The shrinking rupee

Earlier this month I criticized the architects of India's recent note demonetization for not using the traditional overstamping technique for replacing large quantities of banknotes.

This week I want to examine another feature of Modi's demonetization: the concurrent change in note sizing. The new series of ₹500 and ₹2000 notes are smaller in size than the ₹500 and ₹1000 series that they have since replaced. This has caused huge logistical problems. Since each cartridge in an ATM must be manually configured to handle a certain note size, ATMs were not equipped hold the newly issued ₹500s, ₹2000s, or additional ₹100s for that matter. Instead, they were forced to operate at a fraction of their capacity. Indians, desperate to replace their demonetized notes with good cash, were left on the lurch.

Let's explore the reduction in banknotes size. I'd argue that independent of the decision to crack down on black money, the decision to go smaller makes a lot of sense. But twinning a banknote size reduction with a demonetization was a recipe for disaster.

Consider that the length of the current issue of rupee banknotes grows as the denomination increases, like this:

Denomination: width x length

₹100: 73mm x 157mm

₹500: 73mm x 167mm

₹1000: 73mm x 177mm

To Americans and Canadians, this may seem odd since all our money is the same size. However, a pattern of progressively longer notes is quite common in other countries. Euro banknotes, for instance, also increase in size as denomination rises as do Swiss francs and Japanese yen. Presumably this format is chosen to to make manual sorting easier.

Now if the Reserve Bank of India, the nation's central bank, had continued to follow its traditional size progression, the newly issued 2000 rupee note would have had these measurements:

₹2000: 73mm x 187 mm

This would have been an awfully big note, one of the largest in the world by surface area. It would have clocked in 32% larger than a US$20 bill, for instance, and 43% larger than a 20 euro note. Not only would a note of this size have been expensive to print, but the combined costs of storage and handling incurred by hundreds of millions of Indians over time would have been quite large. Reducing the size would cut down on both expenses.*

The trend among central banks is to reduce the dimensions of banknotes. For instance, euro banknotes are quite a bit smaller than the francs, deutschmarks, and other notes that they replaced. The five euro note is one of the smallest notes in the world (see this pdf). When the Swiss began to introduce the ninth generation of Swiss banknotes in 2016, they lopped around 11 mm off the length of the 50 franc note and 4mm off its height (it now clocks in at 70 x 137 mm, down from 74 x 148).  By doing so, the Swiss National Bank will be lowering manufacturing and handling costs of the currency. In the chart below, you can see the evolution of the dimensions of Swiss cash over time.

Data source: Wikipedia

So India's decision to reduce the size of the new notes is very much modern practice. 17mm has been removed from the length of the ₹500 note; it measures 150 mm rather than 167mm. As for its height, it has gone from 73mm to 66mm. The new ₹2000 note measures 66mm x166mm, a 20% reduction from what it would have measured had the RBI continued with its old progression. Presumably the RBI will eventually do the same with the smaller denomination like the ₹100 as well.

While a note size reduction makes sense, twinning it with an aggressive demonetization was a bad decision. To reduce the odds of damaging the economy, the void left by demonetized notes must be filled as rapidly as possible. In India's case, the discontinuity in banknote size interfered with this re-cashification process. The authorities should have split the two policies apart, say by enacting a gentle two or three-year conversion of existing notes to a new and smaller series, and only announcing a surprise aggressive demonetization of the two highest denomination notes four or five years from now, say in 2021.

Alternatively, the authorities could have proceeded with their November 8 aggressive demonetization, but without enacting a note size reduction. The RBI should have taken incoming demonetized 500 and 1000 rupee notes and stamped them for re-circulation to ensure the banknote supply was sufficient, as I went into here. By using existing banknotes, ATMs cartridges would not have required adjustment. As for the new ₹500 note, it should have been the same size as the old series to ensure that cash distribution worked smoothly. Then—say five years from now—the Reserve Bank of India could have gradually phased in reduced note sizes for the entire range of denominations from the ₹10 to the ₹2000. This would have cut down on the chaos of the last few months.

The RBI seems not have been involved much in the planning stage of demonetization. According to recent press reports, the Board was "asked" to consider the demonetization just a day before it was enacted and had not discussed the matter before then. This is a shame. While an aggressive demonetization needs to be planned in secret, as I pointed out here, having at least a few closed-mouth central bank types involved from the outset seems like a basic requirement. They might have been able to fix the mistake of combining a demonetization with a note reduction.

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*On the other hand, there are arguments for increasing note size too. See Garber.

The strange mania for Swiss National Bank shares

The shares of the Swiss National Bank (SNB), Switzerland's central bank, have almost doubled since July, despite there being no real news. Yep, you read that right, the SNB is listed on the stock market. There are four other central banks with listed shares: Belgium, Japan, Greece, and South Africa. I discussed this odd group back in 2013.

Why are SNB shares catapulting higher? This is a staid central bank, after all, not a penny stock.

Let's look at the fine print. Swiss National Bank shares aren't regular shares. To begin with, the dividend is capped at 6% of the company's share capital. The SNB was originally capitalized back in 1907 with 25 million Swiss francs, an amount that hasn't changed in 109 years. Which means that the dividend is, and always has been, limited in aggregate to a minuscule 1.5 million francs per year (about US$1.5 million). Because this amount must be divvied among the 100,000 shares, each share gets just 15 francs per year.

The SNB has faithfully paid this 15 franc dividend since its founding (apart from 2013, when it was omitted due to massive capital loss on its gold holdings). For instance, here it is paying the dividend throughout the 1980s:

Once the 1.5 million franc dividend is paid, Swiss law dictates that all remaining profits get sent to the Swiss central government and the cantonal governments. It further stipulates that if the SNB is to be liquidated, shareholders will only receive a cash payment equal to the nominal value of their shares. This means that if shares are trading for 1025 Fr, but there is residual firm value (after paying debtors) of 10,000 francs per share, well too bad—shareholders only get 1025 Fr.

Given these peculiar details, an SNB share isn't really equity; it's best thought of as a perpetual government bond with a 6% coupon, sometimes known as a consol. It throws off 15 francs per year for the rest of time. With the SNB as issuer, these securities are pretty much risk-free.

The math behind SNB shares is straightforward. Just use the Finance 101 formula for a perpetual bond, PV=c/r, or present value (PV) equals yearly cash flow (c) divided by yield (r). With annual interest payments of 15 francs and SNB shares trading at 2000 Fr, the yield comes out to 0.75%.

Here's what I think explains the rise in SNB shares. In July, an odd thing happened. The yield on the Swiss 50-year bond, the closest instrument in Switzerland to a perpetual government bond, fell below 0%. SNB shares (i.e. perpetual bonds) were themselves trading at around 1000 francs at that point for a yield of 1.5%. A few large investors probably began to ask themselves: Why the devil are we accepting a negative nominal return on our ultra long-term government bond portfolio if these other government bonds, which happen to be issued by the central bank and masquerade as shares, still have a positive yield? And so they started to buy SNB shares in quantity, driving the price up and the yield down.

This sort of thinking explains why SNB shares have risen, but not necessarily the explosive nature of the move. The shares haven't just risen by a few bucks, after all. They've almost doubled!

Let's take a closer look at the perpetual bond formula. If nominal interest rates fall from 1.5% to 0.5%, a fifty-year bond with a par value of 1000 francs and a 15 franc yearly coupon will rise from 1000 to 1,441 francs. Not bad, but compare that to a perpetual. For the same decline in rates, SNB shares will double in value from 1000 to 2000 francs. As rates continue to fall towards zero percent, the price of a perpetual goes parabolic. At 0.25%, the perpetual will be worth 6000 Fr, at 0.1% it trades at 15,000 Fr, and at 0.01% it sells for 150,000 francs. At 0.001%, they'd be valued at 1,500,000 francs each!

In the table below, I've illustrated the relative dynamic of a 50-year bond and a perpetual as rates fall to zero.

Price of a 50-year bond and perpetual at various interest rates

At the limit of 0%, SNB shares will have an infinite price. If all existing and yet-to-be-issued government fixed term bonds are guaranteed to lose money over the course of their existence, but there exists a government security that is guaranteed to perpetually offer a positive cash flow, then an investor will pay *any* amount of money to own those cash flows. There is no price to which SNB perpetual bond can rise that chokes off their demand.

The behavior of perpetual bonds at low interest rates *might* explain why SNB shares have gone hyperbolic. It also means that if Swiss rates continue to fall, the shares could have another double or two in the tank. So much for staid Swiss central banking.

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Hat tip to Leon Oudejans for alerting me to the recent rise in SNB shares.

P.S. Does anyone know how rare perpetuals are, specifically perpetuals like SNB shares that don't provide the issuer with the option to call it? My understanding is that this sort of security just isn't issued anymore, at least not since British consols.

What the difference between an SNB share and a 1000 Swiss banknote? Not much, right? They're both perpetual bonds, one paying 15 francs a year, the other paying zero francs per year. If you were to write the number 1000 on an SNB bearer share, and 500 on a half share, and 100 on a fifth share, etc you'd have the entire series of Swiss banknotes. Cut the dividend on shares to zero, and won't banknotes and shares be exactly the same?

Here's a chart of the Bank of Japan, which is also a perpetual bond underneath the hood.

Those new Japanese safety deposit boxes must all be empty

Remember all the hoopla about Japanese buying safety deposit boxes to hold cash in response to the Bank of Japan's decision to set negative rates? Here is the Wall Street Journal:

Look no further than Japan’s hardware stores for a worrying new sign that consumers are hoarding cash--the opposite of what the Bank of Japan had hoped when it recently introduced negative interest rates. Signs are emerging of higher demand for safes—a place where the interest rate on cash is always zero, no matter what the central bank does.

Well, three month's worth of data shows no evidence of unusual cash demand. As the chart below illustrates, the rate at which the Bank of Japan is printing the ¥10,000 note shows no discontinuity from its pre-negative rate rise. In fact, demand for the ¥10,000 is far below what it was in the 1990s, when interest rates were positive.

I should remind readers that the Bank of Japan, like any central bank, doesn't determine the quantity of banknotes in circulation; rather, the public draws those notes into circulation by converting deposits into notes. So this data is a pure indicator of Japanese cash demand.

The lack of interest in switching into yen notes should come as no surprise given the experience of other nations that have set negative interest rates. Data from Sweden, Denmark, and Switzerland has consistently shown that it takes more than just a slight dip into negative territory before the dreaded "lower bound," the point at which the public converts all their deposits into banknotes, is encountered.

For instance, despite the setting of a -0.5% repo rate by Sweden's Riksbank, Swedish cash in circulation continues to decline. I won't bother to provide a chart, you can go see the data here.

As for the Danes, the growth rate in Danish cash demand continues to hover near its long term average of 3.7%/year. This despite the fact that the Danmarks Nationalbank, the nation's central bank, is setting a deposit rate of -0.65%. I've charted it out below:

Definitely no lower bound in Denmark, at least not yet.

Finally, we have Switzerland where the Swiss National Bank has maintained a -0.75% rate since December 2014. Back in February, the WSJ and Zero Hedge were making a fuss out of the sudden jump in the demand for the 1000 franc note, in effect blaming the build up on the lower bound. I wrote a rebuttal at the time, Are Swiss fleeing deposits and hoarding cash, pointing out that the demand for Swiss francs is often driven by safe haven concerns. The observed increase in 1000s might therefore have very little to do with the SNB hitting the effective lower bound and everything to do with worries about falling equity prices, China, deteriorating credit quality, and more.

With many of these concerns subsiding in 2016, one might expect the safe haven demand for 1000 franc notes to be falling again. And that's exactly what we see in the chart below; the Swiss are accumulating notes at a decelerating pace, even though the SNB has not relaxed its negative deposit rate one iota.

What these charts all show is that the effective lower bound to central bank deposit rates has not yet been engaged, even after many months in negative territory. You can be sure that the global community of central bankers is watching this data too; it is telling them that, should the need arise, their respective interest rates can be pushed lower than the current low-water mark that has been set by the SNB and Danmarks Nationalbank at -0.75%, say to -0.85% or even -1.0%.

There are a few factors that might be dampening the demand for paper notes. Remember that the Swiss and the Japanese have installed cash escape inhibitors; mechanisms that reduce the incentive for banks to convert central bank deposits into cash. I've written about them here.

Secondly, the SNB and the BoJ, along with the Danes, have set up an array of interest rate tiers. While the marginal deposit earns a negative rate, the majority of the tiers are only lightly penalized or not penalized at all. This tiering represents a central bank subsidy to commercial banks; in turn, banks have passed this subsidy on to their retail depositor base in the form of higher-than-otherwise interest rates, the upshot being that very few banks have set negative deposit rates on retail customers. This has helped stifle any potential run on deposits.

Tiering and cash escape inhibitors have helped dissuade cash withdrawals by two members of the public, retail depositors and banks, but not the third; large non-bank institutions. That these latter institutions haven't bolted into cash shows that the natural costs of storing wads of paper are quite high, and that the effective lower bound quite deep.

Are the Swiss fleeing deposits and hoarding cash?

Have Swiss interest rates fallen so low that the public is finally bolting into cash? The Wall Street Journal and Zero Hedge think so. They both point to big jump in 1000 franc notes outstanding as evidence that Switzerland has finally breached the effective lower bound to interest rates.

Let's not get too hasty. Yes, the current run into paper francs may have something to do with Switzerland having hit its effective lower bound, the point at which paper francs provide a superior return to electronic francs. But Swiss francs also serve as a global safe haven asset. And this safe haven demand, operating entirely independent from effective lower bound demand, could be motivating people to amass 1000 franc notes in vaults.

The effective lower bound problem is the idea that if a central bank drops rates low enough, a tipping point will be reached at which it becomes cheaper to hold 0% yielding banknotes and incur storage fees than to stay invested in negative yielding deposits. The large spike in demand for the 1000 franc note, Switzerland's largest value note and thus the lowest cost Swiss storage option, may be the first indication that a tipping point has been reached.

Let's look at the data. Below is a chart that shows the year-over-year change in Swiss franc banknotes outstanding as well as deposits. For comparison sake I've divided the banknote data into a 1000 franc series and all other franc notes.

The current jump in demand for 1000 notes, the blue line, is just one of six spikes over the last two decades. You can see that some of these spikes have been accompanied with jumps in demand for smaller notes and deposits, and some haven't.

In the next chart I've subtracted the yearly percentage change in Swiss bank deposits outstanding from the percent change in 1000 franc notes in circulation to show the degree to which the demand for large value cash is exceeding that of deposits.

If we are at the effective lower bound, we'd expect to see simultaneous implosion in deposit growth and an explosion in cash growth. The blue line should be at its highest point ever. What we actually see is a mere 10.3% differential. The quantity of notes in circulation is growing at 11% while deposits are growing at just 0.7%. This level is by no means extreme; five other spikes in the cash-to-deposit differential are apparent in the chart, most of which plateaued at or above the current level. These previous spikes in demand for 1000 notes occurred when Swiss interest rates were above zero, so something other than lower bound concerns must have motivated them. What are they?

The jump in 1999 is certainly Y2K-related as people fretted that the banking system would collapse and thus hoarded paper francs. And the 2001-02 spike in demand for 1000 franc notes is probably linked to 9/11 as well as the ongoing collapse in stock markets. The sudden rise in demand in 2008 coincides nicely with the credit crisis. Finally, the 2011-12 rise occurred in parallel with growing fears about Target2 imbalances and a potential euro break up, the run into 1000 franc notes coming to a halt almost to the month of Draghi's famous speech to do 'whatever it takes.'

So the lesson is that Swiss 1000 notes play a role as a safe haven asset. When bad things happen, they are preferred to other note denominations and franc deposits.

Fast forward to the present, I can use this safe haven status to tell a story about the current spike in demand. The coming to power of Syriza late in 2014 and a slow-moving euro crisis led to a sudden preference for 1000 franc notes, much like how the period of euro skepticism in 2011-12 stoked demand for Swiss cash. Concerns over China, the oil price collapse, growing credit worries, and a bear market in equities have further incited investor movement into large denomination francs. At the same time, deposit growth is relatively neutral, a pattern reminiscent of the credit crisis. As these concerns abate, the run into 1000 franc notes will subside, even if Swiss interest rates stay locked in negative territory.

I think that's a pretty reasonable story. The upshot is that while the run into 1000 franc notes could certainly indicate that the effective lower bound has been triggered, it is by no means the only explanation. People may simply be accumulating the 1000 as a safe asset in the context of growing global worries. Absent a smoking gun, Tommy Jordan, head of the Swiss National Bank, will probably not be using the increase in large denomination notes outstanding as a reason to avoid further rate cuts, at least not yet. When demand growth for 1000 notes is exceeding that of deposits by 30% or so, then he should be concerned.

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Previous articles on Swiss cash demand:

- - {1} - -The ZLB and the impending race into Swiss CHF1000 bank notes
- - {2} - - Central banks' shiny new tool: cash escape inhibitors
- - {3} - - Plumbing the depths of the effective lower bound

Central banks' shiny new tool: cash escape inhibitors

Thomas Jordan, Chairman of the Governing Board of the Swiss National Bank

Negative interests rates are the shiny new thing that everyone wants to talk about. I hate to ruin a good plot line, but they're actually kind of boring; just conventional monetary policy except in negative rate space. Same old tool, different sign.

What about the tiering mechanisms that have been introduced by the Bank of Japan, Swiss National Bank, and Danmarks Nationalbank? Aren't they new? The SNB, for instance, provides an exemption threshold whereby any amount of deposits that a bank holds above a certain amount is charged -0.75% but everything within the exemption incurs no penalty. As for the Bank of Japan, it has three tiers: reserves up to a certain level (the 'basic balance') are allowed to earn 0.1%, the next tier earns 0%, and all remaining reserves above that are docked -0.1%.

But as Nick Rowe writes, negative rate tiers—which can be thought of as maximum allowed reserves—are simply the mirror image of minimum required reserves at positive rates. So tiering isn't an innovation, it's just the same old tool we learnt in Macro 101, except in reverse.

No, the novel tool that has been created is what I'm going to call a cash escape inhibitor.

Consider this. When central bank deposit rates are positive, banks will try to minimize storage of 0%-yielding banknotes by converting them into deposits at the central bank. When rates fall into negative territory, banks do the opposite; they try to maximize storage of 0% banknote storage. Nothing novel here, just mirror images.

But an asymmetry emerges. Central bankers don't care if banks minimize the storage of banknotes when rates are positive, but they do care about the maximization of paper storage at negative rates. After all, if banks escape from negative yielding central bank deposits into 0% yielding cash, this spells the end of monetary policy. Because once every bank holds only cash, the central bank has effectively lost its interest rate tool.

If you really want to find something innovative in the shift from positive to negative rate territory, it's the mechanism that central bankers have instituted to inhibit the combined threat of mass paper storage and monetary policy impotence. Designed by the Swiss and recently adopted by the Bank of Japan, these cash escape inhibitors have no counterpart in positive rate land.

The mechanics of cash escape inhibitors

Cash escape inhibitors delay the onset of mass paper storage by penalizing any bank that tries to replace their holdings of negative yielding central bank deposits with 0%-yielding cash. The best way to get a feel for how they work is through an example. Say a central bank has issued a total of $1000 in deposits, all of it held by banks. The central bank currently charges banks 0% on deposits. Let's assume that if banks choose to hold cash in their vaults they will face handling & storage costs of 0.9% a year.

Our central bank, which uses tiering, now reduces deposit rates from 0% to -1%. The first tier of deposits, say $700, is protected from negative rates, but the second tier of $300 is docked 1%, or $3 a year. Banks can improve their position by converting the entire second tier, the penalized portion of deposits, into cash. Each $100 worth of deposits that is swapped into cash results in cost savings of 10 cents since the $0.90 that banks will incur on storage & handling is an improvement over the $1 in negative interest they would otherwise have to pay. Banks will very rapidly withdraw all their tier-2 deposits, monetary impotence being the result.

To avoid this scenario, central banks can install a Swiss-style cash escape inhibitor. The way this mechanism works is that each additional deposit that banks convert into vault cash reduces the size of the first tier, or the shield, rather than the second tier, the exposed portion. So when rates are reduced to -1%, should banks try to evade this charge by converting $100 worth of deposits into vault cash they will only succeed in reducing the protected tier from $700 to $600, the second tier still containing the same $300 in penalized deposits. This evasion effort will only have made banks worse off. Not only will they still be paying $3 a year in negative interest but they will also be incurring an extra $0.90 in storage & handling ($100 more in vault cash x 0.9% storage costs).

Continuing on, if the banks convert $200 worth of deposits into vault cash in order to avoid -1% interest rates, they end up worsening their position even more, accumulating $1.80 in storage & handling costs on top of $3.00 in interest. We can calculate the net loss that the inhibitor imposes on banks for each quantity of deposits converted into vault cash and plot it:

The yearly cost of holding various quantities of cash at a -1% central bank deposit rate

Notice that the graph is kinked. When a bank has replaced $700 in deposits with cash, additional cash withdrawals actually reduce its costs. This is because once the first tier, the $700 shield, is used up, the next deposit conversion reduces the second tier, the exposed portion, and thus absolves the bank of paying interest costs. And since interest costs are larger than storage costs, overall costs decline.

If banks go all-out and cash in the full $1000 in deposits, this allows them to completely avoid the negative rate penalty. However, as the chart above shows, storage & handling costs come out to $9 per year ($1000 x 0.9%), much more than the $3 banks would bear if they simply maintained their $300 position in -1% yielding deposits.

So at -1% deposit rates and with a fully armed inhibitor installed, banks will choose the left most point on the chart—100% exposure to deposits. Mass cash conversion and monetary policy sterility has been avoided.

How deep can rates go?

How powerful are these inhibitors? Specifically, how deep into negative rate territory can a central bank go before they start to be ineffective?

Let's say our central banker reduces deposit rates to -2%. Banks must now pay $6 a year in interest ($300 x 2%). If banks convert all $1000 in deposits into cash, they will have to bear $9 in storage and handling costs, a more expensive option than remaining in deposits. So even at -2% rates, the cash inhibitor mechanism performs its task admirably.

If the central bank ratchets rates down to -3%, banks will now be paying $9 a year in interest ($300 x 3%). If they convert all $1000 in deposits into cash, they'll have to pay $9 in storage & handling. So at -3%, bankers will be indifferent between staying invested in deposits or converting into cash. If rates go down just a bit more, say to -3.1%, interest costs are now $9.30. A tipping point is reached and cash will be the cheaper option. Mass cash storage ensues, the cash escape inhibitor having lost its effectiveness.

The chart below shows the costs faced by banks at various levels of cash holdings when rates fall to -3%. The extreme left and right options on the plot, $0 in cash or $1000, bear the same costs.

The yearly cost of holding various quantities of cash at a -3% central bank deposit rate

So without an inhibitor, the tipping point for mass cash storage and monetary policy impotence lies at -0.9%, the cost of storing & handling cash. With an inhibitor installed the tipping point is reduced to -3.1%. The lesson being that cash escape inhibitors allow for extremely negative interest rates, but they do run into a limit.

The exact location of the tipping point is sensitive to various assumptions. In deriving a -3.1% escape point, I've used what I think is a reasonable 0.9% a year in storage and handling costs. But let's assume these costs are lower, say just 0.75%. This shifts the cash tipping point to around -2.5%. If costs are only 0.5%, the tipping point rises to around -1.7%.

This is where the size of note denominations is important. The Swiss issue the 1000 franc note, one of the largest denomination notes in the world, which means that Swiss cash storage costs are likely lower than in other countries. As such, the Swiss tipping point is closer to zero then in countries like the Japan or the U.S.. One way to push the tipping point further into negative terriotry would be a policy of embargoing the largest note. The central bank, say the SNB, stops printing new copies of its largest value note, the 1000 fr. Banks would no longer be able to flee into anything other than small value notes, raising their storage and handling costs and impinging on the profitability of mass cash storage.

Good old fashioned financial innovation will counterbalance the authorities attempts to drag the tipping point deeper. Cecchetti & Shoenholtz, for instance, have hypothesized that in negative rate land, a new type of intermediary could emerge that provides 'cash reserve accounts.' These specialists in cash storage would compete to reduce the costs of keeping cash, pushing the tipping point back up to zero.

The tipping point is also sensitive to the size of the first tier, or the shield. I've assumed that the central bank protects 70% of deposits from the negative deposit rate. The larger the exempted tier the bigger the subsidy central banks are providing banks. It is less advantageous for a bank to move into cash when the subsidy forgone is a large one. So a central bank can cut deeper into negative territory the larger the subsidy. For instance, using my initial assumptions, if the central bank protects 80% of deposits, then it can cut its deposit rate to -4.6% before mass paper storage ensues.

Removing the tipping point?

There are ways to modify these Swiss-designed cash escape inhibitors to remove the tipping point altogether. The way the SNB and BoJ have currently set things up, banks that try to escape negative rates only face onerous penalties on cash conversions as long as the first tier, the shield, has not been entirely drawn down. Any conversion after the first tier has been used up is profitable for a bank. That's why the charts above are kinked at $700.

If a central bank were to penalize cumulative cash withdrawals (rather than cash withdrawals up to a fixed ceiling) then it will have succeeded in snipping away the tipping point. This is an idea that Miles Kimball has written about here. One way to implement this would be to require that the tier 1 exemption, the shield, go negative as deposits continue to be converted into cash, imposing an obligation on banks to pay interest. The SNB doesn't currently allow this; it sets a lower limit to its exemption threshold of 10 million francs. But if it were to remove this lower limit, then it would have also removed the tipping point.

What about retail deposits?

You may have noticed that I've left retail depositors out of this story. That's because the current generation of cash escape inhibitors is designed to prevent banks from storing cash, not the public.

As central bank deposit rates fall ever deeper into negative territory, any failure to pass these rates on to retail depositors means that bank margins will steadily contract. If banks do start to pass them on, at some point the penalties may get so onerous that a run develops as retail depositors start to cash out of deposits. The entire banking industry could cease to exist.

To get around this, the FT's Martin Sandbu suggests that banks could simply install cash escape inhibitors of their own. Miles Kimball weighs in, noting that banks may start applying a fee on withdrawals, although his preferred solution is a re-deposit fee managed by the central bank. Either option would allow banks to preserve their margins by passing negative rates on to their customers.

Even if banks don't adopt cash escape inhibitors of their own, I'm not too worried about retail deposit flight in the face of negative central bank deposit rates of -3% or so. The deeper into negative rate territory a central bank progresses, the larger the subsidy it provides to banks via its first tier, the shield.  This shielding can in turn be transferred by a bank to its retail customers in the form of artificially slow-to-decline deposit rates. So even as a central bank reduces its deposit rate to -3% or so, banks might never need to reduce retail deposit rates below -0.5%. Given that cash handling & storage costs for retail depositors are probably about the same as institutional depositors, banks that set a -0.5% retail deposit rate probably needn't fear mass cash conversions.

So there you have it. Central banks with cash escape inhibitors can get pretty far into negative rate land, maybe 3% or so. And with a few modifications they might be able to go even lower.

Hike rates when you hear the creak of inflation at the door, not when you see the whites of its eyes

A common argument against the Fed raising interest rates next week is the asymmetry in risks that it faces. If it keeps rates low too long and sets off inflation, no problem: it can quickly hike rates a few times to bring prices back in line. However, if it boosts rates too early and an unintended slowdown sets in, the Fed won't have room to cut a few times in order to fix its mistake. That's because the Fed is at the zero lower bound, the edge of the world in monetary policy terms. To avoid this conundrum, the Fed should hold off as long as possible before raising, at least until it "sees the whites of inflation's eyes."

As Paul Krugman points out, the asymmetry argument is only a recent one. Historically U.S. interest rates have hovered far above zero. If the Fed made a mistake, it didn't have to worry about falling off the edge of the world in order to fix the situation, it could simply ratchet rates down a few times. Rather than waiting till the last minute to see the whites of inflation's eyes before hiking, the FOMC only had to hear the creak of inflation at the door.  

I don't buy the current asymmetry argument. I might have bought it back in 2013, but the data has changed.

Over the last year, Sweden, Switzerland, Denmark, and the ECB have all demonstrated to the world that central banks can safely lower rates into negative territory without setting off the sorts of ill effects that economists have always feared, the main one being a race into 0% yielding cash. The theory here is that if a central bank reduces rates to, say, -0.1%, then paper cash—which pays a superior 0% return—starts to look pretty attractive. An arbitrage process begins whereby central bank deposits are converted into cash until all deposits have disappeared. Thus rates can't be reduced below 0%.

Evidence over the last 12 months shows otherwise. Denmark's Nationalbank has kept its deposit rate at -0.75% since early February. Danes, however, are not scrambling for banknotes, as the chart below shows. After seven months of negative rates, cash and coin outstanding are growing at a rate that lies pretty much at its two decade average.

The Swiss National Bank has maintained a -0.75% overnight rate since January, yet there's been no spike in Swiss paper franc demand, as the next chart shows. In fact, cash outstanding seems to be growing at one of its slowest rates in years.

We'd expect the demand for Swiss cash to be especially sensitive when interest rates fall below zero because the SNB issues the world's largest value banknote; the hefty 1000 sFr. The more valuable the banknote the lower the cost of storing wealth in cash form. These carrying costs are particularly important in determining the profitability of flight into cash at negative interest rates. A central bank can push rates a sliver below 0% without setting off a flight out of deposits into banknotes as long as there are inconveniences in storing cash. The greater these inconveniences, the larger that sliver.

The fact that the SNB has been able to keep rates at -0.75% for seven months now without setting off a stampede into 1000 notes indicates that the burdens of holding Swiss currency are higher than everyone had previously thought. It would seem that investors would rather lose 0.75% each year than bear the costs of storing 1000s. At some negative interest rate, maybe -1.5%, the flight into Swiss notes will start. But it hasn't yet. As for the U.S., its highest value banknote is the lowly $100, so it's fair to assume that the costs of storing U.S. paper money are significantly higher than Swiss money. Which means that if the Swiss can safely cut to -0.75% without setting off cash arbitrage, the Fed should be able to descend to at least -1.0% before panic ensues.

The second greatest fear surrounding sub zero U.S. rates has always concerned money market mutual funds. The worry here is that should the Fed reduce rates too deep, a financial intermediary known as a money market mutual fund (MMMF) will 'break the buck,' causing panic and terror among ordinary investors.

MMMFs are like regular mutual funds except their share price stays fixed at US$1.00. Investors can cash out at that price whenever they want, enjoying low but steady dividend payments until then. MMMFs maintain par conversion by investing in safe, highly liquid short term debt. However, if the Fed were to drive short term rates into negative territory, MMMFs would be forced to invest in assets that promise a negative return. $1000 invested in t-bills, for instance, would be worth only $999 upon maturity. That means that an MMMF simply wouldn't have a sufficient quantity of assets to allow everyone to redeem their shares at US$1.00. The fund will "break the buck," or mark its share value down to something like 99 cents to allow for full redemption. Since MMMFs are supposed to be cash-like—in fact, many of them offer cheque-writing capability—such a development would be disastrous, or so goes the story.

I don't consider breaking the buck to be a terrible outcome, but even if it is, European money market mutual funds—faced with negative interest rates—have already found an ingenious way to avoid it; a Reverse Distribution Mechanism. Rather than reducing redemption below par, MMMFs simply dock the number of shares that each shareholder has in his or her account. For example, as rates slide below zero, instead of 100 units being worth only $0.99 each, a shareholder forfeits one unit and ends up with 99 units worth $1.00 each. The deeper rates fall, the less units each investor owns. The genius of this patch is that the purchasing power of each share stays constant, but the negative interest rate is efficiently passed on to the owner of the MMMF.

So fears of a dash into cash at 0% and a collapse of MMMFs are just bogeymen. If the Fed hikes to 0.5% this month—and this proves to be a mistake—it still has plenty of room to make things right. Given how well Europe has coped over the last twelve months, the Fed can easily cut rates another 1.5% to -1.0%; that's six quarter-point reductions or thirty ten-point cuts. Only when rates falls beyond Swiss or Danish levels, say to -1.0%, will the Fed find itself in truly asymmetrical territory. (If necessary, here are some simple ways to allow for even more negative rates).

To be clear, that doesn't mean I think the Fed should hike rates next week. The fact that the FOMC continues to undershoot its 2% core inflation target would seem to indicate that holding off might be the right thing to do. Rather, I don't think that Fed policy makers need to wait to see the white's of inflation's eyes before they hike, they need only wait to hear the creak of inflation at the door.

Plumbing the depths of the effective lower bound

Unfathomable Depths by Ibai Acevedo

Denmark's Nationalbank and the Swiss National Bank are the world's most interesting central banks right now. As the two of them push their deposit rates to record low levels of -0.75%, they're testing the market's limit for bearing negative nominal interest rates. The ECB takes second prize as it has been maintaining a -0.2% deposit rate since September 2014.

At some point, investors will flee deposits into 0%-yielding cash. This marks the effective lower bound to rates. Has mass paper storage begun? The last time I ran through the data was in my monetary canaries post, which was inconclusive. Let's take a quick glance at the updated data.

To gauge where we are relative to the effective lower bound, I'm most interested in the demand for large denomination notes, which bear the lowest costs of storage. Once a central bank reduces its deposit rate so deep into negative territory that the carrying cost of deposits exceeds the cost of storing a nation's largest value banknote, then it has hit the effective lower bound. Small denominations notes, which have higher storage costs, are not a pivotal part of the picture given the ability of note holders to freely convert low value notes into higher ones.

European Central Bank

The ECB issues the €500 note, which has the second highest purchasing power out of the world's currency notes. I've charted the quantity of €500 euro notes in circulation below, as well as the percent change in the value of all euro denominations:

After declining through 2012 and 2013, we saw a sharp rise in demand for €500 notes, particularly in December 2014 and the first few months of 2015. The red line illustrates the general demand for all denominations of euro cash. Over the last four months the seasonally-adjusted growth rate of banknotes outstanding has risen to its highest level in the last five years.

It's hard to determine how much of this increase can be attributed to the ECB's negative rate policy, initiated when Mario Draghi brought the deposit facility rate to -0.1% in June and -0.2% in September, and how much is due to the Greek fiasco. Growing fears that Greece will either leave the euro or impose capital controls have led to a steady jog out Greek banks. There are two escape routes: Greek's can convert their deposits can into German deposits or into cash.

In an interesting article, Bloomberg's Lorcan Roche Kelly backs out the Greek-specific demand for European cash. Read it for the full details, but the shorter rendition is that a line item on the Bank of Greece's balance sheet allows us to see how many banknotes Greeks are demanding in excess of the Bank of Greece's regular allocation. Kelly finds a large spike beginning in December and extending into 2015, which we can attribute to the bank jog. I've recreated the chart below:

Source: Bloomberg, data to end of March

The approximately €12 billion jump in Greek cash demand corresponds nicely with the recent €7.2 billion spike in €500 notes in circulation across the entire eurozone. The upshot is that a large chunk of the rise in €500 notes over the last few months is probably due to a run on Greek banks, not an escape from negative-yielding ECB deposits. Remove the run and the rise in demand for €500 notes would have been unremarkable, indicating that the eurozone is still far from hitting the effective lower bound.

Swiss National Bank

Because Swiss banknotes are not a direct escape route from the ongoing Greek bank run, SNB cash data should provide a clearer signal of the whereabouts of the effective lower bound than ECB data. The SNB issues the world's most valuable banknote in terms of purchasing power; the 1000 franc note. Below I've plotted the yearly percent change in demand for both the 1000 note and Swiss cash-in-general to the end of February.

There's been slight pickup in the demand for Swiss cash, but nothing dramatic. Its worth pointing out that Swiss paper currency has historically played a safe haven role. Demand tends to spike during episodes of uncertainty, including the 2008 credit crisis and the 2011-12 period, when it seemed like the euro could be torn apart. This means that it is difficult to be sure how much of the recent pickup in demand for Swiss cash stems from the SNB's -0.75% deposit rate and how much is due to fear of a Greek government default, which would create havoc in world markets.  

Danmarks Nationalbank

Our final canary is the Danmarks Nationalbank. Unlike the demand for Swiss paper francs, the demand for Danish paper krone does not usually spike during times of crisis. For instance, during the 2008 credit crisis demand remained muted. This leads me to believe that demand for paper krone provides the clearest indicator yet of the presence (or not) of the effective lower bound. I've charted the year-over-year change in Danish currency in circulation.

In the 55 days that have passed since the Danmarks National bank reduced its rates to -0.75% (February 5), there has been a sustained rise in the demand for cash, as the red data indicate. But I don't think we can describe it as anything out of the ordinary, at least not yet.

Interestingly, in late March the Nationalbank granted Danish banks some wiggle room by providing them with greater access to the Bank's 0% current-account facility. This small adjustment would have reduced Danish banks' incentives to emigrate from -0.75% deposits into cash. Was the central bank's decision to provide this wiggle room a response to private data showing that it had hit the effective lower bound? Who knows.

It may be worth noting even if a central bank finds itself at the effective lower bound, it can forestall the demand for large denomination notes by using moral suasion. Willem Buiter mentions this possibility in his recent note High Time To Get Low, but maintains we have no evidence of this sort of pressure. I'm tempted to agree with him. If either the Danish or Swiss central bankers have put informal embargoes on cash, we would have known about it by now.

The use of moral suasion to prevent large denomination banknote storage would effectively freeze the quantity of high value notes in circulation. In such a scenario, we'd expect the 1000 Sfr note to rise to a slight premium to face value, say 1050 Sfr in bank deposits for each 1000 Sfr in banknotes. Traders would be willing to pay this premium as long as the storage costs on high value notes are lower than the -0.75% penalty set by the SNB on deposits, thus allowing them to earn an excess return on their note holdings. As long as moral suasion remains successful in choking off Swiss banks' demand for cash, each subsequent cut by the SNB into ever deeper negative territory would drive the premium on notes higher. (Assiduous readers will recognize this as the second of three ways for a lazy central banker to escape a liquidity trap.)

In sum, we probably haven't hit the effective lower bound yet. Stay tuned.

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.

No, Swiss National Bank shareholders are not pulling the strings

Swiss National Bank share certificates

Gavyn Davies blames the Swiss National Bank's corporate structure for the floating of the Swiss franc. Paul Krugman intimates the same, as does Cullen Roche. Here is Davies:

But the SNB is 45 per cent owned by private shareholders, many of whom are individuals, who receive dividends from the SNB. The rest is owned by the cantons, which have been complaining recently about insufficient cash transfers from the SNB.

Davies goes on to say that the influence of shareholders, combined with the peg, means that the SNB is particularly concerned about balance sheet losses. The idea seems to be that currency pegs often result in large balance sheet fluctuations, forcing a suspension of shareholder dividends.

I disagree, as a quick peek at the details shows:

1) The dividend to which Davies attributes so much importance is minuscule. In aggregate it comes out to just CHF 1.5 million per year, or US$1.7 million. Private shareholders, who own just 40.3% of the SNB's shares, are entitled to around 700,000 CHF per year in total. And these crumbs are shared among 2,219 private shareholders, most of whom hold ten shares or less. Are we to assume that these private interests care so much about the possible forfeiture of this trickle of cash (and just for a year or two) that they'd bother marshaling the significant effort required to influence Tommy Jordan, Chairman of the SNB, to drop the fixed exchange rate? Not a chance. These are nickles and dimes we're talking about.

2) Even if the shareholders organized themselves and tried to pressure Jordan, why would Jordan care? Jordan is Chairman of the three member Governing Board, which calls the SNB's monetary policy shots. He is appointed by the Federal Council, Switzerland's federal government, not by shareholders. Nor can the shareholders get him fired, as a quick reading of the National Bank Act reveals. Jordan can only be removed from office by the Bank Council. And while shareholders can elect five members to the Bank Council, the Federal Council, Switzerland's federal government, chooses the other six members, thus monopolizing the process. The upshot is that SNB shareholders have been neutered and exercise no control whatsoever over Tommy Jordan's thought process.

3) As for the interests of the Cantons, Tony Yates deals with them here.

I'm not sure why everyone is making such a big fuss of the SNB's corporate structure—it's hardly unique among central banks. The Federal Reserve, for instance, is 100% owned by private banks. We never worry about U.S. banks having an undue influence of U.S. monetary policy for the same reason we shouldn't worry about SNB shareholders having an influence on SNB policy—their power has been legislatively usurped by the government, as a quick reading of the Federal Reserve Act will show.

The deeper question is this: should the SNB (or any other central bank for that matter) take into account potential losses on its asset portfolio? In general, I think that the quality of a central bank's assets *should* be a factor that every central banker considers. If a central bank's assets have permanently ceased to yield enough income to cover the bank's salaries and expenses, then the central bank will have to cover this operating deficit by printing new money. Inflation will rise above target, forcing the central bank to sell assets in order to tighten the money supply. While this momentarily solves the inflation problem, it only further crimps the bank's supply of income-yielding assets and its ability to cover operating costs. A progressively slippier slope of ever more inflationary money printing to cover bills ensues.

This won't be a problem as long as the nation's government promises to recapitalize the central bank once problems emerge, thus topping it up with the resources to pay salaries and restore its inflation targets. Slippery slope avoided. But as I learnt a few years ago when reading a classic paper by Peter Stella, governments have been known to leave their central banks stranded. The Philippines' Bankgo Sentral is the best example of such a bank, the recapitalization it was promised by the government having been perpetually delayed. And as Stella points out, the central bank of Costa Rica has made losses for close to two decades consecutively, impeding the central bank’s ability to achieve low inflation. Prudence dictates a central banker be aware of the risk of being stranded.

All that being said, the SNB is really not at the point of having to be concerned about its operating position. The Bank's recent (and potential) losses are paper losses, not real ones. Bank expenses--including banknote printing, personnel, and overhead--still come out to just several hundred million francs a year, while its investments are providing billions worth of francs in interest and dividends. With Tommy Jordan's CHF 865,000 salary and all other expenses easily being covered, there's no slippery slope here. In sum, it is highly unlikely that the unhitching of the euro was motivated either by shareholder concerns or SNB worries about the effect of losses on its portfolio.

Links: 
Central Banks That Trade on the Stock Market
Does the Swiss National Bank need equity? - Speech by Thomas Jordan, 2011 (HT Vaidas Urba)

The ZLB and the impending race into Swiss CHF1000 bank notes

Two things worth noting:

1. As many of you know by now, the Swiss National Bank (SNB), Switzerland's central bank, just reduced the rate that banks earn on deposits held at the SNB by half a percentage point to -0.75% (from -0.25%). The SNB had only recently instituted a negative deposit rate, having reduced it to -0.25% from 0% this December. The SNB will also be targeting a 3-month LIBOR rate of -1.25% to -0.25%, down from the previous range of -0.75% to +0.25%


2. The SNB issues the world's largest paper bearer note denomination, the hefty CHF 1000 note (pictured above). It's worth around US$1143.

The first is significant because as yet, no central bank has ever brought rates this deep into negative territory. The ECB's current deposit rate is set at -0.2% while Denmark's central bank, the Danmarks Nationalbank (DNB), applied a negative deposit rate of -0.2% on deposits that banks placed with the DNB in 2012. Neither of these top the SNB's ultra-low -0.75% rate.

The second point is significant because neither the ECB nor the DNB issue a note that approaches the real value of the CHF 1000.

Why is the conjunction of these two observations important? In short, we get to observe in real time how tightly the so-called zero-lower bound (ZLB) binds. When a central bank reduces the rate it pays on central bank deposits below 0%, arbitrage dictates that all other short term interest rates will follow along, including rates on government t-bills and insured bank deposits. However, one asset interferes with this adjustment: cash. Cash carries an implicit yield of 0%. If deposits or t-bills are being penalized at a rate of 0.25% per year, there are significant incentives for everyone to convert these assets into zero-yielding paper equivalents in order to avoid the 0.25% penalty. Not only will commercial banks all convert their deposits at the central bank to cash, but the public will clear out their bank accounts in order to hold paper. The upshot is that interest rates can't fall below 0% lest the  entire country turn into a 100% cash economy.

In practice, the 0% bound isn't a tight one since paper currency incurs storage and transportation costs whereas electronic deposits don't. What this means is that a depositor will grudgingly accept a slightly negative deposit rate in order to avoid having to bear the inconveniences of ungainly cash. So the zero lower bound actually lies a bit lower than 0%, let's say -0.4%. However, reduce rates far enough below that and the dash to cash beings.

This is where the CHF 1,000 note comes into the picture. The larger the denomination of paper currency issued by a central bank, the lower the storage and transportation costs. Take CHF 1,000,000 worth of CHF 20 notes. That's 50,000 paper notes. The costs incurred in counting, double counting, checking for counterfeits, packaging, loading into an armoured car, unloading into a vault, paying storage costs on that vault, and finally insuring the hoard will be quite high. Now imagine CHF 1,000,000 worth of CHF 1000 notes. That amount to just 1,000 slim paper notes, a fiftieth of the amount. Handling and storage costs come out to much less. The point being that thanks to the CHF 1,000 note, the zero lower bound binds a bit more tightly in Switzerland than anywhere else in the world.

What I'd expect over the next few months is a mad dash out of deposits into these colourful bits of paper. Luckily, the SNB provides data on its note denominations, which I've charted below going back to 1990.

The value of CHF 1000 denomination notes in circulation. Source: SNB

You can see that in general, the value of CHF 1,000 notes outstanding has grown quite quickly since 1990 and now comprises around 61% of the entire value of the Swiss note circulation. While that tally retreated a bit in 2014, it should start to grow at an above-trend rate in 2015 now that negative rates are in effect. The actual process will go something like this; the Swiss public will ask to convert their bank deposits into CHF 1000 notes, the banks being obliged to provide these notes by going to the SNB and converting their SNB deposits into cash.

If this process doesn't occur, the implication is that the costs of holding 1000 notes are even higher than 0.75% a year, thus giving the SNB even more breathing room to reduce rates.

I'd expect ongoing conversion into 1000 notes to impose a significant burden on the SNB, threatening both the banking system's deposit base and the effectiveness of monetary policy. There are a number of fixes that the Swiss might consider to offset this burden. First, the SNB can bump interest rates back up in order to stem the mania for 1000 notes, hardly an alternative if it is trying to get inflation back up to  its target. Alternatively, the Bank may decide to call in and demonetize the CHF 1000 notes, forcing everyone to accept five CHF 200 notes in its place (an idea discussed here). Since the 200 incurs more carrying costs than the 1000, the conversion into cash will be forestalled and the lower bound will have effectively been loosened downwards. Lastly, the Swiss might consider adopting a crawling peg between cash and deposits, as advocated by Miles Kimball.

The next and last option is the most interesting. When the public asks the banks for CHF 1000s, and the banks ask the SNB for 1000s, the SNB can just say no. In doing so, the SNB will have frozen the quantity of 1000s in circulation.

What will happen next will amount to an instance of Gresham's law. Since a CHF 1000 note is better than five CHF 200 notes due to its lower carrying costs, and 200s can no longer be converted on demand into 1000s thanks to the SNB's freeze, the 1000 should trade in the market at a premium to its face value, say CHF 1012 or 1013. However, legal tender laws typically stipulate that a note cannot discharge debts at more than its face value, thereby resulting in the forced undervalution of the 1000 note in trade. As a result, the Swiss public and its banks will hoard their 1000s rather than spending them, preferring instead to make payments and settle debts with lower denominations notes. Thus we get a modern version of Gresham's law, whereby 'good' CHF 1000 notes are driven out of circulation by 'bad' lower-denomination CHF notes. Think of it as an unofficial demonetization of the 1000.

Ultimately, I think that this last solution is the easiest and lowest cost alternative for the Swiss to fix their impending problem of mass paper storage at the negative interest rates. It's a temporary fix, however. A permanent solution will require outright demonetization of large denomination notes, or something like Miles Kimball's plan.

Central banks that trade on the stock market

Most people don't realize that the central banks of Belgium, Japan, Greece, Switzerland, and South Africa are all publicly-traded. In times past, central clearinghouses were typically privately-owned while the issuance of bank-notes was the domain of competing banks. The fact that a few central banks still retain traces of their former private nature is a good reminder that centralized banking isn't necessarily the domain of the public sector.

The Swiss National Bank, for instance, was founded in 1907 to take upon itself the issuance of national bank notes, hitherto provided by private banks. According to Hübscher and Kuhn (pdf), efforts to establish a wholly government-owned central bank were defeated in an 1897 national referendum. Opponents of the plan drew up an alternative proposal for a privately owned bank the structure of which would, according to Bordo, "not allow for state socialism or the public control of credit policy." One fifth of the new bank's capital would be given to the private banks to compensate them for the loss of their power to issue notes.

Nowadays, SNB shares trade on the SIX Swiss Exchange. The original 100,000 shares are still outstanding, with 2,185 private shareholders owning about 37% of the float. Another 53% is owned by the cantonal governments and cantonal banks and the last 10% by other public institutions. The Swiss Federal council (Switzerland's federal government) doesn't own a single share, a contrast to most central banks which are 100% owned by their federal government. The largest private investor is Theo Siegert, who owns 5.95% of the float. The SNB provides all breakdowns here.

Though the shareholders of the five central banks may to some extent "own" their nation's central bank, they don't exercise the same degree of control over their company that regular shareholders do. Here are some of the drawbacks to owning central bank shares:

1. Capped dividends: The SNB's dividend is capped at 6% of the company's paid-up share capital. Because the SNB was originally capitalized with CHF 25 million, a large amount a hundred years ago but today a minuscule slice, aggregate dividend payments to all shareholders are limited to a mere CHF 1.5 million a year (around US$1.6 million), or CHF 10.50 per share. At today's stock price of CHF 1115, the shares yield just 1% or so.

This is a stable dividend. The SNB has paid it going back to at least 1996 (the last annual report I could get my hands on). But unlike the typical common share, there is no chance of this dividend growing.

2. Profits siphoned away: Nor will the profits that are not distributed to shareholders stay with the Bank. The lion's share of the SNB's remaining profits go to the state. Specifically, two-thirds of earnings are paid to the cantonal governments, and another third to the Federal council. In 2011, for instance, the SNB earned CHF 4.9 billion. A tiny CHF 1.5 million sliver was paid to shareholders while the various governments received CHF 1 billion (the balance was held over as reserve for the next year).

Much like the SNB, the Bank of Japan (BOJ) pays a fixed dividend. The BOJ, established in 1882, trades on the JASDAQ for around ¥46,500 a share. The Bank is not permitted to pay more than 5% of its  ¥100 million in paid-up capital to shareholders. As is the case with the SNB, this was a large amount back in 1942, the last time the BoJ was capitalized, but today its amounts to just ~$10 million. The upshot is that the BOJ can only provide shareholders a piddling ¥5 million in aggregate dividends a year, or  ¥5 a share. This equates to just US$50,000 in aggregate dividend payments, or around 5 cents a share. Considering that total profits earned by the BOJ in 2011 amounted to  ¥503 billion (around $5 billion), the shareholders are getting peanuts.

3. Minority position: Unlike the SNB, the Japanese federal government owns 55% of the Bank's shares. This puts private shareholders at an even larger disadvantage since they must play second fiddle to a dominant shareholder at all shareholder meetings.

4. No residual claim: The Bank of Japan Act stipulates that should the Bank be dissolved, shareholders only get a return of initial paid-up capital. All residual assets belong to the national treasury. Thus shareholders get a mere  ¥100 million (around $1 million) back in case of dissolution, or around  ¥100 per share -- far less than the current  ¥46,500 a share. Genuine common shares would allow shareholders to get all residual assets.

According the the National Bank Act, SNB shareholders are also restricted in their ability to claim residual assets:

In case of a liquidation of the National Bank, the shareholders shall receive in cash the nominal value of their shares as well as reasonable interest for the period of time since the decision to liquidate the National Bank became effective. The shareholders shall not have any additional rights to the assets of the National Bank. Any remaining assets shall become the property of the new central bank.

This means that each SNB shareholder is entitled to CHF 250 a share upon dissolution, far less than the current CHF 1150 per share price.

4. Inability to select management. Even with their voting power, SNB shareholders have little influence over the composition of bank management. The supreme managing and executive body of the Bank is the three-member Governing Board. All three members are appointed by the Federal Council upon recommendation of the SNB's Bank Council. Here shareholders do exercise some power. They have the ability to vote 5 members of the Bank Council. But the remaining 6 are appointed by the Federal Council, which means that the Federal Council can always stack the deck to ensure that its people get appointed to the Governing Board.

In the BOJ's case, it appears that shareholders have no ability whatsoever to select BOJ officials.

5. Voting limitations: The SNB limits non-public shareholders to a maximum of 100 votes. Even though Theo Siegert owns 5,950 shares, he only gets 100 votes. Most common shares carry the privilege of one share, one vote.

The South African Reserve Bank (SARB) also imposes artificial limitations on shareholders. No single shareholder is allowed to hold more than 10,000 of the 2 million shares outstanding. This limits the ability of individuals shareholders or blocks of shareholders to exercise voting control, a key element of modern shareholder activism.

The SARB was established in 1921 and, much like the SNB, replaced the existing network of private bank-note issuers then operating in South Africa. Its shares currently trade for about R7.00 on a SARB-hosted OTC market rather than the local Johannesburg Stock Exchange from which the shares were delisted a few years ago. The market is thin, although according to the bank's records there are over 600 shareholders. Like the SNB, the federal government does not own a single share of the Bank.

Similar to the SNB and BOJ, the SARB can only pay a fixed dividend of 10% on paid-up capital. With just R2 million in paid-up capital outstanding (about $225,000), the Bank only distributes R200,000 a year, or R0.10 a share. Compared to the R53 million in central bank profits paid to the government in 2011, shareholders get next to nothing.

Because the return on all three central bank shares so far discussed is calculated on a nominally fixed amount of paid-up capital from a bygone era when a few million dollars was still a large amount of money, they trade more like perpetual bonds than stocks. But this isn't the case for our fourth publicly-traded central bank -- the Bank of Greece (BoG). In 1927, the private National Bank of Greece waived its right to issue bank-notes in return for handling the IPO of the new Greek central bank. The BoG currently has some 19,000 shareholders and trades on the Athens Exchange for around €16.

What makes the Bank of Greece unique is that it pays a fixed 12% dividend on paid-up capital and an additional dividend based on remaining profits. Whereas the first payment is fixed relative to paid-up capital, the second is floating, thereby allowing shareholders to get exposure to continued growth in the Bank's business. The floating dividend also exposes shareholders to declines in the Bank's business, which is what has happened over the last few years:

Due to the euro crisis, the floating portion of the dividend has collapsed from over €40 million to zero. The upshot is that BoG shares are much more volatile than the shares of their fixed-rate cousins the BOJ, SNB, and SARB. Below is the share price of the BoG, which seems to trade much like a regular bank common share:

The National Bank of Belgium (NBB) falls in the same mold as the BoG. The NBB was founded in 1850 as a limited liability company, with shares distributed to private banks who in exchange agreed to forgo the privilege of issuing bank-notes. The Belgian government subscribed to 50% of the shares in 1948. The Bank's constituting articles specify a minimum 6% dividend on paid-up capital and an additional dividend to be paid after the reserve fund has been topped up:

Article 32. - The annual profits shall be distributed as follows:
1. a first dividend of 6% of the capital shall be allocated to the shareholders;
2. from the excess, an amount proposed by the Board of Directors and established by the Council of Regency shall be  independently allocated to the reserve fund or to the available reserves; 
3. from the second excess, a second dividend, established by the Council of Regency, forming a minimum of 50% of the net proceeds from the assets forming the counterpart to the reserve fund and available reserves shall be allocated to the shareholders;
4. the balance shall be allocated to the State; it shall be exempt from company tax.

In 2011, the bank earned €900 million. Of this, a healthy  €61.6 was paid out to shareholders, with €225 and €618 allocated to the reserve fund and government respectively. The first dividend, it should be noted, amounts to a mere €600,000 a year, since it is based on a percentage of legacy paid-up capital from the 1800s. The second dividend provides pretty much all of the returns. Thanks to the floating nature of the second dividend, the NBB's dividends have appreciated nicely over the last decade:

Despite this stability, its shares, which trade on Euronext Brussels, have been volatile, falling from over  €4,000 per share in 2010 to under €2,000 last year:

Compare the NBB and BoG variability to the relative stability of the SNB, with its fixed coupon:

According to the SNB's 1997 Annual Report, the massive 1997 price spike was anomalous and due entirely to speculation surrounding the effects of the Bank's planned marking-to-market of their gold holdings:

The rise was apparently due to recommendations made in various broker reports, which were based on hopes that the planned revaluation of the gold reserves would generate additional earnings for the National Bank’s shareholders. However, the authors of these recommendations failed to note that the law earmarks for public use any profits in excess of the maximum dividend of 6%.

A sure example of the EMH not working.

It mystifies me why BOJ shares are so volatile. They promise a fixed and stable dividend, yet have collapsed from over ¥170,000 a share to ¥30,500 over the last few years. What happened in September 2005 that caused the shares to almost triple in value? Shares have recently rallied on the news that the BOJ will target 2% inflation, which is odd, since as a bond-like investment, the shares should fall with the promise of more inflation, not rise:

Below are the five central banks with their respective dividends and market capitalizations:

The NBB has the largest market cap, and justifiably so since it pays an attractive floating second dividend and, unlike the BoG, is a relatively stable institution. I find it amusing that the entire SARB can be bought for a mere $1.5 million. You can own a nation's central bank for the price of a large house!

What is even more odd is the terrific valuation being put on BOJ shares. In aggregate, BOJ shareholders earn a miserable $53,763 a year in dividends, only twice what SARB shareholders earn in aggregate. Yet the Japanese market is putting a value of $500 million on that cash flow, or 500x more than the value that shareholders put on SARB cash flows. BOJ shareholders have absolutely no claim on residual assets. What are they thinking?

Which one would I buy? Gun to my head, I'll take BoG shares. When things get back to normal they'll be paying a  €3 dividend which you can buy now for  €16 or so. But if you're going to take any profit from this post, hopefully its because it gives you another perspective from which to view centralized banking.