The law of reflux

One of the coining press rooms in the Tower of London, c.1809 [link]

[This is a guest post by Mike Sproul.]

The law of reflux thus assures the impossibility of inflation produced by overexpansion of bank credit. (Blaug, 1978, p. 202.).

It is the reflux that is the great regulating principle of the internal currency; and it was by the preservation of the reflux, throughout all the perils and temptations of the period of the restriction, that the monetary system of these kingdoms was saved from the utter wreck and degradation which overwhelmed every paper-issuing state on the Continent… (Fullarton, 1845, p. 68.)

If you want to understand the law of reflux (and you should), then think of silver spoons. The silversmith shown in figure 1 can stamp 1 oz. of silver into a spoon. If the world needs more spoons, then silversmiths will find it profitable to stamp silver into spoons. If the world has too many spoons, then people will find it profitable to melt silver spoons. Unwanted spoons will “reflux” back to bullion. In this way, the law of reflux assures that the world always has the right amount of silver spoons. We could hardly ask for a simpler illustration of the Invisible Hand at work. But it costs something to stamp silver and to melt it, so the price of spoons will range within a certain band. It might happen, for example, that silversmiths only find it profitable to produce spoons once their price rises above 1.03 oz., while people only find it profitable to melt spoons once their price falls below 0.98 oz. If the costs of minting and melting were zero, then a spoon would always be worth 1 oz.

This is a point worth emphasizing: The value of a spoon is equal to its silver content. An increase in the demand for spoons would not raise the price of spoons much above 1 oz, since new spoons would be produced as soon as the price rose above 1 oz. A drop in the demand for spoons would not push the price much below 1 oz, since spoons would be melted when the price fell below 1 oz. Likewise, if the quantity of spoons supplied became too large or too small, market forces would restore the quantity of spoons to the right level, while keeping the price at or near 1 oz.

In figure 2, the silversmith starts being called a mint, and instead of stamping silver into spoons, the mint stamps silver into 1 oz. coins. The law of reflux works the same for coins as for spoons, always assuring that the world has the right amount of coins, and that the value of each coin always stays at 1 oz., or at least within a narrow band around 1 oz.

The usual thought experiments of monetary theory don't work in this situation. For example, economists often imagine that if the money supply were to increase by 10%, then the value of money would fall by about 10%. But the law of reflux won't allow this to happen. Mints would only issue 10% more coins if the public wanted coins badly enough to part with an equal amount of their silver bullion. And even if mints went against their nature and issued more coins than the public wanted, those coins would be melted or stored, and the value of a coin would not deviate very far from its silver content of 1 oz.

In figure 3, the mint re-invents itself again, this time as a bank. Rather than stamping customers' silver into coins, the bank stores the silver in a vault, and issues a paper receipt called a bank note. (Checkable deposits would also work.) This system has several advantages over coins. (1) It saves the cost of minting and melting. (2) It avoids wear of the coins. (3) Bank notes are harder to counterfeit, easier to carry, and easier to recognize than coins.

The law of reflux still works the same for bank notes as it did for coins. If the economy is booming and people need more bank notes, then people will deposit silver into their banks and the banks will issue new bank notes. If the economy slows and people need fewer bank notes, then people will return their unwanted notes to the banks and withdraw their silver.

Once again the thought experiment of imagining a 10% increase in the quantity of bank notes is pointless. Banks would only issue 10% more notes if the public wanted those notes badly enough to bring in 10% more silver. And even if we imagine that the banks took the initiative, printing 10% more notes and using those notes to buy 10% more silver, every bank note is still backed by 1 oz. and redeemable into 1 oz of silver at the bank, so every bank note remains worth 1 oz.

In figure 4, the bank makes one more important change. Rather than requiring customers to bring in 1 oz of actual silver to get a bank note, the bank also accepts an equal or greater value of bonds, bills, real estate deeds, or anything else that can fit in the vault. This system has several advantages: (1) Handling bonds, etc. is easier and safer than handling silver. (2) The silver formerly deposited can be put to productive use. (3) The quantity of bank notes is no longer constrained by the amount of silver available. (4) The bank earns interest on its bonds, bills, etc.

The law of reflux still operates as before, except that when people want more notes, they can bring in either silver or bonds, and when people have excess notes, the notes can be returned to the bank for either silver or bonds. As before, it makes no sense to ask questions like “What if the bank issues 10% more bank notes?” And as before, so long as every bank note is backed by, and convertible into, 1 oz. worth of assets, every bank note will be worth 1 oz. Just as reflux assures that the value of a spoon is equal to its silver content, reflux also assures that the value of a bank note is equal to the value of the assets backing it.

The Channels of Reflux

Here is a list of some of the many channels through which bank notes might reflux to the issuing bank:
1. The silver channel: Unwanted notes are returned to the bank for 1 oz. of silver. Alternatively, the bank sells its silver for its own notes, which are retired.
2. The bond channel: The bank sells its bonds in exchange for its notes, which are retired.
3. The loan channel: The bank's borrowers repay loans with the bank's own notes.
4. The real estate channel: The bank sells its real estate holdings for its own notes.
5. The rental channel: The bank owns rental properties, and tenants pay their rent in the bank's notes.
6. The furniture channel: The bank sells its used furniture for its own notes.

As long as enough reflux channels are open, it does not matter if a few channels are closed. Customers would not care if the furniture channel was closed, as long as major channels, like the bond channel, stayed open. The bank could take a more drastic step and close the silver channel, or could delay silver payments by 20 years, and as long as enough other channels stayed open, the law of reflux could operate as always, except that notes might be redeemed for 1 oz. worth of bonds, rather than 1 oz. of actual silver. The bank could even un-peg its notes from silver. Rather than redeeming a refluxing dollar note for 1 oz. worth of bonds, it could redeem dollar notes for 1 dollar's worth of bonds. As long as the bank's assets are worth so many oz., it doesn't matter if those assets are denominated in oz. or in dollars.

Once metallic convertibility is suspended, it would be an understandable mistake if people forgot all about the other channels of reflux, and started to think that bank notes were no longer backed by, or convertible into, anything at all. Unfortunately, this mistake has made it into the textbooks:

You cannot convert a Federal Reserve Note into gold, silver, or anything else. The truth is that a Federal Reserve Note has no inherent value other than its value as money, as a medium of exchange. (Tresch, 1994, p. 996.)

There you have it. The closing of just one channel of reflux (the metallic channel), has fooled economists into wrongly rejecting the idea that modern bank notes like the US paper dollar are backed and convertible. Once economists reject this simple and obvious explanation for why modern paper money has value, they are forced to resort to the more exotic explanations offered by textbook monetary theories, which are anything but simple and obvious.

References
Blaug, Mark, Economic Theory In Retrospect, 3/e. Cambridge: Cambridge University Press, 1978
Fullarton, John, Regulation of Currencies of the Bank of England (second edition), 1845. Reprinted by Augustus M. Kelley, New York: 1969.
Tresch, Richard, Principles of Economics, St. Paul, Minnesota: West, 1994

A brief history of the Guinea

1685 Guinea with the bust of James II (link)

The guinea makes a fascinating story because its evolution reveals so many different monetary phenomena. It began its life in 1663 in the Kingdom of England as a mere coin, one medium of exchange in a whole sea of competing exchange media that included crowns, bobs, halfpennies, farthings, not to mention all the foreign coins that circulated in England, Bank of England paper notes, as well as the full range of portable property—like jewelery and art—and property-not-so-portable, say houses and land and such. If things had stayed that way, the guinea's life would be a boring one and I wouldn't be writing about it.

But in the late 1600s the guinea crossed a line and became a very different thing. Rather than functioning as just one exchange medium among many, the guinea suddenly emerged as one of Britain's two media of account, the items used to define a nation's unit of account, in this case the £. Within a few decades it had wrested the medium of account function for itself, holding this pre-eminent spot until 1816, at which point the guinea was decommissioned.

Interestingly, while the guinea ceased to exist in 1816, its memory was sufficiently strong that it continued to function as a unit of account, albeit a relatively unimportant one, well into the 1900s. More on that later.

Just a regular coin

Whereas most of England's coinage at the time was silver,  the guinea was a gold coin. Introduced in 1663 during the reign of Charles II, it was initially rated at 20 shillings, or one pound (£), by the monetary authorities (the mint and the king). Pounds, shillings, and pence, or £sd, comprised the English unit of account—the set of signs that merchants affixed to their wares to indicate prices. The pound unit had been defined in terms of silver coins for centuries, but the the decision by the mint to give a 1 pound (or 20 shilling) rating to the guinea meant that the pound would now be dually defined in terms of both gold and silver coins.

However, according to Lord Liverpool, both the public and the authorities ignored this 20 shilling rating so that a market-determined price emerged for the guinea. In this way the guinea was no different from any other item of merchandise; its price floated independently according to the whims of buyers and sellers.

This stands in contrast to England's silver coinage. Silver pennies, halfpennies, and farthings had an extra function; they served as the nation's medium of account. The pound unit, the £, the symbol with which merchants set prices or denominated debts, was defined by the nation's silver coinage. Put differently, by setting a farm's price at £10, a seller was stipulating that the farm was worth the amount of silver residing in a collection of pennies and farthings.

When something serves as the medium of account, it's price doesn't float independently. Rather, the whole universe of other prices shifts to accommodate changes in the value of the medium of account. For example, if the value of silver were to have risen in the 1670s due to increased demand for silver jewelery, then the entire English price level would have had to fall. Alternatively, if the amount of silver in the nation's coinage was debauched, then the English price level would have risen. A change in the demand for gold in the 1670s, however, would have produced an entirely different result; the relative price of the guinea would have shifted, but little else. That's why a medium of account is so special. Unlike all other items, the price of everything pivots around it.

The fact that the guinea's initial 1663 rating had been ignored was very important. Imagine that the authorities had been stern about enforcing it. Returning to our farm example, in setting the farm's price at £10, our seller would have been stipulating that the farm was worth either the amount of sliver residing in a collection of pennies and farthings, or the amount of gold residing in the guinea. A very different monetary system would have emerged; bimetallism. But more on that later.

Liverpool tells us that the guinea fluctuated between 21 and 22 shillings in its first decades, but in 1695 its price rose rapidly to 30 shillings. This wasn't because of an increase in the demand for gold but a function of the quickening pace of clipping and sweating of pennies, which reduced the quantity of silver in the coinage. Guineas weren't the only commodity to rise in 1695; the entire array of English prices had to pivot around the diminishing value of the silver penny. Once the silver coinage was reformed (its silver content being restored) in the Great Recoinage of 1696, the price of guineas quickly returned to 22 shillings.

The switch to bimetallism

Things all changed in 1697 when the Exchequer, the department responsible for receiving taxes, announced that all guineas were to be accepted by the Exchequer's tellers at 22 shillings. Prior to then, the Exchequer had accepted guineas at the going market rate. As Sykes points out, after 36 years of floating this was tantamount to fixing the price of the guinea relative to silver. Guinea couldn't circulate for less than this stipulated amount, say 21 shillings, because an arbitrageur would mop up those guineas at 21 shillings and use them to pay 22 shillings worth of taxes, earning him or herself a 1 shilling gain. (The next year, the Exchequer would reduce this rate to 21 shillings 6 pence.)

Britain, which had been on a silver standard up to 1697, was now on a bimetallic standard, with the £ unit defined as the amount of silver residing in the English penny, and simultaneously the amount of gold residing in the guinea.

The guinea takes over

The problem with the new standard was that in setting the guinea at 21s 6p, the Exchequer had overvalued gold relative to the market price, more specifically the silver-to-gold ratio prevalent in the rest of the world. By how much? In 1702 Sir Isaac Newton, Master of the Mint since 1699, concluded that 'Gold is therefore at too high a rate in England by about 10 pence or 12 pence in the Guinea.' In other words, the Exchequer should have announced it would only accept guineas at around 20s 6p, or 4.6% less than it had.

What were the consequences of this over-valuation? All of the silver pennies began to leave Britain, gold coins filling the void. Given the choice between paying a debt or a tax in either an overvalued or undervalued instrument, people will always select to use the overvalued one. After all, buying 20 shillings 6 pence's worth of gold in France and using it to discharge a 21s 6p shilling tax liability in England resulted in a 4.6% profit (less transportation and minting costs). The undervalued instrument, in this case silver, is best used in other parts of the world where it is capable of purchasing a larger real amount of goods (or discharging a larger real quantity of taxes) than in the country in which it is artificially undervalued. This is, of course, Gresham's law; the bad drives out the good.

So our guinea, which had started its young life as a mere medium of exchange, had not only graduated to becoming one of only two English media of account, but was responsible for the mass flushing out of silver from England.

By 1717, the silver outflow was getting significantly bad that the authorities decided to do something about it. Newton, still Master of the Mint, noted that the market price for the guinea was around 20s 8d, given the exchange rate between silver and gold in other European markets, and suggested an initial rate reduction from 21s 6d to 21 shillings.

But even at this lower price the English authorities were still overvaluing the yellow metal. They had now fixed the silver to gold ratio at 15.069 to 1, but because the rate was 14.8 to 1 in Holland and France, a profit still remained on exporting silver and importing gold. This silver outflow would continue over the decades until most silver was gone. England had gone from a bimetallic standard to a monometallic standard. Though it was still de jure bimetallic, de facto it had become a gold standard. And the guinea, which was now the controlling element in English prices, was to blame (or at least the decision to misprice it was).(1)

The end of the guinea

For the next century, the English price level pivoted around the value of the gold guinea, until the Great Recoinage of 1816, at which point the guinea's life suddenly came to an end. Since the days of Isaac Newton, the guinea had been awkwardly rated at 21 shillings, or one pound one shilling. This must have made payments somewhat arduous since there was no coin that could satisfy an even 1 pound bill or debt, and people like round numbers. The decision was made to introduce a less awkward gold coin, the sovereign, with slightly less gold. The sovereign was conveniently rated at exactly 1 pound, or 20 shillings, the upshot being that the pound unit of account still contained just as much physical gold as before, but now a coin existed that corresponded with the exact pound unit. The guinea was dead.

_______________________


Well, not entirely. Though is was no longer being minted, the guinea continued to be used as a way to price items. According to Willem Buiter (pdf), auction houses and "expensive and pretentious shops" continued to set prices in terms of guineas through the 1800s and 1900s. Bespoke tailoring and furniture, for instance, was quoted in the legacy gold coin. The unit used was g, or gn, with the plural being gs or gns, although payments were made in sovereign coins or Bank of England notes.

Gillette advertisement (link)

Doctor's and lawyer's fees, often known as "Guinea fees" we're advertised in terms of the legacy gold coin. Whereas common laborers were paid in pounds, payments in guineas was considered more gentlemanly. You can see it pop up in the literature of the time. In Arthur Conan Doyle's Sherlock Holmes tale the Adventure of the Engineer's Thumb a stranger offers Mr Hatherly, a hydraulic engineer who is down on his luck, a unique proposal. "How would fifty guineas for a night's work suit you?"

An ad from 1929 (link)

The standard rate paid by Charles Dickens for contributions to his weekly periodicals Household Words and All The Year Round was half a guinea a column or a guinea a page. In his novels, the guinea pops up often. In Oliver Twist (set in the 1840s), a 5 guinea reward for information on Oliver is posted by the kind Mr. Brownlow.

In more modern times, horses continue to be auctioned in terms of guineas.

Dancing Rain sold for 4 million guineas (link)

Now of course this is a bit of a come-down for the once almighty guinea. Serving as the unit at Tattersalls isn't the same as underpinning the entire price level. But at least its better than the sovereign, the coin that replaced the guinea, which has gone silent, or most other medieval coins for that matter, which neither circulate nor serve as legacy units.

---

(1) The 1717 reduction of the guinea to 21 shillings was accompanied by the requirement that those guineas be accepted as legal tender at that price. Prior to then, only silver had functioned as legal tender, meaning that a debtor could only discharge a debt with silver coins. After the change, a debtor could choose to use either guineas or silver coins to pay off their debt, a decision made easier given gold's overvaluation.

Some References:

Lord Liverpool, A Treatise on the Coin of the Realm, 1805.
Sargent & Velde, The Big Problem Of Small Change, 2001.
Selgin, Good Money, 2008.
Sykes, Banking and Currency, 1905. 
Macleod, Bimetallism, 1894.

Getting naked: in praise of naked short selling

Photo by Spencer Tunick, Netherlands 8 (Dream Amsterdam Foundation) 2007 [link]

If short sellers are considered to be the Mussolinis of the financial market, then naked short sellers are its Hitlers.

In this post I'll show that naked short selling isn't solely a hedge fund or equity market phenomenon. In fact, the good old fashioned practice of deposit banking amounts to what is essentially naked short selling, thus making staid bankers, and not hedge funds, the world's largest naked short sellers. This means that anyone who vilifies the naked short selling of equities must also be against the common practice of banking—a crack pot position if there ever was one.

Short selling is when an investor borrows shares of, say, Microsoft, then sells those shares in the open market. At some point—either at the lender's behest or the investor's—the borrower will repurchase the shares in the open market and return them to the lender. A short seller hopes that the price of Microsoft has declined in the interim so that when the time comes to repurchase them, it will cost less money, thus resulting in a profit to the short seller.

Naked short selling is similar in every respect save for one: when our investor sells Microsoft shares short in the open market, they do so without borrowing those shares ahead of time. (To get more specific, read this SEC page)

Which sounds odd, right? How can someone sell something if they haven't either purchased it or borrowed it ahead of time? No wonder people wrinkle there noses at the practice of naked shorting—it seem like sleight of hand!

The best way to think about naked short selling is to turn to banking. Why? Because bankers engage in short selling every.single.day. Just as an equity short seller will borrow and then sell Microsoft with the intention of repurchasing it at a better price, bankers borrow and then sell dollars with the intention of repurchasing them at a better price. Apart from the respective instruments involved, dollars vs stock, there's no difference between what an equity short seller and banker are doing.

So if bankers engage in short selling, do they act as mere regular shorts sellers or do they get naked?

In the previous paragraph you may have noticed that I described banking as the borrowing of depositors' dollars in order to lend those dollars out. Because the dollars were borrowed prior to sale, this would qualify their activity as regular short selling, not naked short selling.

But hold on, this isn't at all how banks function. Bankers don't wait for physical Federal Reserve dollars to be deposited by the public before selling them away—they short dollars whenever they wish, creating electronic deposits out of nothing in order to buy things like bonds or personal IOUs. Banks are engaged in naked shorting pure and simple: they sell a financial instrument that they never actually had in their possession.

How do they do this? The key here is that banks don't actually sell Fed paper dollars short, rather, they sell dollar-linked IOUs (i.e. deposits) short. A deposit is a claim on the bank's capital that mimics Fed paper dollars by being indexed, or denominated, in terms of those paper dollars. It's similar to a Fed dollar, but it's an entirely different instrument.

Circling back to naked equity short sellers, the same thing is occurring when a naked short is initiated. The instrument that they are selling short isn't a Microsoft share, but a newly-created IOU that is denominated in Microsoft shares. It would be as if I gave you scrap of paper with the words "I owe you one Microsoft share" on it. Rather than buy a real share, you could just hold the IOU I gave you. The instrument would look like a share, walk like a share, and even circulate alongside shares, however it would be an entirely new financial instrument.

This ability to "print" new IOUs denominated in terms of Federal Reserve dollars (in the case of the banker) or in terms of Microsoft shares (in the case of the short seller) often results in a quantity of derivative units that far exceeds the underlying issue of base units. We get an inverted triangle of sorts where on top of a narrow base of Fed paper dollars is arrayed a much larger quantity of dollar-denominated deposits, often 10 or 20 times more. Likewise, the number of Microsoft-denominated IOUs that naked short sellers create may eclipse the number of actual Microsoft shares outstanding.

It is the naked short seller's possession of a so-called printing press that draws the wrath of CEOs. The accusation is that a hedge fund can make a good profit by manufacturing and selling massive quantities of Microsoft-denominated IOUS in order to drive Microsoft's stock price down to zero, thus benefiting its short position. Emblematic of this belief is the battle waged by Overstock CEO Patrick Byrne against short sellers who had been engaging in naked selling of his firm's stock, which had fallen on hard times. As early as 2005, Byrne accused short sellers of creating a fake supply of Overstock shares (at one point reputably six times more than actual shares issued) in order to drive its price lower. Byrne went so far as to launch several lawsuits against the perpetrators.

How legitimate is Byrne's concern? Let's return to our bank analogy. Is there anyone who would argue that because banks can create and short deposits willy nilly, they'll drive down the underlying Fed dollar's price towards zero (ie. create hyperinflation) and thus earn outsized profits? Of course not. Banks in the U.S. and Canada have been creating deposits for centuries without causing hyperinflation. It simply isn't a concern because the issuer of underlying dollars, the Federal Reserve, stands ready to support the value of the dollars it has issued. It can provide this sort of anchor because it holds a variety of assets that can be mobilized to repurchase and cancel paper dollars, thereby removing any excess supply that might emerge thanks to competing issues of dollars by banks.

Likewise, if naked short selling creates a glut of Overstock IOUs and begins to drive down the price of Overstock, then in the same way that the Fed can deploy its assets to remove the supply of Fed dollars to stabilize their value, Overstock's Patrick Byrne could have used his firm's assets to repurchase stock. If he chose not too do a buy back, one might wonder if his company had the assets on hand to begin with.

To sum up, in the same way that bank issuance of dollar-denominate IOUs cannot drive the purchasing power of underlying Fed dollars down as long as the Fed has sufficient assets and chooses to use them, neither can naked short sellers drive Overstock prices down if the company has sufficient assets and is willing to conduct the necessary repurchases.

So haters of naked short selling, are you consistent in calling for an outright bank on banking? You say that naked shorting drives down stock prices, which means you no doubt also believe that banks inevitably create hyperinflation, right?

Addendum:
JKH has a post on the topic here, the Full Monty on Naked Short Selling.

Getting rid of the monetary triumvirate

The textbook definition of money is anything that functions simultaneously as a store of value, a medium of exchange, and a medium of account. This is the monetary triumvirate, and we need to get rid of it.

The first problem with this explanation is that all goods and assets function as stores of value, some better than others. Items that can't 'store' value would be be worthless because their lives would be too fleeting to provide any utility. Even an ice cream cone serves as a store of value, at least for a few minutes.

So if everything serves as a store of value, then money must be that peculiar good that functions as both a medium of exchange and a medium of account, right?

Wrong. All valuable things function as media of exchange, or, put differently, they all have a degree of exchangeability. A head of cabbage is a cabbage farmer's medium of exchange, since he uses it exchange with a food distributor, and it also functions as one of the distributor's many media of exchange, since he uses it to exchange with a grocer, and it also functions as one of the grocer's many media of exchange, since the grocer holds an inventory of cabbage in order it to exchange with the public. We can quibble over the general acceptability of any given medium of exchange; a dollar bill is more exchangeable than a cabbage, after all. But a dollar bill, like a cabbage, is not universally acceptable—try buying a house with it, or Microsoft stock.

So if everything serves as a store of value to some degree or other, and everything serves as a medium of exchange to some degree or other, then money must be that peculiar good that functions as a medium of account.

The upshot is that the only binary difference between the various goods and assets in this world is along the medium of account-or-not axis, both the store of value and medium of exchange functions being ranges or spectra, not binary categories. This means that a good is either a medium of account, or it isn't. There's no point in using an umbrella word like "money" anymore, since medium-of-account stands on its own as a useful definition.

A medium of account, if you don't remember, is the good that we use to quote prices. There are only a handful of media of account in the world, with the great majority of things not functioning as media of account. Dollar bills are certainly a medium of account. Credit cards (combined with network fees) also function as a medium of account. There are weird artificial media of account, like whatever is used to define Chile's Unidad de Fomento. Commodities like cloth, or macutes, have served as media of account in West Africa, as have silver pennies in Europe.

So let's retire that tired old triumvirate. The word money is redundant and meaningless; if we really want to divide the world into these and those, the medium-of-account bucket is about all we need. The other two functions, store of value and medium of exchange, are pervasive rather than exclusive (everything has at least a little bit of each), and therefore can't serve as the basis for drawing strict lines between goods.

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

A market for corporate votes

Berkshire Hathaway annual general meeting

When you purchase a share you're not only getting the opportunity to make some extra cash. You're also buying a vote. Put differently, a share offers two different features: a) a claim on earnings and b) the right to exercise partial control over the corporation.*

Why not separate the two features and put each of them up for sale? Let's have one market for corporate votes, and a separate one for corporate returns.

Here's how it would work. Imagine you want to buy some Microsoft shares but don't care to participate in the governance of Microsoft. The quoted price on the market, $44.93, is for a whole share of Microsoft, both its attached voting rights and its capitalized return. So you buy 500 whole shares for $27,465.

Next you turn to the parallel public voting market. Microsoft votes are trading for around 25 cents each, say. You 'detach' each of the 500 votes from the shares you've just bought and sell those votes for 25 cents each in the voting market for a combined $125. Not a bad day's work. In selling the votes that you never wanted anyways you've defrayed your initial purchase cost.

A few years later you decide to get out of Microsoft. One way is to find a set of buyers who, like yourself, don't care to vote, and sell the voteless shares directly to them. Alternatively you can repurchase the 500 votes in the voting market, reattach them to the shares, and sell them in the whole share market.

Here's another hypothetical: imagine that you have 500 shares of Microsoft but feel that it's your destiny to have a much more active role in Microsoft governance than your 500 votes would otherwise provide. Say you'd like ten times the votes, or 5,000 votes. To amass that quantity of votes it would normally cost you the price of 4,500 additional shares at $44.93 each, or about $207,000, but that's far out of your league. That's where the market for Microsoft votes comes in. For a mere $1125 you can pick up 4,500 detached votes, assuming they trade at 25 cents each. Without having stumped up too much capital, you've become a much more formidable shareholder activist.

So why have a market for corporate votes?

According to Broadridge, some 70% of retail shares go unvoted. Participation rates are better on the institutional front where some 90% of institutionally-owned shares are voted, but this is due to a legally-mandated fiduciary responsibility to vote. The responsibility for voting these shares is usually outsourced to a proxy advisory company like ISS which, according to one account, advised on over 50% of corporate votes cast in the world. ISS's success is due in part to the fact that institutional shareholders have scarce resources, most of which are ready allocated to searching for new investments and monitoring existing ones. They can't spare the cost of setting up expertise in corporate governance.

So to a large proportion of retail and institutional investors, votes represent little more than a nuisance. In order to play the stock market game, these investors hold their noses and pony up enough cash to buy a share and its combined vote; but they'd really be quite happy if they didn't have to buy the latter, especially if it meant reducing their overall costs.

If those who view votes as a nuisance comprise the sell side of the corporate vote market, then the buy side would be comprised of a cadre of institutional investors who specialize in corporate governance and shareholder activism. Activist investors, say someone like Bill Ackman, have developed expertise and a set of practices that allow them to efficiently put votes to work, instituting change in a company's structure or management in order to make it more profitable. They place a much higher marginal value on the votes attached to shares than the majority of their not-so-active colleagues.

A market in corporate shares would allow both the apathetic and the active to meet, with the final result being a more efficient allocation of returns and voting rights.

What I'm proposing may sound a bit sci fi, but what if I told you that such a thing already exists?

The fact is that we already have an informal market of sorts in corporate votes. In Canada, for instance, firms often issue both non-voting, voting shares, and multiple voting shares. In the U.S. the practice is less common, one example being Google which has issued 'A' shares with one vote apiece; 'B' shares with ten votes each; and 'C' shares with no votes. Or consider Warren Buffet's Berkshire Hathaway. An owner of $10,000 worth of Berkshire Class B shares has 0.15% of the votes that an owner of $10,000 worth of Class A shares has.

When companies have dual share structures, to buy votes, an investor need only short the non-voting shares in order to fund a long position in the voting class. And to sell votes, do the opposite. The cost one would incur on this transaction indicates the dollar value the market places on the right to vote.** Canadian readers may well remember that Mason Capital engaged in this strategy with Telus shares back in 2012 when it purchased Telus voting shares and shorted its non-voting shares.

But there's a more interesting way to get one's hands on extra votes. Start by borrowing whole shares just prior to a vote, much like a short seller borrows shares prior to selling them short. Rather than selling the borrowed shares, however, an activist holds them in order to exercise their voting rights, then returns the shares soon after the vote to the lender. The cost they'll pay on this round trip represents the price of a vote. From the perspective of the the owner who has lent the shares out, they require a high enough fee in order to compensate them for having foregone their franchise over the interim.

For instance, in 2002, Laxey Partners, a hedge fund, held about 1% of the shares of British Land, a major U.K. property company. However, on the day of British Land's shareholder meeting Laxey controlled 9% of the votes, note Hu and Black, all the better to support a proposal to dismember British Land. Just before the record date, Laxey had borrowed 8% of British Land's shares.

The term used for having more votes than shares is empty voting. Someone with 5,000 votes and only 500 shares is in possession of 4,500 empty votes, since those 4,500 votes have been 'emptied' of their economic interest. Empty voting is welfare-improving when an activist investor with a good plan acquires votes beyond his or her economic interest in order to ensure that their plan is adopted. However, at the extreme, empty voting can get downright spooky.  Consider a fund that has amassed short position in a stock (ie. it expects the shares to fall in value) while building a long position in votes. Perversely, this 'rogue' fund could very well use their franchise to implement changes that hurt the firm, not help it, and thereby bolster their short position.

Hu and Black, who refer to the decoupling of votes and economic interest as "the new vote buying", note that vote transactions are often hidden from the public and regulators. All the more reason to have a formal market for votes as described at the start of this post rather than the terribly confusing one that already exists. A transparent price for voting would help reveal rogue attempts to corral large empty voting positions. Those activists who truly want to create shareholder friendly changes would be able to accurately price out the cost of resisting the rogues.

And all those investors who are too unsophisticated to understand the murky world of stock lending, ie. retail investors, would be able to use widely-disseminated prices to better gauge the value of their vote and access an open market for the transferral of those votes.

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* A share also offers a third feature, a liquidity return. I've pointed this out many times before. For the sake of this post, we'll ignore the liquidity portion.
** Strictly speaking, if the non-voting shares you short also happen to be less liquid than the voting shares you are long, then you are not only buying votes, you're also buying liquidity. But as I pointed out in the above bullet point, I'm ignoring liquidity returns for the sake of simplicity.
*** I have an ulterior motive for a market for corporate votes. I think the phenomenon of naked shorting doesn't deserve the vilification it receives in the press and on blogs. In fact, naked shorting is a necessary part of ensuring that liquidity premia on equities are kept at market clearing prices. The proper functioning of what I've referred to as the 'moneyness market' depends on naked shorting. The problem with a naked short is that the resulting synthetic security that the short seller creates doesn't have a vote. It is a non-standard instrument. With the existence of a corporate vote market, a naked short seller might re-standardize the instrument by purchasing a vote and attaching it to the IOU that they've created via their naked short. I do plan on writing about this next month, so if you didn't understand my point, just wait. 

Links:
Hu & Black, 2006. The New Vote Buying: Empty Voting and Hidden (Morphable) Ownership
Aggarwal, Saffi, & Sturgess, 2010. Does Proxy Voting Affect the Supply and/or Demand for Securities Lending
Financial Post, November 2012. Empty Voting Clouds Shareholder Rights Law
Black, 2012. Equity Decoupling and Empty Voting: The Telus Zero-Premium Share Swap
Brav & Mathews, 2011. Empty voting and the efficiency of corporate governance

Chopmarks and other distributed verification methods

A 1795 Spanish dollar, minted in Mexico, with several chopmarks

One of the most interesting things about bitcoin, ripple, and other cryptocurrencies is how they are maintained by a dispersed user base rather than some central issuing authority. These users (miners in the case of bitcoin, nodes for ripple) ensure that each "coin" is a legitimate member of the total population of cryptocoins comprising that particular ledger. They are what stand between good coin and bad coin.

I've run into two historical cases of a dispersed method of policing of the quality of exchange media: the endorsement of bills of exchange and the chopmarking of silver coins. It may be worthwhile to explore these two cases.

The Watchdog role

The watchdog or verification function is an important one, especially in anonymous trade where the unlikelihood of a repeat meeting between buyer and seller increases the incentives to be dishonest and pass off lousy coin. Not-so-liquid goods, say sofas, are insulated from the bad coin problem. Due to physical characteristics that impede their liquidity, sofas tend to be sold from fixed locations, or shops. Because a merchant is shackled to his shop and thus unable to preserve his anonymity, any attempt to pass off bad sofas will hurt his business reputation. In the end, only good sofas get stocked by the merchant.

Unfortunately for him, the merchant faces the danger that his much more mobile customers may try and sell him bad coin. The merchant can always threaten them with an embargo should they fob off a fake, but his customers will simply avoid his penalty by shopping at a competing merchant the next time they want a sofa.

In the case of paper money and coinage, the merchant is somewhat protected from the bad coin problem by difficult-to-counterfeit designs printed on the bill or engraved on a coin's face by the issuing authority. In the case of bank money, he is protected by the owners of the credit card networks who approve the legitimacy of a card prior to consummation of trade. These are centralized watchdog systems. What is interesting is that a number of decentralized, or dispersed systems have evolved in times past to offer further protection, including the use of chopmarks:

Chopmarking

In the 16th C, Spanish silver dollars, or pieces of eight, began to appear in China. These coins were minted in Spanish-controlled Mexico, shipped by Spanish vessels to the Philippines where they were exchanged for Chinese goods like porcelain and spices, and finally brought to China by Chinese and other foreign merchants.

Minted on the reverse side with a Christian cross and the obverse side with a Spanish coat of arms, and covered over with Latin characters, the patterning of the Spanish dollar would have meant little to the typical Chinese consumer or merchant. In fact, any pattern would have done just as well since silver was traditionally not accepted at its face value in China, but by its weight (this contrasts to the west, where Spanish dollars were typically accepted at face value). This may have been partly due to the fact that silver ingots, or sycee, had circulated in China long before the piece of eight ever made an appearance, with each city having its own particular standard. Because these sycee circulated according to weight, prior to consummating a trade, merchants would use a set of scales, or dotchin, to determine the value of each ingot.

While anyone with a set of scales could easily ascertain the weight of a particular coin, the difficult part would have been determining the purity of that coin. Counterfeit Spanish dollars were not uncommon, after all, but not everyone would have had the skills to detect them. This is where chopmarking came in handy. Merchants and professional money exchangers, or shroffs, would assay a coin to verify its silver content. The theory goes that once the coin had passed their purity test, a shroff would stamp that coin with his own peculiar chopmark—a Chinese character, an emblem, symbol, or a pseudo character.

Numismaticist Bruce Smith describes the reason for chopping thusly:

I think the chop was only a guarantee that it was acceptable silver. It didn't really matter if the coin was genuine or not. As long as it had the right weight and right fineness as far as they could tell. I mean they were only looking at it by eye and by sound. If it looked like the silver was good and it sounded good [the ‘ring’] and the weight was acceptable then it was okay.

According to Frank Rose, a numismatist who published an early text on chop marks, certain merchants chopmarked every legitimate coin that came into their possession and would readily take back any coin bearing one of their earlier marks. So by chopmarking a coin, a merchant would have been taking on a liability of his own, almost as if he had issued a redeemable paper note or a deposit.

In any case, foreign coins often became so covered in chop marks during the course of trade that their initial design became unrecognizable, as the coin below shows.

1807 Spanish dollar with chopmarks

The genius of this system is that a naive Chinese consumer could safely accept a coin knowing that as long as it was chopped it had successfully passed the smell test of professional appraisers--and the more chops the better. Chopping, like bitcoin mining, transformed a virgin coin into the native exchange medium, with chopmarks serving as a way for disparate users to verify a coin's membership in the set of good silver pieces.

Endorsing

Another interesting form of dispersed verification was the system of bills of exchange, especially the system that developed in Lancashire, a county in northern England. A bill of exchange was a paper contract between two sides in a transaction. It was created or 'drawn' up by the person who provided goods or services, the 'drawer'. The counterparty who had taken position of goods stood as the 'acceptor' and by signing the bill, promised to render up a certain amount of coins to the drawer, usually three months hence. The drawer kept the bill in his desk until three months had passed upon which he presented it to the acceptor, got his gold, and the two parted ways.

A bill of exchange, 1843 [link]

In the early 1700s, English commercial law began to accept the practice of transferring debts, or negotiability. Rather than the drawer keeping the note in desk, he could transfer it to a third party. The drawer would typically do so in exchange for some good or service, and would go about this by endorsing it, or signing his own signature on the back. By endorsing the bill, the drawer had become a co-signatory.

When the bill was due the third party could call on the original acceptor for payment, even though the original agreement had been between the drawer and the acceptor. Should the third party find the acceptor unable to pay the gold upon maturity, he could make a claim on the endorser for full payment. Alternatively, the third party could in turn endorse the bill on to someone else, who could it turn endorse it to someone else, etc. turning what had been an illiquid bill into a highly liquid and potent medium of exchange.

This is exactly what happened in Lancashire, according to this paper by T.S. Ashton. Not only were bills used by large scale industry, but according to Ashton they were used in small transactions too. While coin was generally reserved for the payment of wages, those a little higher in economic status than hired workers, small-capitalist spinners and small time manufacturers with an apprentice or two, were induced to accept payment in Lancashire bills. According to Henry Thornton, who Ashton quotes, all payments at Liverpool and Manchester - then part of Lancashire - were carried out either in coin or bills of exchange. Henry Dunning Macleod describes bills "which had sometimes 150 indorsements on them before they became due."

The practice of endorsement was hugely advantageous for the general populace, for as Ashton points out:

"Since each successive holder endorsed it, the more it circulated the greater the number of guarantors of its ultimate payment in cash. Even if some of the parties to it should be men of doubtful credit it might still circulate, for it was unlikely that they would go down simultaneously."

So in the same way that multiple chop marks and blockchain confirmations ensure that a coin is a good one, multiple endorsements converted an IOU into a member of the population of verified IOUs, and therefore suitable for broad circulation. In the end, what bitcoin and the other cryptocoins is certainly novel, but we have seen parts of this story before.

Quibbling with the language of trade

The way we ascribe labels to things results in the creation of categories, and this in turn affects the construction of our mental landscapes—best to get the words and categories right from the start lest our thinking goes astray. In this post I quibble with some of the common words and categories we use to describe trade.

Walking out the front door last night, I told my wife that I was going to buy a few items at the grocery store. But as I trekked down the street, I asked myself why I hadn't chosen to tell her an alternate version: that I was going to the grocery store to sell my cash. The problem with this wording, I figured, was that if I was to be the one selling stuff in the upcoming transaction, then by process of elimination the grocery store could no longer be the seller in the deal but the buyer—of my cash. And that would be a weird way to view things.

Linguistic convention requires that there be a seller and a buyer in any trade. One side spends, the other receives. That separate terms are given to participants in an exchange implies that the two parties are irreconcilably different. By spending, buyers are doing something that stands in binary opposition to whatever it is that sellers are doing.

I don't think this dichotomization is a good way to characterize the intuition behind a transaction. All parties to any deal are essentially engaged in the same activity: trade. Escaping linguistic convention for a moment, let's put things this way: when I go to the grocery store I am a seller of coloured bits of paper, and the store is in turn spending its food to buy those bits. The binary opposition between buyers and sellers melts away since both myself and the store are simultaneously buyer and seller, spender and receiver. The exclusivity that previously characterized our positions no longer exists, rather, we are each engaged in mutual trade.

For the sake of simplification we should just drop all references to buyers, sellers, and spending. Instead, so-called buyers and sellers are best described as being equal counterparties to a swap. In last night's trip to the grocery store, the store and me were counterparties to a swap of paper notes for groceries.

It could be argued that the use of the terms 'buyer' and 'seller' are useful in that they capture the fact that one party to the trade is offering 'money' and the other asking for it. But the word 'money' is just as arbitrary. What is to fall into this category, what is to be excluded?

For instance, fan's of Arrested Development may remember the scene where Tobias and Lindsay walk into C.W. Swappigan's and trade a cocktail tray for mozzarella sticks. With neither item classified as money, is Lindsay the buyer or the seller? What is being spent: mozzarella sticks or a cocktail tray? We hem and haw when we try to describe this scene because we can't apply the language of buying/selling, spending/earning to situations involving the exchange of goods that are relatively illiquid. But these sorts of exchanges shouldn't be excluded from discussion just because we can't use regular language to describe them. Nor are they categorically different from exchanges that involve slightly more liquid goods. The language of swapping comes to the rescue: Lindsay and C.W. Swappigans are equal counterparties to a swap that involves two illiquid goods.

Classifying people as buyers or sellers is just as tricky when we start talking about exchanges of one currency for another. When you walk into a currency exchange shop to trade Canadian money for US money, are you the buyer or is the shopkeeper the buyer? Which one of you is spending? Again, the more universal language of swaps makes things easier: both you and the exchange shop are engaged in a swap of two highly-liquid items. Even if one item is slightly more liquid than the other (perhaps greenbacks are a shade more liquid than loonies), what separates the two of you in this trade isn't a Chinese wall of buyer vs seller, but simply a difference in the degree of liquidity (or not) of the items you are swapping.

And while I'm griping, why not exorcise the words borrower and lender? Like buyer and seller, the terms borrower and lender imply a stern barrier between two participants to a temporary trade when these participants are in fact undertaking the very same activity—trade. If we unbundle a transaction between a customer and a bank, what is happening? A consumer, the "borrower", is providing their personal IOU to the bank which in turn is offering its own IOU, a deposit, to the customer. While it is usually said that the customer borrows deposits from the lender bank, we might just as likely say that the customer is lending his or her IOU to the bank, and the bank is borrowing the customer's IOU.

So if we can boil a banking transaction down to a swap that reverses after a period of time, participants in this swap needn't be ring-fenced with their own unique noun. Rather, each can be simultaneously described with the same term: as counterparties.

But what about interest? Isn't the payment of interest a distinguishing enough feature that necessitates the terms debtor and lender? Interest emerges (in part) when parties agree to swap equally risky IOUs for a period of time, but one IOU is more liquid than the other. The counterparty that accepts the illiquid IOU while providing the liquid IOU, usually the bank, will ask for a fee, or a stream of interest payments, from the counterparty customer to compensate (the bank) for forgone liquidity. The other party to the trade, the customer, will be willing to pay an interest penalty as restitution for the superior liquidity return that the bank's IOU provides them. This doesn't change the fact that both bank and customer are engaged in a swap.

Things get tricky when a temporary swap involves exchanges of IOUs that are equally-liquid (and equally risky). Since no one forgoes liquidity over the course of this swap, interest doesn't arise. A good example of this is the repo market, where short term swaps of deposits for highly-liquid treasury bills occur at rates no different from 0%. The lender/borrower lexicon breaks down here since without interest we don't know which party is to earn which moniker. Is the bond owner the lender or the borrower? The deposit-taker?

Again, the clearer way to describe this situation is to default to more universal swap terminology. Both participants are counterparties to a swap of items of equal or varying liquidity profiles.

In sum, our language tries to find strict differences between participants in an exchange when there are none. There are no buyers nor sellers, no spenders, no lenders nor borrowers. Instead, we are all engaged in the same activity—trade. The things we own have varying degrees of liquidity and in endeavoring to swap them for things that are more, equally, or less liquid than that which we already own, we make efforts to grope towards a preferred final state of either greater or diminished liquidity.

Using restricted stock studies to measure liquidity

I like to say that everything is money, which is just another way of saying that all goods are liquid to some degree or other. Whether it be a house, a banknote, or ice cream, each of these items carries a liquidity premium. How large are these liquidity premia? It's difficult to get good measurements, but there are a few venues that offer a glimpse of this rare beast. One of them is equity markets. More specifically, we can use restricted stock studies to tease out liquidity premia.

Imagine that your shares in Microsoft, normally so easily exchanged on various stock markets like the New York Stock exchange or NASDAQ, were restricted for a period of time in a way that prevented you from trading them. Apart from this impairment, your illiquid Microsoft shares are exactly like any other Microsoft share: they provide you with a dividend, voting power, and a contingent claim on firm assets should Microsoft decide to wind up the business. The price you'd be willing to pay to own these rather unique shares would reflect their lack of liquidity. Or, put differently, the difference between the price of regular Microsoft shares and restricted Microsoft shares would precisely represent the value that you ascribe to the liquidity of regular Microsoft shares, or their liquidity premium.

Luckily for us, the practice of placing restricted stock, or unregistered stock, with investors provides an opportunity to measure this  difference. When you buy a blue chip stock on the NYSE you're purchasing registered stock—the issuer has registered the original offering of securities with the SEC. This is an expensive and time consuming process involving all sorts of lawyers and fees. If the issuer wishes to avoid these fees, it can choose to forgo registration and issue what are called unregistered shares, as long as the issue is presented to private accredited investors and not to the general public. However, securities law stipulates that investors who receive unregistered stock must accept a number of restrictions, all of which limit the liquidity of unregistered stock. In general, laws proscribe a holding period over which the owner of restricted stock cannot sell in public markets. After the holding period expires, unregistered securities can be sold in public transactions but only by complying with certain “dribble out,” or volume limit, provisions that may impede a stockholder from liquidating a position sufficiently fast. (For instance, an owner of restricted stock might not be able to sell more than x% of the stocks monthly trading volume).

Restricted stock studies measure the difference between the price at which a company has issued restricted stock and the publicly-traded price of that same company's non-restricted, or registered, stock . This difference represents the liquidity premium on the firm's registered stock; the very same liquidity that restricted stock owner forgo.

The chart below provides a partial listing of restricted stock studies and the average discount to market value displayed by restricted stock in each:

Source

The earliest restricted stock studies show a ~30% difference between the price of restricted stock and its publicly-traded equivalent. This implies that the liquidity premium over the combination of the holding period (initially set at two years) and dribbling out period on an average stock amounted to about 30 cents per each dollar of stock. That number doesn't include the value of liquidity after the holding period has expired and dribbling out rules have ceased to have a significant effect; if the entire lifespan of a stock were incorporated, we can imagine that 40-50 cents of each dollar worth of a typical stock might be due to liquidity. That's quite a lot!

As the chart shows, over time studies have found that the measured gap between the price of restricted shares and regular publicly-traded shares has steadily shrunk. This is due in part to changes in SEC rules concerning the sales of restricted shares. Owners of restricted shares initially faced a 2-year holding period, but this was reduced to 1-year in 1997 and then six months in 2008. Non affiliate owners (those who are not insiders and don't own controlling blocks of stock) initially faced an indefinite dribbling out period (ie. volume limitations) but this was reduced to 3 years of volume limitations in 1983, 2 years in 1997, and just six months in 2008. In 1990, something called the “tacking” rule was changed. Prior to this amendment, any sale of unregistered stock, even in privately negotiated transactions, would result in the required holding period restarting, a large inconvenience to the buyer. The 1990 amendment allowed non-affiliate purchasers to “tack” the previous owners’ holding period to their own holding period. Because all of these rule changes improved the liquidity of restricted shares, over time investors have needed less of an inducement to hold restricted stock relative to regular shares—thus the downward trend in average discount size.

Why so many restricted stock studies? In the field of business appraisal, evaluators are often called upon to estimate the values of illiquid assets in estates and divorce proceedings, typically small privately held company shares. One way to go about this is to apply an earnings multiple from a comparable publicly- traded companies trade to the privately held firm's earnings. But this assumes an "as if marketable" value for what is actually a very illiquid asset. A discount for lack of marketability (DLOM) must be applied to correct for this problem. A DLOM is the amount an appraiser deducts from the value of an ownership interest to reflect the relative absence of marketability. It will often be the single largest value adjustment than an appraiser will have to make. The results must be defensible in a court of law, necessitating a well structured argument backed by data. Restricted stock studies offer a way for an appraiser at a reasonable DLOM. Of course, an owner of an asset may want as large a discount as possible, usually for tax reasons. They therefore will be tempted to use a study with the highest discount, perhaps an older study that assumes 2-year holding periods, even though six month holding periods now prevail. The IRS has made efforts to shift the profession to using smaller DLOMs, for obvious reasons.

A major weakness of restricted stock studies is the assumption that the entire price gap between a restricted stock price and its publicly traded counterpart can be traced to the liquidity factor. But this isn't necessarily the case. Companies will often artificially underprice private offerings as a way to pay for services rendered (say to suppliers), to reward insiders, or to curry favor. This is the barter function of stock. We need to separate the portion of a restricted share discount that arises for liquidity reasons from that which arises due to this barter function. One way to do so is to compare the prices at which private offerings of restricted stock are carried out relative to private offerings of regular stock. Since both forms of private stock issuance are equally likely to be used for barter, the barter function can be canceled out, thereby leaving liquidity as the only explanation for the gap between the prices of restricted and non-restricted private stock issues.

Wruck (1989) found that the difference in average discounts between the restricted share offerings in her study and registered share offerings was 17.6%, while the difference in median discounts was 10.4%.  Bajaj et al found that private issues of registered shares were conducted at average discounts of 14.04% to their publicly traded price, while the average discount on placements of unregistered shares were conducted at 28.13% to their public price, 14.09% higher than the average discount on registered placements. This puts stock liquidity premiums at about 10-15 cents on the dollar, far below levels found in other studies.

Nevertheless, the fact that around 10 cents of each $1 worth of Microsoft stock can be attributed to the value that the market ascribes to one or two years of liquidity is still a significant number. And remember that restricted stock studies don't measure the long-term liquidity factor, only the value of liquidity foregone over the holding period and a dribbling out period. If the studies did isolate longer term measures of liquidity, we might find that 15-20 cents of each $1 of Microsoft stock is comprised of liquidity value.

All of this means that a share of Microsoft isn't a mere financial asset—a portion of any Microsoft share is providing its owner with a stream of consumable services, much like one's lawyer or neighborhood policeman or pair of shoes provides a service. If some sort of shock were to reduce the liquidity that Microsoft provides, then everyone would be made worse off. (All the more reason to adopt liquidity-adjusted equity analysis). Of course, all of this applies just as well to other securities like bonds and derivatives. And it also applies to consumer and capital goods, houses, land, and collectibles. Everything carries a degree of liquidity, and if we could compare the price of that asset to some illiquid copy of itself (restricted houses, restricted land, restricted paintings) then we'd have a pretty good idea for how much value the market ascribes to that liquidity.

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Other links worth exploring:

Blogs
Using Illiquidity Premiums on the Risk Free Asset to Measure Illiquidity Discounts by Joshua B. Angell

Papers
Revisiting the Illiquidity Discount for Private Companies by Robert Comment
Determining Discounts for Lack of Marketability: A Companion Guide to The FMV Restricted Stock Study
The Discount for Lack of Marketability by Reilly and Rotkowski
Market Discounts and Shareholder Gains for Placing Equity Privately by Hertzel and Smith (RePEc)