Wednesday, August 20, 2014

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:


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. These sycee circulate according to weight, so that 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.

This coin has so many chops it is almost unrecognizable [Link]

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.


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.

Saturday, August 9, 2014

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.

Thursday, July 31, 2014

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 stockthe 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:


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 sharesthus 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 asseta 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.

Other links worth exploring:

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

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)

Monday, July 21, 2014

Fedwire transactions and PT vs PY

Milton Friedman's alleged license plate, showing the equation of exchange

The excruciatingly large revisions that U.S. first quarter GDP growth underwent from the BEA's advance estimate (+0.1%, April 30, 2014) to its preliminary estimate (-1.0%, May 29, 2014) and then its final estimate (-2.9%, June 25m, 2014) left me scratching my head. Isn't there a more timely and accurate measure of spending in an economy?

One interesting set of data I like to follow is the Fedwire Fund Service's monthly, quarterly, and yearly statistics. Fedwire, a real time gross settlement interbank payment mechanism run by the Federal Reserve*, is probably the most important financial utility in the U.S., if not the world. Member banks initiate Fedwire payments on their own behalf or on behalf of their clients using the Fedwire common currency: Fed-issued reserves. Whenever you wire a payment to another bank in order to settle a purchase, you're using Fedwire. Since a large percentage of U.S. spending is transacted via Fedwire, why not use this transactions data as a proxy for U.S. spending?

Some might say that using Fedwire data is an old-fashioned approach to measuring spending. Irving Fisher wrote out one of the earliest versions of the equation of exchange, MV=PT, where T measures the "volume of trade" or "real expenditure" and P is the price at which this trade is conducted. Combined together, PT amounts to the sum of all exchanges in an economy. More specifically, Fisher's T included all exchanges of goods where his chosen meaning for a good was broadly defined as any sort of wealth or property. That's a pretty wide net, including everything from lettuce to publicly-traded equities to land.

Practically speaking, Fisher wrote that it was "utterly impossible to secure data for all exchanges" and therefore his statistical approximation of T was limited to the quantities of trade in 44 articles of internal commerce (including pig iron, rice, hogs, boots & shoes), 23 articles of import and 25 of export, sales of equities, railroad freight carried, and letters through the post office. This mishmash of items included everything from wholesale goods to securities to and consumption goods. Using Fedwire transactions to track total spending is very much in the spirit of Fisher, since any sort of transaction can be conducted through the interbank payments system, including financial transactions.

Nowadays we are no longer taught the Fisherian transactions version of the equation of exchange MV=PT but rather the income approach, or MV=PY. What is the difference between the two? Y is a much smaller number than T. This is because it represents GDP, or only those goods and services that are qualified as final, where "final" indicates items bought by a final user. T, on the other hand, includes not only the set of final goods and services Y but also all spending on second hand goods, stocks and bonds, existing homes, transfer payments, and more. Whereas GDP measures final goods in order to avoid double counting, T measures final and intermediate goods, thus counting the same good twice, thrice, or even more if the good changes hands more often than that.

A good illustration of the difference in size between Y and T is to chart them. The total yearly value of Fedwire transactions, which are about as good a measure of PT that we have (but by no means perfect), exceeds nominal GDP (or PY) by a factor of 40 or so, as the chart below shows. Specifically, nominal GDP came in at $17 trillion or so in 2013 whereas the total value of Fedwire transactions clocked in at $713 trillion.

So why do we focus these days on PY and not Fisher's PT? We can find some clues by progressing a little further through the history of economic thought to John Keynes (is it a travesty to omit his middle name?). In his Treatise on Money, Keynes was unimpressed with Fisher's cash transactions standard, as he referred to it, because PT failed to capture the most important human activities:
Human effort and human consumption are the ultimate matters from which alone economic transactions are capable of deriving any significant; and all other forms of expenditure only acquire importance from their having some relationship, sooner or later, to the efforts of producers or to the expenditure of consumers.
Keynes proposed to "break away from the traditional method" of tabulating the total quantity of money "irrespective of the purposes on which it was employed" and focus instead on the narrow range of trade in current consumption and investment output. Keynes's PY measure (the actual variables he chose was PO where O is current output) would be a "more powerful instrument of analysis than their predecessor, when we are considering what kind of monetary and business events will produce what kind of consequences."

And later down the line, Milton Friedman, who renewed the quantity theory tradition in the 1950s and 60s, had this to say about the shift from PT to PY:
Despite the large amount of empirical work done on the transactions equations, notably by Irving Fisher and Carl Snyder ( Fisher 1911 pp 280-318, Fisher 1919, Snyder 1934), the ambiguity of the concept of "transactions" and the "general price level", particularly those arising from the mixture of current and capital transactions—were never satisfactorily resolved. The more recent development of national income accounting has stressed income transactions rather than gross transactions and has explicitly and satisfactorily dealt with the conceptual and statistical problems of distinguishing between changes in prices and changes in quantities. As a result, the quantity theory has more recently tended to be expressed in terms of income rather than of transactions
So there are  evidently problems with PT, but what are the advantages? Assuming we use Fedwire transactions as the proxy for PT (and again, Fedwire is by no means a perfect measure of T, as I'll go on to show later) the data is immediate and unambiguous. It doesn't require hordes of government statisticians to laboriously compile, recompile, and check, but arises from the regular functioning of Fedwire payments mechanism. There are no revisions to the data after the fact. And rather than being limited to periods of time of a month or a quarter, there's no reason we couldn't see Fedwire data on a weekly, daily, or even real time level of granularity if the Fed chose to publish it.

Even Keynes granted the advantages of PT data when he wrote that the "figures are available promptly without the necessity for any special calculation." In Volume II of his Treatise, he took U.S. "bank clearings" data (presumably Fedwire data), and tried to remove those transactions arising from financial activity by excluding New York City, the nation's chief financial centre, thus arriving at a measure of final spending that came closer to PY.

What are the other advantages of PT? While PT counts second-hand and existing sales, might that not be a good thing? Nick Rowe, writing in favour of PT, once made the point that it's "not just new stuff that is harder to sell in a recession; it's old stuff too. New cars and old cars. New houses and old houses. New paintings and old paintings. New furniture and antique furniture. New machine tools and old machine tools. New land and old land." As for the inclusion of financial transactions, anyone who thinks asset price inflation or deflation is an important property of the economy (Austrians and Austrian fellow travelers no doubt) may prefer PT over PY since the latter is mute on the subject.

I'd be interested to hear in the comments the relative merits and demerits of PY and PT. Why don't the CNBC talking heads ever mention Fedwire, whereas they can spend hours debating GDP? Why target nominal GDP, or PY, when we can target PT?

For now, let's explore the Fedwire data a bit more. In the figure below I've charted the total value of Fedwire transactions (PT) for each quarter going back to 1992. I've overlaid nominal GDP (PY) on top of that and set the initial value of each to 100 for the sake of comparison.

It's evident that the relative value of Fedwire transactions has been growing faster than nominal GDP. However, the financial crisis put a far bigger dent in PT than it did PY. Only in the last two quarters has PT been able to break to new levels whereas nominal GDP surpassed its 2008 peak by the second quarter of 2010. Is the financial sector dragging down PT? Or maybe people are spending less on used goods and/or existing homes?

Fedwire data is further split into price and quantity data. Below I've plotted the number of transactions, or T, completed on Fedwire each quarter. On top of that I've overlaid real GDP, or Y. The initial value of real GDP has been set to 16.6 million, or the number of transactions completed on Fedwire in 1992.

After growing at a relatively fast rate until 2007, the number of transactions T being carried out on Fedwire continues to stagnate below peak levels. In fact, last quarter represented the lowest number of transactions since the first quarter of 2012, a decline that coincided with the atrocious first quarter GDP numbers.

Finally, below I've plotted the average value of Fedwire transfer by quarter. On top of that I've overlaid the GDP deflator. To make comparison easier, I've taken the liberty of setting the initial value of the deflator at the 1992 opening value for Fedwire transaction size.

As the chart shows, the average size of Fedwire transfers really took off in 2007, peaked in late 2008 then stagnated until 2013, and has since re-accelerated upwards. In fact, we can attribute the entire rise in the quarterly value of transactions on Fedwire (the second chart) to the growth in transaction size, not the quantity of transactions. Fedwire data is telling us that inflation of the PT sort has finally reemerged.

A few technical notes on the Fedwire data before signing off. As I've already mentioned, Fedwire provides a less-than complete measure of PT. To begin with, it doesn't include cash transactions (GDP does, or at least those that have been reported). This gap arises for the obvious reason that cash transactions aren't conducted over Fedwire. Nor do cheque transactions appear on Fedwire, or at least they do so only indirectly. Check payments are netted against each other and canceled, with only the final amounts owed being settled between banks via Fedwire, these settlements representing just a tiny fraction of the total value of payments that have been conducted by check over any period of time.

The same goes for securities transactions. Fedwire data underestimates the true amount of financial transactions because trades are usually netted against each other by an exchange's clearing house prior to final settlement via Fedwire. The transfer of reserves that enables the system to settle represents a small percent of the total value of trades that have actually occurred.

Another limitation is that Fedwire data doesn't include wire payments that occur on competing payment systems. Fedwire isn't a monopoly, after all, and competes with CHIPS. I believe that once all CHIPS payments have been cleared, final settlement occurs via a transfer of reserves on Fedwire, but this final transfer is a fraction of the size of total CHIPS payments. And finally, payments that occur between customers of the same bank are not represented in the Fedwire data. This is because these sorts of payments can be conducted by a transfer of book entries on the bank's own balance sheet rather than requiring a transfer of reserves.

I'm sure I'm missing other reasons for why Fedwire data undershoots PT, feel free to point them out in the comments. Do Fedwire's limitations cripple its value as an indicator PT? I think there's still some value in looking at these numbers, as long as we're aware of how they might come up short.

Some links:
1. Canadian Large Value Transfer System Data, the Canadian equivalent to Fedwire
2. A paper exploring UK CHAPS data,the British equivalent to Fedwire: Income and Transactions Velocities in the UK

* 'Real time' means that payments are immediate and not subject to delay, while 'gross settlement' indicates that payments are not grouped together for processing but submitted individually upon being entered. Fedwire gets its name from the beginning of the last century, when payments were carried out over the wires, or the telegraph system. 

Thursday, July 3, 2014

To recapitulate...

I'm going on holiday and don't have enough time to write anything new. At the risk of being repetitive, here's a recapitulation of what is one of this blog's major themes: the idea of moneyness. Most of the component parts are spread out over a couple of dozen posts written over many months—here I'll try and piece the whole quilt together in one spot.

Money vs moneyness

The initial point comes from one of my first posts (as well as a later one). There are two ways of thinking about monetary phenomena. The standard way is to draw a line between all things in an economy that are "money" and all those things which are not. Deposits typically go in the money bin, widgets go in the non-money bin, dollar bills go in the money bin, labour goes in the non-money bin and so forth.

The second approach, the one this blog takes, begins with the idea that all things in an economy are money-like. The line we are interested in here is the extent to which the value of each thing is determined by its money-like qualities, or its moneyness, versus the degree to which its value is determined by its non-money like qualities, say its ability to be consumed. We might say that deposits have more moneyness than labour, and labour is more money-like than a second-hand speedo and so forth.

(This second approach isn't without precedent, see Keynes, Hayek, and Friedman.)

Why is moneyness a valuable attribute?

It's all in this post, but here's a quick recap. The greater an item's degree of moneyness, the easier it is for its owner to mobilize that item in trade should some unanticipated eventuality arise. This quality of being easily liquidated provides the owner of that asset with a flow of uncertainty-alleviating services over time, or insurance.

Because moneyness, like insurance, is a valuable property, people must choose on the margin whether to sacrifice moneyness for either consumption or interest. In deciding whether to trade an item with high moneyness for a consumption good with low moneyness, an individual must weigh the present value of the flow of uncertainty-shielding services provided by the former against the one-time zing provided by the latter. In considering a potential exchange between an item with high moneyness and an illiquid interest-yielding asset, the tradeoff is between uncertainty-shielding services and an ongoing pecuniary return.

The supply of moneyness

Moneyness is a valuable good, but it also must be produced at a cost.

Certain characteristics of a good allow it to become more money-like, including durability, verifiability, fungibility, and portability. Network effects may promote an item's degree of moneyness.

The moneyness of an object can be improved by manufacturing these characteristics. Gold, for instance, is rendered more money-like by incurring coinage costs in order to promote verifiability. Adding copper to a gold coin increases its durability. Network effects can be harnessed through marketing. As long as the expected returns of boosting an object's moneyness are higher than the costs, liquidity providers will happily bear the costs.

Whereas only banks and central banks create money, the cast of characteristics involved in supplying moneyness is quite varied. Investor relations teams manufacture it as do hedge fund managers like Cliff Asness and roll-ups like Valeant Pharmaceuticals.

Difficulties in measuring moneyness

It's all here. To summarize, people often use bid-ask spreads and the frequency distributions of various assets in trade as a way to measure an asset's moneyness. But this comes up short. Bid-ask spreads and frequency distributions are objective measures of liquidity. We want to know the price that the market ascribes to things like tight bid ask spreads, not the bid ask spread itself. Moneyness, like value, is a subjective quality, not an objective one.

The other problem is that the value of a good is usually derived from not only its moneyness, but also its 1) consumability and 2) its ability to yield pecuniary returns (like interest and capital gains). Stripping out the moneyness component from these others poses some thorny problems.

Here's how to do it

As I pointed out in this post, the trick is to poll people about how much they expect to be compensated if they are to forgo the ability to sell an asset for some a period of time, say one year, while still enjoying the pecuniary and consumption yields provided by that asset. The question goes something like this:
"How much would I have to pay you in order for you to relinquish all rights to trade away your holdings of asset x for one year?"
The price that an individual lists represents the value they ascribe to that asset's moneyness stripped of its other valuable attributes. It represents how much value they put on that asset's foregone bid-ask spread and other objective liquidity data.

On a larger scale, we want to create a moneyness market

The previous paragraph solves for each individual's assessment of moneyness, but we want to know the value that the market as a whole ascribes to a given asset's moneyness. In this post, I imagined what these markets would look like. We'd want to create a financial product that requires investors to set a price on how much they need to be paid if they are to relinquish the right to trade away asset x for a period of time. Buyers and sellers of these rights would establish a market price for the moneyness of all sorts of assets.

A few practical uses of moneyness and moneyness markets

Right now, equity analysts include an equity's moneyness in their valuation metrics, which is a big mistake. I go into this in plenty of detail here and here. If an analyst wants to accurately value an equity's price relative to its earnings, they need to have a measure of moneyness. That way they can strip out that part of an equity's price that is due to its moneyness and compare the non-monetary residual to earnings. A moneyness market would provide them with the missing data.

To properly value bonds and housing, we should probably do the same. See here and here.

And as I wrote here, financial assets like stocks are 2-in-1 deals meaning that you've got to buy an asset's moneyness along with its pecuniary return. Investors may prefer to have the one without the other. A moneyness market allows investors to split off and sell (or buy) each component separately, resulting in a more optimal allocation of moneyness and pecuniary returns.

Moneyness and monetary policy

Monetary policy is more of a sideline, but here are a few posts on the subject. A central bank issues liabilities with a high degree of moneyness. By increasing the quantity of outstanding liabilities, a central bank can reduce the marginal value that people are willing to pay for that moneyness, thereby lowering the purchasing power of central bank liabilities and increasing the price level. By tightening the supply of liabilities, it increases their marginal value, boosting their purchasing power and lowering the price level.

So in short, a central bank manipulates the moneyness of its own liabilities.

However, once it reduces the moneyness of its liabilities to zero across all time frames, a central bank can't create more inflation. This is the zero-lower bound from a moneyness perspective, which I go into here.

And in the future

I'm hoping to write a few posts on liquidity crisis and moneyness markets, and how moneyness markets can displace central banks as lenders of last resort (or at the very least help central banks improve).

Sunday, June 29, 2014

It was the best of times, it was the worst of times

You may know by now that the final revision of U.S. first quarter GDP revealed a shocking 2.9% decline while its mirror image, gross domestic income (GDI), was off by 2.6%.

As Scott Sumner has pointed out twice now, the huge decline in GDI is almost entirely due to a fall in corporate profits. Whereas employee compensation, the largest contributor to GDI, rose from $8.97 to $9.04 trillion between the fourth quarter of 2013 and the first quarter of 2014, corporate profits fell from $2.17 to $1.96 trillion (see blue line in the above chart) This incredible $198 billion loss represents a 36% annualized rate of decline!

A number of commentators have pointed out the difficulty in squaring this data bloodbath with reality. After all, Wall Street has not been announcing 36% quarter on quarter profit declines. Rather, earnings per share growth has been pretty decent so far this year. If earnings were off by so much, then why are equity markets at record highs? Why have there been no layoffs? It's hard to believe that a bomb has gone off when there's no smoke and debris. Investors are patting themselves down to make sure they had no wounds or broken body parts and, coming up clean, are shrugging and buying more stocks.

I'm going to argue that the odd disjunction between the numbers and reality may have arisen due to something called money illusion. We live in a historical-cost accounting world in which stale prices are used as the basis for much of our profit and loss calculations. But the gunshot rang out in a different universe, one in which accountants rapidly mark costs to market. At some point we in the historical-cost world will feel the repercussions of the gunshot since everything is eventually marked to market. For now, however, no one seems to have noticed because we're all caught up in an the illusion created by accountants focused on the ghost of prices past.

More specifically, the folks at the Bureau of Economic Analysis who compile GDI report a different corporate profit number than the profit numbers being bandied around on Wall Street during earnings season. Wall Street profits are by and large paid out after depreciation expenses, and these have been accounted for on a historical-cost basis. This is the red line in the above chart. The BEA's number, represented by the blue line in the chart above, represents the profits that remain after depreciation expenses have been marked to market. The choice between mark-to-market depreciation accounting and historical-cost accounting can result in large differences in bottom-line profit, as the last data point in the chart illustrates.

For instance, consider a manufacturing company that earns revenues of $100 per year from a machine that it bought for $600. It depreciates the machine by $60 each year over 10 years, earning a steady $40 in profits ($100 - $60). Now imagine that all over the world machines of this type are suddenly sabotaged so that, due to their rarity, the cost of repurchasing a replica doubles to $1200. If the manufacturing company uses historical cost deprecation, it will continue to bring in revenues of $100 a year, deducting the same $60 in depreciation to show $40 in earnings. All is fine in the world. But if the firm uses mark-to-market depreciation, the cost of using up the machine will now reflect the true cost of replacing it: $120 a year ($1200/10 years). Subtracting $120 from the annual $100 in revenues means the company is losing $20 a year, hardly a sign of health.

It's easy to work out an example that shows the opposite, how a glut in machinery supply (which would drive the replacement cost of the machine down) is quickly reflected in a dramatic improvement in earnings after mark-to-market depreciation expenses, but earnings after historical-cost depreciation show nothing out of the ordinary.

Thus we can have one profit number that tells us that all is fine and dandy, and another that indicates the patient is on death's door. An individual's perception of the situation depends on which universe they live in, the historical cost universe or the mark-to-market one. The GDI explosion has gone off in the latter (the BEA uses a mark-to-market methodology), but since we experience only the former (the Wall Street earnings parade is entirely a celebration of historical-cost earnings per share data) we haven't really felt it... yet.

Yet? Even a company that lives in a historical cost accounting universe will eventually have to face the market price music. Imagine our sabotage example again. If our company uses mark-to-market accounting, it will immediately know it is facing a problem since its $100 revenue stream is failing to offset the $120 cost of machinery depreciation. However, if it uses historical cost accounting then our company continues to enjoy what it perceives to be a revenue stream that more than offsets its historically-fixed $40 cost of machinery. However, once that machine inevitably breaks down and needs to be replaced with a $1200 machine, a new historical cost base will be established and depreciation will suddenly rise to $120. Several quarters too late the company will realize that it is now operating in the red. Had it marked deprecation to market, that realization would have come much sooner.

If I had to speculate, here's a more detailed story about the last quarter. US corporate revenues were particularly underwhelming between Q4 2013 and Q1 2014 due to the cold weather. At the same time, we know that a number of government stimulus acts that had introduced higher than normal historical cost depreciation allowances (this allows firms to protect their income from taxes) were rolling off. Flattish revenues were therefore offset by smaller deprecation costs, resulting in a decent bump to headline earnings numbers, as the red line in the chart shows. Everything looked great to majority of us who inhabit the historical cost accounting universe.

However, mark-to-market depreciation accounting used by the BEA strips out the effect of the expiring depreciation allowances, thereby removing the bump. The combination of flattish revenues and higher market-based depreciation expenses (perhaps due to some inflation in the cost of capital goods) would have conspired to create a fall in the blue earnings series, and therefore a groaningly bad quarter in our mark-to-market universe.

In any case, the crux of the issue is that Wall Street's headline numbers indicate that corporate America did a better job in the first quarter of 2014 generating the cash necessary to replace worn out capital than it did in Q4 of 2013. The BEA numbers are telling us the opposite, that corporate America did a poorer job of covering the costs of wear & tear. Neither of the two numbers is wrong per se, but as I've already point out in my example, mark-to-market methodology is the first to reveal problems while historical cost accounting will follow after a lag.

As I've already hinted, the fact that Wall Street hasn't yet noticed that it just lived through a miserable quarter can be attributed to money illusion: a phenomenon whereby people focus on nominal rather than real values. In this specific instance, investors are so obsessed with headline changes in earnings that they fail to adjust that number for the true cost of using up machinery. Irving Fisher himself described a version of this mistake in his book The Money Illusion:
...during inflation the cost of raw materials and other costs seem to be lower than they really are. When the costs were incurred the dollar was worth more than it is later when the product is sold, so that the dollars in the original cost and the dollars in the later sale are not the same dollars. The manufacturer is deceived just as was the German shopkeeper or the Austrian paper manufacturers who thought they were making profits.
How likely is it that Wall Street, full of so many bright individuals, is being fooled by money illusion? It's not inconceivable. Even Scott Sumner volunteers that he doesn't believe the BEA's numbers due to soaring stock prices and strong earnings, thus falling prey to that very same affliction that serves as his blog's namesake. Money illusion can happen to the best of us.

Sunday, June 22, 2014

The monetary economics of the roll-up

The so-called corporate "roll up" lies at the conjunction of finance and monetary economics. For those monetary economists who aren't familiar with the term, a roll-up is a company that tries to consolidate an entire industry by serially acquiring competitors, usually using its own stock as currency. Valeant Pharmaceuticals, currently in the midst of a battle to take over botox-maker Allergan for $53 billion, is one of the more well-known roll-ups in the world of finance these days, having acquired around 75 companies in the specialty pharmaceutical niche over the last six years. But there have been many others over the years who have pursued the roll-up strategy.

Plenty of analysts dislike the corporate roll-up. They criticize it for not creating value organically but merely accumulating other people's castaway businesses. Roll-up equity is generally viewed as ridiculously overvalued and destined to implode. Valeant, for instance, has been variously described as a house of cards, Kool Aid, and something from the Wizard of Oz.

I'm going to argue in this post that a roll-up is less nefarious than some people think. A roll-up does the same thing that a bank does—it is a liquidity provider. In the same way that a bank expects to be compensated for turning the illiquid into the liquid, a roll up deserves to be paid a fee for doing the same. Like banks, roll-ups are monetary phenomena.

Let's build a roll-up from scratch. Our roll-up begins its life as a regular business, say a fishing store. Like all other fishing stores in the area, the store yields its owner, Bob, about $10 a year. Fishing stores generally distribute all their earnings to their owners so that nothing is retained in the business. A store can generally be bought and sold for around 5 times earnings, or $50 ($10/year x 5), although due to their illiquidity it may take a lot of time and effort to match buyers of fishing stores with sellers.

Bob's first task is to make the ownership position in his store more liquid. He decides to divide his $50 stake into 100 shares, each worth 50 cents, thus rendering it easier for people to purchase bite-sized positions in his business rather than being required to gulp the thing whole. He hires a store manager to take care of day-to-day business, buys himself an Armani suit, and begins to canvas the land marketing his shares. He may even take the time and effort to list on a public stock exchange.

Eventually, shares in Bob's store will have attracted a large crowd of buyers and sellers. Whereas all the other fishing stores in the area remain relative illiquid, an ownership stake in Bob's store has become more moneylike. A liquidity premium attaches to the value of the shares. Each of the 100 shares is now priced at 75 cents which puts a $75 valuation on Bob's business ($0.75 x 100 shares), twenty-five bucks higher than the $50 price tag that was originally placed on Bob's store and is currently being placed on competing fishing stores. Since Bob's store continues to earn the same $10 a year that other stores make, the twenty-five buck premium is entirely related to the superior ease that owners of Bob's business enjoy in transacting with their shares. Both Bob's Armani and his hard work have paid off.

Here's another way of looking at the scenario. Whereas all fishing stores trade at around 5 times earnings, Bob's shares trade at 7.5 times earnings due to their superior liquidity.

Bob now embarks on the next stage of executing his roll-up strategy—issuing new stock to buy up his competition. He begins by printing up 66.6667 new shares and offers to buy Joe's fishing store down the street for a total value of $50 (66.6667 shares x $0.75/share) . This is where the magic of the roll up strategy begins. If Joe accepts, Bob will now have two stores earning a combined $20, each share earning $0.12 ($20 / 166.667 shares). Notice that this is an improvement over the $0.10 per share being earned prior to the deal with Joe ($10/100 shares). Since the market continues to value Bob's shares at 7.5x earnings due to their excellent liquidity, each share will now trade for 90 cents (7.5 x $0.12 earnings per share), higher than their pre-purchase price of 75 cents (7.5 x $0.10). Thus Bob's shareholders enjoy an immediate 15 cent pop in the share price once Joe's store is bought! Not bad for a day's work. This is what is called an accretive acquisition.

Intuitively what is happening here is that Joe's illiquid ownership rights are being brought under Bob's umbrella. They are immediately rendered just as liquid as Bob's ownership position, and since liquidity is a service that the market is willing to pay a premium for, Joe's ownership rights will now be worth more than before.

It makes sense for Bob and his shareholders to push for the deal with Joe since they enjoy an immediate gain. But what about Joe? Why would he agree to the deal? Consider that before the agreement was struck, Joe was comfortably earning $10 a year selling rods and hooks. After the transaction is over, he'll own 66.6667 shares of Bob's business, each share yielding $0.12 in earnings, for a total of just $8 a year vs $10 before. So if he signs on the dotted line, he'll be earning $2 less each year. A terrible deal for Joe, right?

Not necessarily. The reason Joe may very well take the deal despite earning less finds an answer in Carl Menger. For finance types, Menger was a 19th century economist who pretty much nailed down the idea of liquidity, or what he preferred to call marketability, the fact that "different goods cannot be exchanged for each other with equal facility." Menger gives the example of a black smith who, when going to market with his newly made armour, has difficulties locating someone willing to trade food and fuel. Rather than seeking to directly trade, it is in the smith's interest to take an indirect route by accumulating some good that though useless to him, has greater marketability than the armour he has produced. In this way, the smith gives up his less saleable commodity for others of greater marketability since "possession of these more saleable goods clearly multiplies his chances of finding persons on the market who will offer to sell him the goods that he needs."

Returning to our story, let's say that Joe is tired of working and wants to retire so that he can travel around the world. Travel will require cash, but Joe's business isn't very easy to sell. In a strategy that Menger would approve of, Joe may choose to give up his shares in exchange for other, more saleable, shares, even if he doesn't not need them, because it brings him closer to the final position he desires. So while Joe doesn't get cash when he signs the bottom line, he does get the next best thing, Bob's liquid shares, which are far easier to turn into cash than his own. The amount that Bob asks as a fee for superior liquidity is the forfeiture of $2 a year in potential earnings, hardly a large price for Joe to stump up if he is desperate for a getaway from the fishing industry.

After gobbling up Joe's store, Bob continues rolling up the fishing store industry by constantly printing up new shares to buy out folks like Joe who want an exit. Bob and his merry band of shareholders are content to fabricate this desired liquidity as long as they get a portion of each exiting store owners' earnings and the ensuing boost to the share price. The Joe's of the world are happy to give up a bit of earnings to Bob for a bit of his liquidity.

This is exactly what a bank does. Just like Bob buys up illiquid ownership positions in fishing stores, banks buy up illiquid IOUs that have been issued by individuals and businesses. Where Bob issued new shares in exchange, a bank offers a different sort of financial asset; the bank's own highly-liquid IOUs, or deposits. Bankers don't engage in liquidity creation for free. In the same way that Bob requires that Joe give up some earnings in return for the liquidity benefit of Bob's shares, bankers require that the person who initially receives the bank's deposits pays an ongoing fee to enjoy the benefits of their superior liquidity, a fee that is otherwise known as interest. The only difference between a banker and Bob is that one is using debt, or bank deposits, as their liquidity carrot, while the other is using equity.

Banks spend large amounts of capital to ensure the superior liquidity of their deposits. Branch networks, ATMs, card payment infrastructure, and secure internet systems must all be built and maintained. Should a bank's deposits lose their liquidity advantage, the benefit of owning those deposits will diminish to the point that no one will willingly pay a fee to purchase them. Individuals will costlessly convert their illiquid deposits into liquid deposits of competitors (banks typically offer free 1:1 conversion among each others deposit brands). If this continues indefinitely, the bank will eventually go bankrupt.

Bob too faces these same sorts of limitations. His roll-up strategy can only continue as long as his shares are more liquid than those of his universe of targets. Once they are no longer special, folks like Joe won't see it worthwhile to forfeit a bit of their earnings to Bob for his shares. Put differently, Bob can continue rolling-up fishing stores only as long as the multiple that the market is willing to pay for his earnings remain significantly elevated relative to those stores that he wants to buy.

Like banking, rolling-up an industry requires continued investment in the mechanisms that promote share liquidity. Bob must buy ever fancier suits, travel ever further afield to advertise the quality of his shares, and list on more stock markets. One of the threats he must constantly face is that of competing roll-ups who also spend to promote the liquidity of their own shares. If the cost of suits is driven too high by the roll-up competition, it may no longer be profitable for Bob to maintain his shares' liquidity.

Roll-ups will also compete for acquisition opportunities. When folks like Joe who want to exit the fishing business receive multiple bids from roll-ups like Bob interested in buying him out, Joe can play Bob off against his competition so that Bob must sell Joe liquidity for less than he would otherwise prefer, perhaps below his cost of creating that liquidity.

When competition among roll-ups creates too much liquidity then investors will start to cut the liquidity premium that they attach to Bob's shares. Bob's acquisition targets will no longer be willing to forfeit as large a piece of their earnings to Bob as they once did in order to enjoy the liquidity of which he was once the only provider. As a result, acquisitions provide ever small returns, the immediate increase in per share earnings and the good old jump in the share price that Bob once enjoyed is increasingly a thing of this past . At some point, it makes no sense for Bob to continue his roll-up strategy. His business will have lost its banking function and now operates like any other fishing store chain—it grows in line with population growth and the market's desire for fishing products.

If investors had been pricing Bob's shares on the assumption of further growth in its banking function, upon the realization that acquisitions are no longer worthwhile they will all sell in earnest, a large decline in Bob's share price being the result. The roll-up game is officially over, as are Bob's days as a banker.

But let's say that Bob successfully guards the liquidity premium that his shares have always enjoyed against the competition. At some point he'll run up against another limitation; there are only so many fishing stores he can buy. Once he has purchased every shop around him, he runs out of accretive acquisitions and the banking function he once profited from suddenly comes to an end.

If he wants to continue his roll-up strategy, one option is for Bob to expand into another line of business, say gun shops. But here he faces a disadvantage in the fact that he has no natural talent in appraising hunting stores. Where his knowledge of the fishing store industry insured him against buying lemons, the odds of him making mistakes as he rolls-up this new industry increases. This risk isn't unique to Bob. A banker who specializes in construction loans faces this same risk when he or she expands into consumer lending, or auto loans. Just like an accumulation of bad loans may cause a run on a bank, bad gun store purchases may cause a run on Bob's shares. The value of both deposits and shares as media of exchange is jeopardized when the underlying assets are in doubt.

So to wrap this up (roll it up?), there's nothing mysterious or nefarious about roll-ups. They are merely entities that provide banking services to the industries in which they operate, namely swapping illiquid assets for liquid ones. They earn a return for producing liquidity in the form of an accretive earnings bump on each acquisition. Once they reach certain natural limits, a roll-up will cease providing banking services to the industry and return to being a normal company.

The larger point I'm trying to make, however, is that there are monetary phenomena at play in all sorts of  situations that don't involve money proper. Monetary economists, those folks who study monetary phenomena, focus laser-like on a narrow range of goods they consider to be money, usually central bank notes and private deposits, thus excluding all other objects from the study of monetary phenomena. This is too bad. When we allow ourselves to think of money not as an either/or proposition but as an adjective that applies more or less to all valuable goods, then you'll see fascinating monetary phenomena all around you, such as the corporate roll-up.

Monday, June 16, 2014

When the good drives out the bad

There's a fairly regular monetary phenomenon that needs a name. It's similar in nature to Gresham's law, yet the inverse version.

Gresham's law is commonly stated as the phenomena by which "bad money drives out the good". But as any economist will tell you, that's not quite it. Bad money chases out the good, but only if authorities have chosen to enforce a fixed exchange rate between the two moneys. When the market ratio diverges from the fixed ratio, the undervalued money—the "good" one—will disappear from circulation while the overvalued money —the bad one—will become the exchange medium of choice. Bad money drives out good money because they pass by law at the same fixed price.

That's the classic Gresham's law. However, it's possible to show how an authority can set a fixed price between two moneys yet rather than the bad coin chasing out the good, the opposite happens: the good coin chases out the bad.

Before I show how, let's first give an example of Gresham's law. Say that new full-bodied silver coins and debased silver coins with the same face value circulate concurrently. If authorities set a law requiring that all coins must be accepted by the populace at face value, buyers and debtors will only settle their bills in debased silver coin (the "bad" money). Full-bodied coins (the "good" money) will be held back as hoarders clip off a bit of each coin's silver content, converting the entire full-bodied coinage into debased coinage. After all, why spend x ounces of silver on goods when a smaller amount will suffice? Thus the bad chases out the good.

Now let's vary our example to have good money chase out the bad. Say authorities promise two-way conversion between all silver coins at face value. Everyone will bring debased silver coins, the "bad" money, to the authorities for conversion into full bodied coins, the "good" money. In essence, they are bringing in x ounces of silver and leaving with x + y silver. This will continue until every bad coin has been deposited into the authority's vaults so that only the good money circulates.

So why in the first case does bad silver coin chase out good yet in the second good chases out bad?

When coins circulate at face value while their true market price differs, a mispricing is created. Any mispricing provides an arbitrage opportunity. In our first example, the arbitrage is such that all those holding full-bodied coin can take a full-bodied coin, file off some silver, and purchase the same amount of goods as before with the now debased coin, all the while keeping the silver clippings to themselves. A different sort of arbitrage opportunity arises in our second example. Because the authorities offer a two-way conversion feature, everyone holding debased coins gets to enjoy a risk-free return by bringing those coins in for conversion into full-bodied coins. They get more silver with less.

So the way that the arbitrage opportunity is structured will either incentivize the population to switch to bad money or to good. We get Gresham's law if people switch en masse to bad coins, and we get an inverse-Gresham effect if they take advantage of conversion and switch en masse to good coins. Since I'm not feeling especially creative, I'll call this effect Mahserg's law (Gresham spelt backwards).

My favorite modern example of Gresham's law is the proliferation of credit cards. In the same way that an owner of a full bodied coin could clip a bit of "bonus" silver off the coin while still being guaranteed the same purchasing power, payment with a credit card allows its owner to maintain their purchasing power while getting rewards to boot.

There are a few modern examples of Masherg's law. In 1978 U.S. authorities created a situation in which two different exchange media with the same denomination circulated concurrently, the Susan B. Anthony dollar and the good old $1 US bill. Because it was novel and untrusted, the Susan B. Anthony was considered to be "bad" money. The dollar bill, which enjoyed network externalities that had been established over a century of use, was the "good" money. The Federal Reserve offered two-way conversion between coin and paper. The inevitable result was that whatever Susan B. Anthony dollars were emitted into the economy were quickly brought back to the Fed to be converted into paper dollars. The good money drove out the bad. To this day Susan B. Anthony dollars are nowhere to be seen.

Another example of Masherg's law is a good old bank run. Take the intra-Eurosystem bank run that began after the credit crisis. There exist many different brands of euros, some issued by Germany, some by Greece. As a condition of membership in the Eurosystem, all nations are required to accept each other's euros at par. With the spectre of euro breakup growing in 2010 and 2011, Greek euros came to be viewed as inferior to German euros. Since it was possible to convert the bad into the good at par, everyone leaped at the opportunity. The quantity of bad Greek euros rapidly contracted while the quantity of good German euros grew, a process that would have eventually resulted in the complete extinction of Greek euros if Mario Draghi hadn't stepped in to short-circuit the run.

My favorite modern example of Masherg's law is the zero-lower bound. A central bank issues two media, dollar bills and dollar deposits. It allows free conversion between the two at par. Say that the central bank reduces the interest rate it pays on reserves to a negative rate so that reserves are inferior, or "bad", relative to 0%-yielding bills, which are now good. Anxious to avoid the negative rate penalty, everyone will race to convert their reserves into cash at the central bank until reserves no longer exist. The good has chased out the bad.

The zero-lower bound can be thought of as the lowest rate that a central bank can institute before setting off Masherg's law. Modern central banks are petrified of encountering this particular law—that's one reason that they aim for a positive inflation target

And what about Gresham? Say our central bank reduces rates below zero. If the central bank ceases allowing convertibility between dollar notes and deposits but continues to require merchants to accept the two media at par, then the incentives change such that the good no longer chases out the bad. With no conversion outlet for bad currency, people will hoard notes while only deposits will circulate. After all, why use good cash to pay for groceries when a negative yielding deposit will suffice? We're back at Gresham's law, or the chasing out of the good by the bad.

Sunday, June 8, 2014

Why loonies circulate but Susan B. Anthony dollars don't

What causes a new currency to survive while others fail? Why do some cryptocoins never see the light of day while others enjoy successful launches? This post explores these questions by looking at the story of the Susan B. Anthony dollar, one of the great modern monetary failures.

Canada came out with a $1 coin in 1987 that remains in circulation to this day. We affectionately refer to it as the loonie as it carries a picture of a loon swimming on its reverse side. (The obverse side of a coin is the one that usually carries a portrait, the reverse side is opposite to the obverse side). The U.S. came out with a $1 coin in 1979, popularly known as the Susan B. Anthony dollar due to the appearance of the social reformer's face on the obverse side of the coin. Oddly, to this day the Susan B. Anthony is nowhere in sight. Americans don't hold it in their wallets or purses, nor do retailers keep them in their tills for change. Why did one monetary experiment fail and the other succeed?

The reason for introducing $1 coins is to replace relatively more expensive $1 bills. While notes are cheaper to produce than coins, the upkeep costs of a note issue are far higher than coin, especially as velocity increases. In general, higher value monetary instruments will circulate at slower velocities than lower value instruments. It makes more sense to use coins at the low-value/high velocity end of the circulation spectrum than bills because coins are both easier to sort and more durable—coins must be replaced every few decades whereas bills deteriorate within a year or two if they are used often. As the price level steadily inflates, what would have once been considered to be a high-value note that circulated only slowly enters the low value/high velocity end of the spectrum. Replacing that note with a durable metallic token makes sense... but that which makes sense isn't always that which succeeds.

One of the more popular reasons the has been put forward for the Susan B. Anthony's failure is that it was too similar to the already existing quarter in shape, size, and colour. This prevented consumers from quickly differentiating between the two coins. The loonie, on the other hand, was gold coloured due its bronze plating as well as having been minted with eleven edges to allow for differentiation when groping in one's pocket or purse. Apart from that, the weight and thickness of the loonie and Susan B. Anthony are almost identical.

I don't buy the argument that insufficient differentiation caused one coin to succeed and the other to fail. In 2000 the U.S. took another shot at debuting a dollar coin with the introduction of the so called "golden dollar" (due to yellowish tint provided by manganese brass), otherwise known as the Sacagawea dollar thanks to the appearance of this Native American interpreter and guide on its obverse.  Despite having the same golden sheen as the loonie, the Sacagawea dollar does not circulate in the U.S. Rather, huge amounts of these coins are held along with their predecessor Susan B. Anthony in the vaults of the Federal Reserve as Fed officials wait in vain for demand to pick up. (See Lotz and Rocheteau for a good explanation of this event). That's two failed monetary experiments and counting.

$1 coins languishing in a vault at the Federal Reserve Bank of Richmond's Baltimore branch
Source: NPR

Could it be that the loonie's eleven edges (the Sacagawea was smooth) were a sufficiently unique feature that the loonie stood out from the quarter and thereby successfully circulated? I don't buy it. That something so cosmetic as the shape of a coin's edge could push it into continued circulation seems silly to me. In all likelihood the Sacagawea dollar would have failed even if it replicated the loonie in every way.

The best explanation for the failure of $1 coins in the U.S. comes from Caskey and St. Laurent (pdf). They point to the network effects that must be overcome in introducing a new monetary instrument:
The benefit an individual attains from the use of a particular currency form depends on how many others are also using that currency form. For example, a new high-denomination coin can increase the range of vending machine transactions open to individuals, but only if vending machine owners convert the machines to accept the coin. Vending machine owners can increase sales from converting their machines to accept the coin, but only if the public commonly carries the coin. Similarly, retailers who learn to distinguish quickly the new coin can make small transaction more rapidly, but only if their customers have also learned to distinguish the coin quickly.
In the presence of these network externalities, anyone who doubts that a new coin will be used by others won't bother spending the time and effort to familiarize themselves with the coin and make the necessary adjustments. If everyone behaves this way, the coin will never get off the ground. We get the unfortunate consequence that even though the substitution of notes by coin makes society better off, a set of perverse self-perpetuating beliefs prevents that solution from ever being selected.

So why did the loonie survive? Caskey and St. Laurent point out that the government stepped in to ensure that the network externalities that would surely have prevented the loonie's success were removed. In 1988, the year after the loonie's debut, the Bank of Canada announced that it would be withdrawing the $1 note from circulation. Consumers and retailers were given no choice but to adapt to the loonie's arrival. U.S. authorities, on the other hand, never tried to dash the existing network effects that favoured the status quo by withdrawing the $1 note. Because $1 bills and coins co-circulated, the public was given a choice between a perceived "good" currency, the existing and comfortable note, and a "bad" currency, an unfamiliar coin. They took the less costly route and stuck with the "good" notes.

Unfortunately this left the U.S. in the worst possible situation. Having failed to arrive at the welfare maximizing solution—the replacement of notes with coins—it was stuck not only with its existing and expensive $1 note circulation but it now had to pay ongoing costs for storing the unwanted coin.

This makes me think about the mad dash to create new cryptocurrencies. I remember a time when there were only five or six of them, but now there are around 313 cryptocoins according to Coin Market Cap. Many of the newer coins that have debuted over the last year are no doubt technically superior to Bitcoin, and the welfare of the universe of cryptocurrency users would surely be improved by the phasing out of bitcoin and the adoption of the best of these new coins. However, as the incumbent, bitcoin enjoys tremendous network effects. The public is already familiar with the various bitcoin wallets and client as well as the markets in which it trades and all the related bitcoin jargon that goes with it. Why bother spending the time and effort to understand a new cryptocoin if there is no guarantee that it will ever be widely accepted? Because everyone thinks this way, the cryptocurrency world has locked itself into an inferior currency structure. While it should be using something like SusanBAnthonyCoin, it still clings to bitcoin.

Or consider the current system. We could make the argument that the world would be better off it stopped using bank deposits, wire transfers, and cash and instead adopted bitcoin due to the latter's superior speed and low cost of maintenance. However, absent the cooperation of a large actor like the U.S. government to overcome the network effects that the existing system enjoys, it is unlikely that the technically superior option will ever be selected. Just like Susan B. Anthony dollars drift around as little more than a curiosity some 34 years after their debut, bitcoin may be no more than a neat curio in 2044 if the network effects that it faces are not overcome.

As for the $1 coin, at some point you can be sure that the U.S. will take its third swing at the bat. Let's hope that when the time comes they won't make the same mistake.