it IS capitalism."

Let's exorcise central bankers entirely from the economy. Imagine that we live in a world where things are priced in grams of gold. People walk around with pockets full of gold dust and a set of scales to measure the appropriate pinch necessary to pay for stuff. In this world, we all have a choice between two states: 1) we can hold gold dust in our pockets or 2) we can lend the dust to someone else for a period of time in return for an IOU. (Let's assume that the borrower is risk free.)

Each state has its own advantages and disadvantages. If we hold the gold dust in our pockets, we'll have instant access to a highly-liquid medium of exchange. Unlike illiquid media of exchange, liquid media provide us with the means to rapidly re-orient ourselves come unexpected events. With gold dust on hand we can purchase the necessities that allow us to cope with sudden problems or to take advantage of lucky breaks. At the end of the day, we may never actually use our gold to purchase things, preferring to keep it horded under our mattress. Even so, it hasn't sat their idly, but has provided us with a stream of consumption over time. The discounted stream of comfort that liquidity provides represents the total expected return on gold dust-held.

If we choose the second state and lend out our gold dust, we lose access to this liquidity and thus forfeit the expected stream of comfort that gold dust provides. Because we need to be compensated for this loss, a borrower will typically pay the lender a fee, or interest. But gold dust is burdensome. It is heavy and must be arduously weighed out and stored overnight in expensive vaults. IOUs, on the other hand, are a breeze to store. By offering to take our gold dust off our hands for a year or two, a borrower agrees to unburden us of storage expenses while providing us with a feather-light IOU in return.

So on the margin, when choosing between gold dust and an IOU, we are comparing the low storage costs of the illiquid IOU against the extra liquidity of cumbersome gold dust.

What might make rates turn negative in our central bankless gold dust world? Here are two ways:

1. Rising storage costs

Say that the costs of storing and handling gold dust grow substantially. At some much higher carrying cost, rather than requiring a fee from a borrower (i.e. positive interest) a lender will willingly pay the borrower a fee (i.e. will accept a negative interest rate) for the benefit of being temporarily unburdened of their gold dust. The loss of liquidity that the loan of gold dust imposes on the lender is entirely overwhelmed by the benefits of being freed from onerous storage costs. We get a sub-zero interest rate.

2. A narrowing liquidity gap

The second way to arrive at sub-zero interest rates is to narrow the vast gap between the respective liquidity returns on gold dust and IOUs. There are a few ways to go about this. Imagine that retailers who had previously only accepted gold dust as payment begin accepting IOUs too. Simultaneously, borrowers innovate by printing their paper IOUs in round numbers, making them far easier to count than grams of dust. All of this narrows the liquidity gap by improving the liquidity of IOUs. If the liquidity of IOUs improves so much that it exceeds the liquidity of the gold dust, an IOU effectively provides a greater stream of relief-providing services than gold. When this happens, lenders will clamour to pay a fee in order to lend their gold dust, since the superior optionality that an IOU provides is valuable to them. This fee represents a sub-zero interest rate.

Another way to narrow the vast liquidity gap between gold dust and IOUs is to create so much liquidity that, on the margin, liquidity becomes like air; it has no value. Neither gold dust nor IOUs can offer a superior liquidity return if society no longer puts any price on liquidity. In this situation, the interest rate on IOUs is purely a function of storage costs. Since an IOU will typically be less costly to store than the dust, the borrower of gold will typically receive a fee from the lender, a negative interest rate, in order to cover storage costs. Paul Krugman takes this tack here to explain negative rates.

So in the end, we can get negative nominal interest rates without central bankers. How far below zero can interest rates fall in a gold dust world? At least as low as the cost of storing gold dust and the degree to which the marginal value of an IOUs liquidity exceeds that of gold dust. Obviously we don't actually use gold dust in the real world, but the same principles apply to a cash-using economy. The theory behind negative rates isn't so surreal after all, Mr. Gross.

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Some links to read:

Beyond bond bubbles: Liquidity-adjusted bond valuation by JP Koning [link]
What's the Actual Lower Bound? by Evan Soltas [link]
How Negative Can Rates Go? by Paul Krugman [link]
It turns out that the US was never at the zero bound by Scott Sumner [link]
What gold's negative lease rate teaches us about the zero-lower bound by JP Koning [link]

On vacation since 2010

On a recent trip to Ottawa, I stopped by the Bank of Canada. The door was locked and the building empty. Odd, I thought, why would the Bank be closed in the middle of a business day? A security guard strolled up to me and told me that the entire staff packed up back in 2010 and left the country. He hadn't seen them since. Bemused I walked back to my hotel wondering how it was that with no one guiding monetary policy, the loonie hadn't run into either hyperinflation or a deflationary spiral.

Exactly 175 months passed between February 1996, when the Bank of Canada began to target the overnight rate, and September 2010, the date of the Bank's last rate change. Some 63 of those months bore witness to an interest rate change by the Bank, or 36% of all months, so that on average, the Governor dutifully flipped the interest rate switch up or down about four times a year. Those were busy years.

Since September 2010 the Governor's steady four-switches-a-year pace has come to a dead halt. Interest rates have stayed locked at 1% for 51 straight months, more than four years, with nary a deviation. I enclose proof in the form of a chart below. Not only has the Bank of Canada been silent on rates, it hasn't engaged in any of the other flashy central bank maneuvers like quantitative easing or forward guidance. In the history of central banking, has any bank issuing fiat money (ie. not operating under a peg) been inactive for so long?

Worthwhile Canadian chart: The Bank of Canada overnight rate target

Now the Bank of Canada will of course insist that you not worry about the lack of activity, its staff is still toiling away every day formulating monetary policy. But maybe the security guard was right. How do we know they haven't all been on an extended four-year vacation, hanging out in Hawaii or Florida? Who could blame them? Ottawa is awfully cold in the winter! With no one left at the Bank to flip the interest rate switch, that's why it remains frozen in time at 1%.

In theory, the result should be disastrous. With no one manning the interest rate lever, the price level should have either accelerated up into hyperinflation or downwards into a deflationary spiral. Why these two extreme results?

Economists speak of a "natural rate of interest". Think of it as the economy-wide rate of return on generic capital. The governor's job is to keep the Bank's interest rate, or the rate-of-return on central bank liabilities, even with the rate-of-return on capital. If the rate of return on central bank liabilities is kept too far below the rate on capital, everyone will want to sell the former and buy the latter. Prices of capital will have to rise ie. the purchasing power of money will fall. This rise will not close the rate-of-return differential between central bank money and capital. With the incentives to shift from money to capital perpetually remaining in effect, hyperinflation will be the result. Things work in reverse when the governor keeps the rate-of-return on central bank liabilities above the rate-of-return on capital. Everyone will try to sell low-yielding capital in order to own high-yielding money, the economy descending into crippling deflation.

In theory, there is no natural escape from these processes. The Bank needs to intervene and throw the interest rate lever hard in the opposite direction in order to pull the price level out of its hyperinflationary ascent or deflationary descent.

By the way, if this is all a bit boring, you can get a good feel for things by playing the San Francisco Fed's So you want to be in charge of monetary policy... game for a while. When you play, try keeping the interest rate unchanged through the course a game—you'll set off either a deflationary spiral or hyperinflation. Be careful, this game can get a bit addicting.

The upshot of all this is that with the Bank of Canada policy team on holiday and the policy rate stuck at 1%, any rise (or fall) in the Canadian natural interest rate is not being offset by an appropriate shift in the policy rate. Prices should be trending sharply either higher or lower.

However, a glance at core CPI shows that Canadian inflation has been relatively benign. Canada has somehow muddled through four years with no one behind the monetary rudder. How unlikely is that? Imagine Han Solo falling asleep just prior to entering an asteroid field only to wake up eight hours later to discover he'd somehow brought the ship through unscathed. We already know that the possibility of successfully navigating an asteroid field is approximately three thousand seven hundred and twenty to one—and that's with Han awake. If he's asleep, the odds are even lower. By pure fluke, each asteroid's trajectory would have to avoid a sleeping Han Solo's flight path in order for the Millennium Falcon to get through.

Success seems just as unlikely for the Bank of Canada. For us to have gotten this far with no one behind the wheel, the return on capital must not have changed at all over the last four years, the flat 1% interest rate thus being the appropriate policy. Either that or the return on capital zigged only to zag by the precise amount necessary to cancel out the zig's effect on the price level. However, I find it unlikely that the economy's natural rate of interest would stay unchanged for so long, or that its zig zagging was so fortuitous as to preclude a change in rates.

Alternatively, it could be that Canadians assume that the Bank is being vigilant despite the fact that the entire staff has skipped town. Even if a difference between the rate of return on capital and a rate of return on money arises thanks to normal fluctuations in natural rate of interest, Canadians might not take the obvious trade (buy higher yielding capital, sell low-yield money) because they think that the Bank will react, as it usually does, in the next period by increasing the rate of return on money. And with no one taking the trade, inflation never occurs. But is it safe to assume that people are willing to leave that much money on the table?

Another possibility is that the traditional way of thinking about monetary policy needs updating. I considered this possibility here. In short, when the return on Bank of Canada liabilities lags the return on capital, rather than a perpetual acceleration developing the price level stabilizes after a quick jump. This sort of effect could arise from central bank liabilities having some sort of fundamental value. Once the purchasing power of these liabilities falls low enough, their fundamental value kicks in, closing the rate-of-return differential between capital and money and preventing a hyperinflation from developing. So even with no one manning the Bank of Canada interest rate lever, the fundamental value of Bank of Canada liabilities provides an anchor of sorts, explaining why prices have been stable over the last few years.

I may as well come clean about the Bank of Canada. They haven't all gone to Hawaii. The real reason its HQ on Wellington Street was shut the day I visited is that it's being renovated. Rest assured the whole crew is hard at work at a temporary spot elsewhere. But does it make a difference? The monetary policy staff may just as well have gone to Hawaii in 2010. With the interest rate lever neglected and rates frozen at 1%, the evidence shows that prices would not have been sent off the rails, despite the fact that returns on capital surely jumped around quite a bit. It's all a bit odd to me.

Draghi's fake zero-lower bound and those pesky €500 notes

Having reduced the ECB's overnight target rate to +0.05% and the deposit rate to -0.2%, Mario Draghi confidently told those assembled at Thursday's press conference that the ECB wants to “make sure that there are no more misunderstandings about whether we have reached the lower bound. Now we are at the lower bound.” So it's official, according to its leader the ECB has run out of powder and can't reduce interest rate anymore.

But that's simply not true. I figure that the ECB has at least a handful of interest rate reductions left in its arsenal before the true lower bound bites, especially given that it's now adjusting rates in smaller increments of 0.1% and not 0.25%. And if the ECB were to get rid of its pesky issue of €500 notes, it would have a whole extra round of reductions up its sleeve (more on that later). Shame on Draghi for claiming impotence when he actually has plenty of rate ammunition still left.

The lower bound starts to bind when interest rates are brought sufficiently low that all those banks who own ECB deposits suddenly start to convert them en masse into euro banknotes. Banknotes yield 0%, after all, so if the ECB were to reduce rates on deposits to, say, -10%, then the prospect of costlessly converting those penalized deposits into holdings of 0% yielding notes starts to get pretty tempting. Central bankers are petrified of hitting this cash tipping point, so they refuse to institute anything below a 0% rate on deposits. That's why they call it the zero lower bound.

But the true tipping point at which mass cash conversion kicks in doesn't happen at 0%, nor at -0.05%, and probably not even -0.5%. The reason for this is that cash comes with its own set of inconveniences. For banks, storing cash is costly: it requires a vault, guards, time and energy to count and sort the stuff, and finally it must be insured. The transfer of cash is also expensive: Brinks armoured cars must be hired and loading bays properly staffed. Compare this to an electronic deposit which can be costlessly stored, instantaneously transferred at no cost, and needn't be insured against robbery.

Banks, anxious to avoid these inconveniences, are more likely than not to accept significantly negative rates on central bank deposits before they switch to cash. Imagine, for instance, cheque payments being cleared with daily shipments of cash rather than a click-of-a-button transfer of central bank deposits. It would be hellish. Or consider the huge inconvenience of conducting interbank payments on behalf of clients by shuttling cases of paper notes across town. No, if next month Draghi were to announce a reduction in the interest rate on the main refinancing operations by 10 basis points to -0.05%, and another one the next month to -0.15%, and another one after that, there would be no mass desertion of deposits for cash. Rates would have to go significantly below those levels before the actual lower bound starts to bind. There is a lower bound, but its certainly not at zero.

How far below zero?

This is where the ECB's pesky €500 note comes into the picture. The ECB has differentiated itself from almost all other developed country central banks by issuing a mega-large note denomination, the €500 note. The chart below shows the largest denomination notes issued by G20 countries in US dollar terms, with the Eurozone easily leading the pack.

According to this WSJ blog post, the architects of the ECB decided to issue the €500 note because six of the founding members already had bills whose value exceeded exceeded €200: Holland, Belgium, Italy, Austria, Luxembourg and Germany, with the Bundesbank's 1,000 Deutsche Mark banknote tipping the scale at about €510. And since the ECB is explicitly modeled on the Bundesbank, that's how Europe got its €500 note.

Nor is the value of €500s in circulation minimal. The chart below shows the nominal value (not the quantity) of euro notes in circulation by each denomination, with the value of €500 notes being eclipsed by only that of the €50.

The €500 note creates a uniquely European problem because its large real value reduces the cost of storing cash and therefore raises the eurozone's lower bound. Think about it this way. To get $1 million in cash you need ten thousand $100 bills. With the €500 note, you need only 1,545 banknotes, or about one-eighth the volume of dollar notes required to get to $1 million. This means that owners of euros require less vault space for the same real quantity of funds, allowing them to reduce storage costs as well as shipping & handling expenses. In other words, the €500 note is far more convenient than the $100 note, the €100, the £100, the ¥10,000, or any other note out there (we'll ignore the Swiss). Thus if Draghi were to reduce rates to -0.25%, or even -0.35%, the existence of the not-so-inconvenient €500 very quickly begins to provide a very worthy alternative to negative yielding ECB deposits. The lower bound isn't so low anymore.

All the more reason to remove the €500 note in order to provide the ECB with further downward flexibility in interest rates. If the existence of the €500 note means that Draghi can't push rates below, say, -0.35% without mass cash conversion occurring (ie. another four easings of 0.1% each starting from today's +0.05% rate), but the removal of said note from circulation allows him to drop that rate to -0.65% before the cash tipping point, then he's bought himself an extra three rate reductions by removing the €500. (Hell, by removing the €200 note next, and then the €100 after that, and then... he'd be able to continue reducing rates until deflation had been reversed and 2% inflation re-instituted)

Who loses by the  €500's removal? Regular folks won't suffer much, but denizens of the underground economy probably will. The large-denomination euro is a convenient medium of exchange for criminals, corrupt government officials, and anyone seeking to avoid paying taxes. For instance, in 2010 the UK's Serious Organised Crime Agency required local banks to cease supplying British customers with €500 notes when it found that 9 out of 10 notes were used for illegal activities. Just look at the different demand patterns for the €50 and the €500 in the chart above for evidence. The €50 shows seasonal spikes at Christmas. That's because people withdraw notes at Christmas to make sure they are equipped for unexpected expenses while traveling. Demand for the €500 doesn't budge at Christmas. That's because crime isn't a seasonal enterprise, it's a year-around affair.

So to sum up, Draghi is confused if he thinks he's actually hit the lower bound. Sure, he's brought rates down to zero, but the actual lower bound is a handful of rate cuts below that. The man has got more ammo than he realizes. And second, Draghi can get his hands on even more ammo by getting rid of that silly €500 note. It's existence only greases the wheels of criminal commerce, and insofar as further rate reductions could very well be necessary to help keep Europe out of a painful deflation, its mere existence raises the lower bound and thereby prevents those reductions from happening, thus hurting the regular European. That's two good reasons to get rid of the dang thing!

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Related posts on cash and the lower bound problem: 

The zero-lower bound as a modern version of Gresham's law
Does the zero lower bound exist thanks to the government's paper currency monopoly?
No need to ban cash to avoid the zero-lower bound problem

The fed funds rate was never the Fed's actual policy lever

The lever on which a central bank pushes or pulls in order to keep its target variable (say inflation) on track is commonly referred to as the central bank's policy instrument. The policy instrument is the variable that is under the direct control of a central banker. The classic story is that the pre-2008 Fed conducted monetary policy via its policy instrument of choice—the federal funds rate. By pushing the fed funds lever up or down, the Fed could change the entire spectrum of market interest rates.

I think this is wrong. The fed funds rate was never the Fed's actual policy instrument. Now this isn't a novel claim. Market monetarists tend to say the same thing. According to folks like Nick Rowe, the quantity of money has always been the Fed's true policy instrument. The fed funds rate was little more than a useful shortcut (a communications device) adopted by the Fed to convey to the public what it intended to do.

I'm sympathetic to the market monetarist's position, although I'm not entirely in the same corner. I agree that the Fed's policy instrument was never the fed funds rate. But I'm going to go one further than the market monetarists and say that the Fed's real policy instrument prior to 2008 was always the non-pecuniary return on reserves.

What do I mean by non-pecuniary return? All assets are expected to provide a sufficient return to their holder. This expected return can be decomposed into a pecuniary and a non-pecuniary component. Financial assets, for instance, tend to provide only pecuniary returns. These come in the form of expected interest payments, dividends, and capital appreciation. Non financial assets like couches, books, and cutlery tend to provide only non-pecuniary returns. These non-pecuniary returns come in the form of future consumption (dated consumption claims), protection from uncertainty, status, etc. Complex assets like houses provide both pecuniary and non-pecuniary returns. We expect to enjoy the shelter provided by our house, and we simultaneously expect it to provide a capital gain when we sell it.

Note that another word for non-pecuniary return is convenience yield. I'll use the two interchangeably from here on in.

For the first time ever on Moneyness, an equation to help clear the waters:

Total expected return of an asset = expected non-pecuniary return + expected pecuniary return

In well-functioning markets, all assets provide the same total expected return. If some asset begins to throw off excess returns, people will buy it up till its price has risen to the point that the cost of acquiring that asset offsets its superior return. Vice versa with an asset that begins to throw off deficient returns.

Central bank reserves are like any other asset. They provide an expected return that can be decomposed into pecuniary and non-pecuniary components. Perhaps somewhat oddly for a financial asset, reserves have never provided a pecuniary return, at least not before 2008. This is because reserves failed to pay interest. (In fact, reserves have always provided a slightly negative pecuniary return. They are generally expected to fall in price, burdening holders with a negative capital gain).

Reserves, therefore, are only held because their non-pecuniary return, or convenience yield, is sufficiently large to compensate their owners for a lack of a pecuniary return. [From here on in, it goes without saying that I am talking about the pre-2008 Fed]. What is the nature of this yield? Reserves are the main instrument used for interbank payments and settlement. Should an emergency arise necessitating an immediate payment, a banker can always put his or her inventory of reserves to use. If a banker foregos holding an inventory of reserves, he or she will have to bear the risk of not being able to quickly obtain sufficient reserves for potential unforeseen payments requirements. Reserves are to a banker what a fire alarm is to a household— while neither provides an explicit pecuniary benefit, both assets provide their owners with ongoing protection from the uncertainty of future events. Bankers and households alike expect to "consume" this convenience over the life of the asset, earning the same total return they would on their other assets.

It is the convenience yield on reserves, and not the fed funds rate, that serves as the Fed's policy instrument. By manipulating the convenience yield—the non-pecuniary return provided by reserves—the Fed exercises monetary policy. When the Fed improves the convenience yield on reserves, reserves will provide a superior expected return relative to all other assets in an economy. Rational agents will bid the price of reserves up, and the price level down. When it hurts the convenience yield, reserves will provide an inferior expected return relative to all other assets in an economy. Rational agents will now cry the price of reserves down, and the price level up.

One way to alter the convenience yield on reserves is to change their quantity via open market operations. As the supply of reserves shrinks via open market sales, the marginal reserve provides an ever improving convenience yield. Rational agents will seek to earn an excess return on their portfolios by buying superior-yielding reserves and selling other assets. This causes a fall in the price level until reserves no longer provide superior returns. Conversely, as the supply of reserves is increased via open market purchases, the marginal reserve provides an ever shrinking convenience yield. Rational agents will try to rid themselves of inferior-yielding reserves, causing a decline in the price of reserves, the mirror image of which is a rise in the price level.

There's a second way to change the convenience yield on reserves. Keep the quantity fixed, but make reserves more convenient! Just like an auto manufacturer can improve the expected convenience yield of a car by adding more features—cup holders, AWD, safety air bags, inboard TV, you name it—the Fed can also improve the expected convenience yield on reserves by souping them up. One popular add-on has always been the required reserve stipulation. As a condition of participation in the payments system, a central bank may require member banks to hold a certain quantity of reserves contingent on the number of deposits that each member has issued to the public. Where before central bank reserves were valued primarily for their role in settlement, now reserves can also be held to fulfill the reserve requirement, enabling the bank to continue as a payments system member in good standing. Voilà, reserves are now doubly-convenient since they can perform two roles, not just one. Henceforth, any increase in reserve requirements improves the convenience yield on reserves and any decrease will hurt their convenience yield.

If the Fed's monetary policy instrument has always been the convenience yield on reserves and not short term interest rates, as is commonly supposed, why all the hoopla about the federal funds rate? Why do central banks talk so much about manipulating overnight interest rates?

The problem with doing monetary policy in terms of convenience yields is that convenience yields are not directly visible. We know that they exist, but we can't really see them. This leaves the Fed in a conundrum, because if it tries to communicate about monetary policy, it can only talk about raising or lowering the hidden convenience yield on reserves, but it can't go into any numeric depth on the issue.

But wait! There are indirect ways to measure convenience yields. One way is to ask people how much money they expect to earn if they forgo the convenience of some asset for a duration of time. The rent they expect to earn in compensation should "shadow" the convenience yield. The more convenient an asset becomes, the higher the rent the asset holder expects to be compensated with if they are to do without that asset for a period of time. The less convenient, the lower the rent.

The federal funds market is the rental market for reserves. Banks can either hold reserves and enjoy their convenience, or they can rent their reserves out to other banks, foregoing the convenience of reserves for a period of time but earning compensatory payments. These payments are the rental value of reserves, or the fed funds rate. The fed funds rate is driven by the convenience yield on reserves. So when reserves are made more convenient by the Fed, banks will expect to earn a higher fed funds rate as compensation from borrowers. When the fed funds rate falls, that means that reserves have been made less convenient.

So the fed funds market provides a numeric manifestation of the unobservable convenience yield on reserves. The Fed can use this manifestation as a stand-in for communicating with the public, describing monetary policy as-if it was directly manipulating the fed funds rate whereas in actuality the convenience yield is the Fed's true policy instrument. In the 1990s and 2000s, when the Fed announced changes in the fed funds rate target, it was doing nothing more than describing to the public how a change in the underlying convenience yield would appear to the superficial observer. As Nick Rowe says, interest rate targeting is not reality, its a way of framing reality.

The fed funds rate also serves the Fed's Open Market Committee as a useful sign post, or indicator, that provides information on the way to hitting its final price target. For each modification it makes in the convenience yield, the FOMC can measure how successful it has been by referring to how far the fed funds rate has moved in response. Alternatively, the FOMC can use the fed funds rate as a guide for stabilizing what would otherwise be an invisible and difficult to manage convenience yield. In general, the Fed has tried to keep the convenience yield on reserves flat for extended periods of time between meetings. Whenever the fed funds market blips up or down in the interim, the Fed can use these blips as indicators that it is not keeping the underlying convenience yield steady. Action, either OMOs or reserve requirement changes, will be used to bring the convenience yield on reserves back into its holding pattern.

But the key point here is that the federal funds rate is NOT doing the heavy lifting in monetary policy. The federal funds rate only responds passively to changes in the Fed's true policy instrument—the convenience yield on reserves. Fed-induced changes in the convenience yield create an instantaneous and simultaneous reaction in all markets, including the fed funds market, bond markets, stock markets, labour markets, goods markets, and commodity markets. The fed funds rate isn't the first price to react, nor is it the pivot around which the full network of other market rates move. That we use the fed funds market to measure the reaction of the economy to a change in the policy instrument rather than using, say, commodity markets, is merely for the sake of ease. The funds rate just happens to be the one that provides the most noise-free signal for how much the convenience yield has been manipulated.

...but not a perfect noise-free signal. The fed funds rate's ability to act at a good reflection of the underlying convenience yield comes to an end when it gets too low. Even as the Fed continues to reduce the convenience yield, the fed funds rate falls to 0% from where it refuses to budge, conveying the impression—an improper one—that the Fed's policy instrument is powerless. But further reductions in the convenience yield, and a higher price level, ARE still possible.

My point here is very similar to the one that Nick Rowe makes when he says that interest rates "go mute" at zero. This is an important point I never grasped intuitively till I began to think of Fed policy as the manipulation of convenience yields. The main difference between the two of us is that  Nick takes the "money" view, which looks at absolute quantities of money, while I take a "moneyness view", which means I'm interested in monetary convenience yields [on money vs. moneyness]. We arrive at the same final destination, though, albeit by different roads.

Plenty of things changed after October 2008. I suppose I could go into this in more detail, but this post is already too long. Suffice it to say that reserves ceased offering a present non-pecuniary return and began offering a pecuniary return. The latter is IOR (interest-on-reserves). The non-pecuniary return has shrunk because there is currently such a glut of reserves in the system that the marginal reserve no longer offers its owner a present convenience yield. All of these changes complicate the picture.

There's plenty more to say on all this stuff, but this post is heavy enough. Just keep in mind that thinking in terms of convenience yields and not the federal funds rate opens up a whole new world. The idea that the funds rate was ever the policy instrument should be confined to the trash bin. More later.