Is the value premium a liquidity premium?

 The "High minus low" strategy: Source 

If you haven't read Clifford Asness and John Liew's recent article on market efficiency, you should. There's plenty of meat in the article, but the one sinew I want to chew on is this above chart.  It shows the cumulative returns to a strategy called HML, or "high-minus-low."

This strategy involves going long cheap U.S. stocks (as measured by their price-to-book ratio) and simultaneously going short expensive stocks. Over the last eighty-five years or so, cheap stocks have roundly beat out expensive ones. This is called the value premium. A large part of Asness and Liew's investing effort revolves around exploiting this premium for their clients at AQR Capital Management.

Now as the authors point out, this outperformance could be due to a combination of two things. The behavioural explanation is that people are irrational, subject to various psychological tics that drive aberrations in prices. Perhaps investors are fickle and would rather plunge into sexy and expensive concept stocks than purchase boring but cheap stocks. Asness and Liew propose the idea that investment committees don't have sufficiently long windows for evaluating the performance of their investments. Whatever the explanation, by trading against the various behavioural tics, investors can earn superior profits.

The other explanation is that the value premium has a very rational underpinning. Those who buy cheap stocks and sell expensive ones need to earn a higher return because they must be compensated for bearing some sort of inconvenience, or because they are providing the market with some extra service.

What is that something? My guess is that if you were to adjust the HML strategy's results to account for the superior liquidity return provided by stocks that seem expensive, you'd probably see the returns on cheap and expensive stocks converge. What appears to be an anomaly on the chart is just the shadow of a liquidity premium. Asness and Liew aren't exploiting an irregularity, they're producing liquidity—and getting paid a fair rate for doing so.

Take two companies that are identical except that the shares of the first are more liquid than the second (yep, I've been down this road before). Given a choice of buying either of the two, investors will always prefer the more liquid share. Owning a stock with low bid-ask spreads and plenty of depth provides investors with the comfort of knowing that should some unpredictable event arise, they can easily sell their shares in order to mobilize the necessary resources to cope with the event.

We can think of people "consuming" the comfort provided by liquid shares, much like they consume the peace of mind provided by a fire extinguisher stored away in a closet. If we want more peace of mind, we need to buy a better quality fire extinguisher and/or shares with a higher degree of liquidity. If we can do with less, then we can buy a smaller fire extinguisher and/or switch into illiquid shares.

We can decompose the price of a share into two parts—the price people pay for the share's earnings, and the premium they are willing to cough up to consume the peace of mind that its liquidity provides. Since the earnings on our two shares are the same, the portion of each share's overall price that is explained by earnings will be equal. However, people will put a small premium on the consumption value of the services provided by the illiquid shares and a large premium on the superior consumption yield provided by liquid shares. The difference in premiums means that the market price of the liquid share will be higher than the illiquid one.

Because of this price discrepancy, people will typically say that the liquid share is "expensive" and the illiquid one "cheap", but these are misnomers. The liquid shares provide a stream of valuable services that the illiquid shares fail to provide, and therefore logic dictates that they must trade at a higher price. They might seem expensive relative to underlying earnings, but only if we intentionally ignore the very real flows of consumption that they provide.

By selling "expensive" stocks and buying "cheap" ones, Asness and Liew are really just selling liquidity while taking on illiquidity. In short, in exploiting the HML line they are acting as liquidity providers. Just like Kidde (a major manufacturer of fire extinguishers) provides the world with a worthy service—peace of mind—Asness and Liew are producing and selling that very same good. They are willingly holding the illiquid long positions that others would prefer not to hold, thus forgoing the peace of mind enjoyed by others. And in borrowing and selling liquid shares, they are feeding liquidity into the market that would otherwise be stranded in someone's account at a depository.

Just like Kidde should be well-compensated for its product, Asness and Liew should be appropriately rewarded for their sacrifices. As compensation, their illiquid long position will typically appreciate at a faster rate than an equivalent liquid long position. And their liquid short position will appreciate at a slower than an equivalent illiquid short position.

This difference in expected price appreciation emerges because in equilibrium, an illiquid share needs to provide the same total expected return as a liquid share. Liquid shares already provide an outsized non-pecuniary return (their ability to act as fire extinguishers). In order to counterbalance this, the illiquid share must provide an outsized pecuniary return, or a faster rate of price appreciation. I'm ignoring dividends here. (Again, see this post).

So the HML line charted above illustrates the financial compensation that flows to folks like Asness and Liew who go out of their way to fabricate financial fire extinguishers. (I don't doubt there are also behavioural reasons for it.) Or, conversely, it represents the financial return that people are willing to forgo in order to consume the services provided by liquid shares.

To some degree, Asness and Liew's HML strategy reminds me of the strategy used by Long Term Capital Management. LTCM did a lot of convergence trades in treasury markets. It shorted "on-the-run" bonds, the most recent vintage of debt issued by the government, while purchasing "off-the-run" bonds. On-the-run bonds attract more liquidity than an equivalent off-the-run bonds, and therefore trade at a premium. Thus we see different prices for what are otherwise two identical securities. After a few weeks go by, the current on-the-run bond is replaced by the next issue and suddenly loses its liquidity premium. As long as the short position in on-the-run bonds is held until the next treasury auction, it yields a guaranteed gain when offset against the long position.

Source

I don't think that the profits that LTCM enjoyed by exploiting the on-the-run convergence trade should be thought of as arbitrage gains accruing as a result of other people's irrationality. Much like Asness & Liew and Kidde, LTCM was fabricating peace of mind for others; it held the illiquid securities others didn't want while borrowing and supplying the market with the liquid securities that others preferred. The "excess" return that LTCM enjoyed was the market's fair reward for providing this service.

The service that Asness and Liew provides also reminds me of what a bank does. A bank purchases illiquid personal IOUs issued by families and businesses while selling highly liquid deposits. The bank needn't offer much of an interest rate on deposits because deposits already provide a high liquidity yield. It requires a high interest rate on the IOUs it purchases because it must be compensated for absorbing their illiquidity. The spread the bank earns by holding illiquid assets and providing liquid assets is similar in nature to the HML spread earned by Asness and Liew, and the on-the-run/off-the-run spread earned by LTCM.

Of course LTCM eventually bit the dust. But that didn't have anything to do with the demise of the convergence trade, it had to do with leverage. When its debtors proved unwilling to roll over LTCM's funding, the fund was forced to liquidate at a loss before its positions had converged. If LTCM had been less aggressive, it could have easily held its positions until payoff. The firm might still be in the business of producing fire extinguishers for the financial community, just like Asness and Liew are doing by participating in the HML trade.

Beware the financial Jeremiahs

Jeremiah, the prophet of impending disaster. By Rembrandt, 1690. See full version.

The 1929 analog model has resurfaced.

The 1929 analog is a recurring visual meme, usually a chart, that periodically plagues financial markets. All versions of this meme invariably map the bobbing and weaving of the 1929 Dow Jones Industrial Average onto movements in the present Dow, with the inevitable conclusion being that we are, by analogy, on the verge of a repeat of the 1929 crash.

The most recent reincarnation originates from noted market timer Tom DeMark. His claim has been amplified by newsletter writer Tom McClellan and irresponsibly blared all over the internet by Marketwatch (see here, here, here). I produce the chart below:

Source: Marketwatch

I've been following various flareups of the 1929 analog for over a decade. They usually crop up in September, just before the anniversary date of the October 29 crash. Extended bull markets are particularly fertile ground for 1929 analog behaviour as the long run-up to the 1929 crash will typically map quite well to the current bull market. Financial Jeremiahs, those whose bread and butter is to perpetually predict hard times, are a major source of these graphics. The meme typically dies a quick death as market movements subsequently fail to conform to the analogy. DeMark's version has received far more press attention than any of the other flareups I've followed, thus this post.

The 1929 analog chart always has been and always will be silly. Worse, there is always a small chance that the chart will have large repercussions (more on that later).

The chart is silly because there's no logic behind it. It simply doesn't follow that the alignment of prices today with prices from eighty years ago means that subsequent prices must adhere to the old path. There's little else to be said.

What makes the chart so effective isn't the logic that underlies it (there is none), it's because it harnesses our brain's automatic ability to rapidly complete patterns. Our brains are always trying to pick out visual regularities in the chaos, or to generalize. This is an incredible power, allowing us to recognize a face at night using only a few cues, or pick out a dalmatian against a camouflaged background (see picture below).

When we look at the 1929-2014 analog, the chart is virtually begging us to complete the pattern. Note, for instance, how the red line has been placed a constant distance below the blue line rather than having the lines cross over each other. This isn't an accident—it's a feature designed to crystallize the comparison in the mind of the viewer. Any crossing over of lines would only impede the viewer's ability to rapidly make the analogy.

In the same way that we get an aha! moment the moment that we finally tease out the dalmatian from its surroundings, the transferral of the 1929 crash onto the as-yet incomplete 2014 plot provides us with a burst of satisfaction. So we stop thinking, the puzzle seemingly complete. The long and sober thought processes that should go into forecasting a major turn like a crash is short-circuited by the superficial sense of completion that the overlay of prices gives us. And that's what the chart maker wants, to short circuit are deeper thought processes by appealing to our innate propensity to rapidly fill in the visual blanks.

Unfortunately, this silly chart has a very small chance of having large repercussions.

Assiduous readers may remember that I wrote about the 1929 analog last October. In that post I hypothesized that the best explanation for the 1987 stock market crash was an emergence of the 1929 analog meme. The mechanism would have worked something like this...

At some point in 1987 stock prices began to randomly overlap with a plot of 1929 prices. Traders found meaning in this fluke and began to trade using the 1929 trajectory as a guide. Paradoxically, their trading helped push prices in the same direction as the 1929 plot, reinforcing the similarity between the two charts. This would have only increased the degree of belief they placed in the analog, causing them to increase their 1929-inspired trading, this activity creating ever more conformity between 1929 and 1987 prices. A feedback loop had been created, a loop that would only have expanded as traders told their friends about the pattern, thus expanding the size of the population who was driving the process. The feedback loop finally culminated in a self-realization of the 1929 crash on Monday, October 19, 1987. (This is just a short summary, go read the full article.)

This is why DeMark's 1929 analog, amplified by the likes of McClellan and Marketwatch, has the potential to be dangerous. Despite being no more than a silly picture, if enough people believe in it, that silly picture could actually inspire a stock market crash. Markets, after all, are reflexive. Fundamentals usually drive the ideas that people use to inform their trading behaviour. But at other times, ideas get a life of their own, and when enough people adopt them, these ideas create the very underlying reality that they only claimed to predict. In markets, silly beliefs can become true.

The way I see it, it's our duty to provide a counterbalance to destabilizing reflexive forces like these by either ignoring financial Jeremiahs or roundly vilifying their ideas. After all, sharp downturns are healthy insofar as they are justified by actual events and changes in the fundamentals, but if they're created by mass faulty thinking, everyone is made worse off.

I couldn't help but notice that DeMark was employed by Tudor Investments from 1988 to 1990. Interestingly, Paul Tudor Jones, founder of Tudor Investments, made a pile of money during the 1987 crash by basing his trades on a 1929 analog model (again, read my old post). It would seem that DeMark isn't doing anything new, he's simply repeating a time tested strategy once used by his former employer. A cynic would say that folks like Tudor Jones and DeMark spread the 1929 analogy not because they actually believe in it, but because they want to harness people's tendency to overgeneralize for their own gain. If enough proles take the hook, then markets could plunge, thus benefiting Tudor Jones's and DeMark's pre-existing trading positions. I'm sure that's not the case and that all parties are being genuine. But advertising a trade after one is already in it, i.e. talking one's book, is a time honoured strategy among finance professionals.

With the Dow having such a good performance in February, the simplistic analogy between 1929 and 2014 is slowly being stretched to the point that it no longer aligns. It looks like the DeMark's analog model could die a natural death. However, there's a simple strategy often used by those calling for the end of times. When Warren Jeffs, president of the Fundamentalist Church of Jesus Christ of Latter-Day Saints, predicted the end of the world on December 23, 2012, and it failed to happen, he changed the date to December 31. The 1929 analog can simply be redrawn, shifting the entire 1929 plot over to give more time for the our current market to ripen towards an imminent crash. Even if DeMark isn't the one to do it, someone else will draw the analogy. The longer the current bull market continues, the more fertile the ground will be for these sorts of destabilizing memes.

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P.S.: Most commentators have been vilifying the chart, which is good. (See Matthew Boesler, The Reformed Broker, Matthew O'Brien, and the Wall Street Journal). Their criticisms are mostly along the line of... "the analog is less apparent if we rescale the axis." They use something like the chart below as their rebuttal in order to decouple the performance of 1929 and today.

Source: Business Insider

This rebuttal is a weak one since it gives too much ground to the supposed logic that underpins the 1929 analogy. Say that the two plots were to be correctly scaled and say that the prices in one era closely aligned with the other. There would still be no good reason to assume that the current period must follow the prior one into a nosedive. In attacking the scale of the chart, critics are missing the larger error that underpins the 1929 analog.

In short, don't give into your brain's rapid ability to complete these facile patterns. A truly well-reasoned crash prediction would require such a massive allocation of mental power to arrive at that no one would ever actually get there. Admittedly I'm being a nitpicker here. Though the various rebuttals all appealed to the same bad logic that the original chart did, at least they helped counter the reflexive properties of the most recent appearance of the 1929 analog. An enemy of my enemy is my friend, I suppose.

When money ceases to be an IOU

Despite its odd denomination, the above is a genuine banknote. Ne Win, Burma's military dictator from 1962 to 1988 and the man pictured in the note, was convinced that his lucky number was nine. So he had notes issued in multiples of nine, including the forty-five and ninety kyat notes (which also each add up to nine 4+5=9, 0+9=9). But I'll get to this story later.

This is a continuation of a post I wrote earlier describing how central banknotes aren't mere bits of intrinsically useless paper. The standard view among economists is that banknotes are bubble assets. Because they are intrinsically valueless, the fact that paper notes earn a positive value can only be explained by the fact that the market expects them to have value in the future, much in the way that a ponzi scheme or chain letter is perpetuated. This view goes back to Paul Samuelson (pdf), who described how a "grand consensus" might be arrived at whereby society could contrive to have "oblongs of paper" pass at a positive value from generation to generation. The creation of such a bubble would allow for an efficient allocation of resources. As long as each generation could fool itself into thinking that the next would accept these worthless bits of paper, the scheme could continue indefinitely.

However, if real life banknotes were in fact pure Samuelsonian bubbles, then no one would bother participating in central bank redenominations. If a central bank were to announce a 10:1 redenomination, why take in your $1000 note to be redeemed for a $100 note? After all, your existing $1000 note will buy you more stuff than a prospective $100. That we do take part in redenominations is due to the fact that the central bank is threatening to do something to its legacy note issue—it is threatening to cease honouring them as its liability, or IOU, an act sufficient to drive that notes' value to zero. This quality of a banknote as a liability or IOU means that a note is not a Samuelsonian asset.

That central banks offer legacy note conversion at all  is another sign of the IOU-nature of bank notes. It explains why we don't see revolutions during redenominations and demonetizations. Those suddenly left holding old paper would riot on the streets upon the sudden displacement of their notes by a new currency. We don't see riots due to redenominations or demonetizations because banknotes aren't Samuelsonian—central bank paper carries an implicit IOU whereby the central banker will typically repurchase the legacy notes that they've issued at a fixed rate rather than letting those notes flap around in the wind.

For instance, when the European central banks ceased their issuance of domestic banknotes they didn't strand them. Rather, they offered a window in which individuals would convert legacy notes into euros. This window varied in size by country. In the case of the Banca d'Italia, for instance, lira could be converted into euros until February 2012, a ten-year window. De Nederlandsche Bank continues to offer to convert old Dutch guilders into euro, and will do so until 2032, while the Bundesbank, Banca D'Espana, and the National Bank of Belgium guarantee to perpetually redeem deutsche marks, pesetas, and francs respectively with euros. Here is a full list:

As a convertibility window narrows toward zero, a central bank's paper loses its IOU nature and approaches the ideal of Samuelsonian money. For instance, when Saddam Hussein decided to cancel the old "Swiss Dinar", he did so by offering note holders a tiny six-day exchange period, a mere crack compared to the massive windows left open by European central banks. Saddam narrowed this aperture even further by deviously shutting down the Iraqi border during the exchange period, preventing the large population of merchants in Jordan and elsewhere from crossing over into Iraq to swap their Swiss dinars for new dinars.

The Burmese kyat, pictured above, is another example of a note that approaches bubble money. In September 1987, Ne Win demonetized the largest denominations of kyat: the twenty-five, thirty-five, and seventy-five kyat notes, issuing in their place the aforementioned forty-five and ninety notes.

As dictator, Ne Win didn't seem to see any problem in burdening the Burmese population with these awkwardly-denominated notes. The legacy notes being replaced that September were already in odd denominations (25, 35, and 75), the hallmark of a redenomination in 1985 that replaced more conventional denominations of twenty, fifty, and one-hundred kyat notes. It seems that the seventy-five note was issued to mark Ne Win's 75th birthday, and the thirty-five replaced the fifty because it was, according to Ne Win's numerologist, the luckier of the two numbers.

To make matters worse, the legacy issue of kyat notes could not be converted into new forty-five and ninety kyat notes, effectively removing the IOU embedded in kyat notes and rendering a large part of the nation's stock of notes worthless. Here is an account of a Burmese individual at the time:

Then on September 5, without alerting even his cabinet, Ne Win passed a sealed envelope to the Information Minister. Inside were instructions to broadcast the enclosed announcement at 11:00 a.m.

I listened to the 1:00 p.m. news on the car radio outside the art exhibition. When the announcer said government employees would receive 450 kyats as emergency funding, I knew our kyat notes in denominations of 75, 35, and 25 had all been instantly devalued. At home that afternoon my family members gathered to pool our currency. Ko Gyi had received cash payment from a client on Thursday, all in 75-kyat notes, and I had not yet opened my two most recent pay envelopes, one containing my salary, the other my bonus, also dispensed in 75-kyat notes. My brother and I together had only 25 kyats in 10- and 5-kyat notes. Our other cash was useless.

Still hoping from compensation after the demonetization announcement in 1987, some people hoped to make a quick profit. Expecting a grace period, they started collecting 75 kyats by paying 50, then collecting 30 kyats for the same amount, then 20, until finally, when no follow up news came from the government, they realized they had lost everything. Two thirds of the total currency in circulation became useless paper, and ordinary citizens lost their entire savings. Even the beggars suffered.  - No Time for Dreams: Living in Burma Under Military Rule, by San San Tin

Ne Win had contrived to create Sameulsonian money.  Rather than greeting Ne Win's contrivance with open arms, popular uprisings began in 1988, eventually leading to Ne Win's resignation. Aung San Suu Kyi would emerge as an opposition leader in these uprisings.

North Korean won are a more recent example of notes devolving into mere "oblongs" of paper. In November 2009, the North Korean government announced a 100:1 redenomination. Nothing unusual here, except that North Koreans were given a seven-day window to convert existing Korean won into new notes. This window, already narrow, was further constricted by a ₩100,000 limit on the amount that could be converted. Given the then prevailing black market exchange rate of ₩3,000 to the dollar, the amount of legacy won that could be converted into new won was limited to around $30. Tragically, any North Korean who had won-denominated savings larger than that amount lost much of what they had.

Public anger forced the government to increase the limit to ₩150,000, but widespread uprisings as in the case of Burma never followed. The perception that future surprise redenominations might rob existing note holders has not promoted the stability of the won. Indeed, the inflation rate in North Korea is one of the highest in the world. Circulation of US dollars and Chinese yuan increased dramatically as a result of the redenomination, since no one fooled once wants to be fooled twice. (A shift to the use of the dollar also occurred in Burma as a result of Ne Win`s 1987 redenomination, as this interesting article points out.)

Though Samuelsonian money is an elegant idea, the reality is ugly. Only the most sinister dictators have tried to perpetuate it. The contrived currencies that have had Samuelsonian characteristics—Burmese kyat, North Korean won, and Saddam dinars—have been among the world's worst currencies. Widely accepted and long-lasting bank notes like dollars and euros are not bubble-like. Their issuers threat these as IOUs, much like a stock or a bond. If they fail to take these commitments seriously, say in the case of redenominations, their currencies will quickly be out-competed by currencies issued by banks that do.

Not all bitcoin are equal or: One dollar, two prices

A page from  Van Court's Bank Note Reporter and Counterfeit Detector (1843), showing multiple prices for various dollars. Notation: do=ditto, same as above | par=no discount | 20 = 20% discount | 1 = 1% discount | no sale = 100% discount | fail'd=failed bank, 100% discount | clos'd=bank closed, 100% discount

For the past year or so, US dollars deposited at the MtGox bitcoin exchange haven't been considered to be particularly good dollars. The problem is that they are illiquid. Due to a number of reasons (see Konrad Graf), MtGox has limited the ability of users to convert MtGox dollars into conventional dollars issued by the likes of Bank of America, Wells Fargo, and the US Federal Reserve. Withdrawals are slow, uncertain, and red tape abounds.

Current holders of "bad" MtGox dollars would very much like to make their dollar-denominated wealth more liquid. Unfortunately the only reliable route available to them is to exchange their bad MtGox dollars for someone else's bitcoin via MtGox's order book, then move these bitcoin off-exchange in order to purchase better and more liquid US dollars elsewhere. But why would a potential counterparty with spare bitcoin want to engage in this trade? After all, if they do then they'll only end up incurring the very same illiquidity risk that the original owner of MtGox dollars seems so desperate to offload. Better for the potential counterparty to sell their bitcoin for "good" (i.e. liquid) dollars at a competing exchange (like Bitstamp) that doesn't impose dollar redemption hassles.

In order for them to accept the burden of MtGox liquidity risk, potential purchasers of MtGox dollars must be cajoled into the trade by the promise of a large discount. Owners of MtGox dollars eager for bitcoin need to mark down the price at which they are offering their MtGox dollars, or, conversely, they need to mark up the price at which they will purchase bitcoin relative to the price at which it trades on other exchanges.

This, in short, is the most likely reason for the historical premium of MtGox bitcoin over bitcoin on other exchanges like Bitstamp and BTC-e , or, conversely, the discount of MtGox dollars relative to dollars on other exchanges. See the chart below, which shows how the MtGox USD/BTC rate has historically traded at a discount to the Bitstamp USD/BTC trade. (Note that I've flipped the traditional bitcoin price chart upside down to emphasize the dollar-side of the equation). In short, because they are relatively illiquid, MtGox dollars can't purchase as many bitcoin as Bitstamp dollars can.

Now as our chart shows, things have dramatically switched around, with MtGox USD/BTC recently flipping to a massive premium over Bitstamp USD/BTC. I'll get to that in a bit, but before I do so let's imagine the opposite situation to the one outlined above, a limitation on bitcoin withdrawals from MtGox. In this case things would tilt the opposite way. The only way to liberate wealth in the form of bitcoin from MtGox would be to buy MtGox dollars and withdraw them, then buy "good" bitcoin elsewhere. Counterparties would only agree to sell dollars for "bad" MtGox bitcoin if they were offered a steep discount on those coins. The price of MtGox bitcoin would have to be marked down relative to elsewhere, or, conversely, the price of MtGox dollars marked up relative to dollars elsewhere.

Let's imagine another scenario. What if redemptions of *both* MtGox bitcoin and MtGox dollars were halted or at least slowed? Put differently, what if both are equally bad, or illiquid?

In this case, an owner of MtGox bitcoin would see no benefit in offering to buy MtGox dollars at a premium since those dollars would be just as illiquid as bitcoin. Nor would an owner of MtGox dollars have any incentive to buy MtGox bitcoin at a premium, since those bitcoin would be just as unmarketable as dollars. The upshot is that the MtGox USD/BTC exchange rate would show neither a premium nor a deficit relative to the prevailing exchange rate on other markets.

However, the fact that we would no longer see any discrepancy in the MtGox USD/BTC exchange rate relative to the Bitstamp USD/BTC would not indicate that all is normal in the bitcoin universe. The freezing up of MtGox would reveal itself in a market we haven't considered yet: the MtGox USD/Bitstamp USD market. Presumably there is some sort of over-the-counter market on which trusted individuals directly swap the dollar deposits of one exchange for another. With MtGox freezing all withdrawals, we'd expect this exchange rate to be trading at a large deficit, investors willing to pay a much higher price to own liquid Bitstamp dollars. The same goes for the MtGox BTC/Bitstamp BTC market. Normally, this market would trade at par, since a bitcoin held on one exchange should be no different from a bitcoin at another. However, with MtGox frozen up investors would probably prefer to own liquid Bitstamp bitcoin and would pay a much higher price to do so.

Now let's get back to the inversion we see on our chart. There's been some interesting news in the bitcoin universe. It appears that MtGox bitcoin withdrawals have been halted, adding to the already-existing liquidity problems facing MtGox dollar owners. Peter Šurda gives more details here. As I pointed out above, if both bitcoin and dollars at MtGox have now been rendered equally illiquid then the MtGox USD/BTC ratio should not vary from prevailing USD/BTC ratio at exchanges like Bitstamp and BTC-e.

But what we've actually seen is a huge rise in the MtGox USD/BTC ratio relative to that of Bitstamp. The discount has become a premium. This would seem to indicate that though MtGox dollars are still relatively illiquid, they are more liquid than now-frozen MtGox bitcoin. Those with bitcoin-denominated wealth stuck in  MtGox desperately want to trade "terrible" MtGox bitcoin for "less terrible" MtGox dollars in order to flee. They are offering an incredibly high USD/BTC rate to tempt counterparties into taking the opposite—and more illiquid—side of this trade.

Now before you start shaking your head about the strangeness of modern cryptocurrency markets—"how weird is it to have multiple prices for the same money!" —note that we've seen this all before. In the first half of the 19th century, there was a bewildering quantity of different US dollar banknotes, with thousands of banks issuing their own brand. Prior to accepting a certain bill from a customer, a shopkeeper would consult his weekly Bank Note Reporter to determine what sort of discount or premium he should attach to the note.* (See the picture at top). In those days, notes were universally redeemable in a certain quantity of gold. What made things tricky was the fact that redemption could be easy or difficult, depending on how far away the issuing bank was. A note issued by a bank based in rural Pennsylvania and spent in South Carolina would have to take a circuitous and potentially expensive route back to its issuer prior to being cashed in for the metal. This resulted in those notes earning a higher discount. One dollar, multiple prices, was the norm back then.

Now compare MtGox to our rural Pennsylvanian bank. Given the long and circuitous route that both the banknote and the MtGox dollar must take prior to being "cashed out", they both trade at a large discount. Once again we have one dollar but multiple prices. Everything old is new again, it would seem.

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*If you're interested, Gary Gorton provides an introduction to Van Court's Bank Note Reporter and Counterfeit Detector (pdf)

The cost of manufacturing liquidity premia

I'm going to use a stock market analogy to work out the costs of manufacturing liquidity premia.

In addition to paying dividends and providing price appreciation, stocks provide an amenity flow in the form of expected exchangeability, or liquidity. Like any other consumption good & service, the provision of such an amenity requires an outlay by the supplier. In the same way that a widget producer won't sell widgets below marginal cost, the marginal seller of stock, the issuing firm, won't manufacture new liquidity if the cost of production exceeds the benefits.

Say that a firm can hire an entire investor relations department for next to no cost. The IR team, full of eager promoters, will double the price that the marginal investor is willing to pay for the liquidity services thrown off by the firm's stock. They go about improving the stock's liquidity services by evangelizing the firm's "story", thereby widening the base of investors who deal in the shares. They make it easier for investors to hop in and out of the market.

The firm can now issue new stock at a much higher price thanks to its swollen liquidity premium. It invests the proceeds of new issuance at the risk-free rate of return. The firm has succeeded in getting something for nothing—at no cost to itself it has increased earnings-per-share. By issuing more shares the firm can continue to earn these extra-normal returns, at least until new issuance has satiated investor demand for liquidity and driven the firm's liquidity premium back to its previous level, at which point the strategy will have exhausted itself. New stock issuance will no longer increase per-share earnings.

Of course, investor relations teams can't be hired for nothing. If firms could perpetually increase earnings per share by costlessly boosting their liquidity premium and issuing new shares, then everyone would be doing it. In general, the price of hiring an IR team should be set such that it just offsets the benefits of the increase in a firm's liquidity premium. If the cost is lower, then firms will all try to purchase IR services in order to enjoy extra-normal profits, driving IR costs higher until the window for extra-normal profits has been closed. If the cost is higher, then firms will fire their IR department, the benefits of the liquidity premium manufactured by the IR department not justifying the expense of paying their salaries. In this case, IR costs will retreat until firms once again see some advantage in trying to hire an IR department to generate liquidity premia.

In short, the price that investors pay to enjoy a liquidity premium will be competed down to the IR costs of producing that premium.

Incurring IR costs are not the only way to do encourage liquidity. Relationships with market makers, dealers, and investment banking research departments will also help boost liquidity premia. Illegal practices like wash-trading can do the trick too.

Keep in mind that there are also large network effects at play. Incumbent stocks that have enjoyed high liquidity premia for decades will remain locked into that position, even if the incumbent's CEO were to fire the entire IR department. Liquidity is sticky. It would take incredibly large marketing outlays for a small rookie stock to displace an incumbent like IBM from its superior liquidity position.

If you get the chance, try visiting ten or twenty websites of publicly-traded companies and note how fancy each IR section is. Some will have only bare-bones text (like Berkshire Hathaway), others will have incredibly fancy flash animation and gorgeous pictures (like any junior gold miner).

These websites will give you some sense for each firm's pool of potential projects and respective strategy. Firms with a plenty of high-yielding investment opportunities will see no benefit in allocating funds to boost their liquidity premium. These sorts of firms will generally have ugly IR sections. Firms with fancy IR websites, on the other hand, have presumably measured all potential investment opportunities and decided that the highest yielding one is to hire aggressive IR so as to boost their liquidity premium, subsequently floating new shares. Investors who value liquidity on the margin would do well to gravitate to firms that see value in manufacturing liquidity premia. If you want liquidity, then buy from the people who make the stuff. Those investors who prefer pecuniary returns rather than liquidity returns should always avoid firms with fancy IR pages. After all, why buy liquidity if you don't value it?

The boundary case of firms pursuing higher liquidity premia are penny stock promotes. These firms have no real underlying business. Their only purpose is to create a temporary liquidity premia, the insiders exiting before those premia collapse to zero.

The general principles behind the manufacturing of liquidity premia described above apply not just to stocks, but to bonds, bitcoin, gold, cars, land, banking deposits, and all sorts of other assets. As long as people face uncertainty, they will always want to own liquidity. Those skilled in the manufacturing of  this liquidity—marketers, salespeople, investor relations execs, promoters, bankers, and evangelizers—will always find their talents in high demand.

A growing liquidity-premium on land

The Cider Mill, by Robin Moline

In general, the real price of land has been increasing all over the world, especially since the early 1990s. (Japan and Germany are the exception). The recent credit crisis hurt this trend in a few countries like Ireland, Spain, Netherlands, and the US, but in other countries like Belgium, Canada, Sweden, and Australia the secular rise in housing prices remains intact.

A popular explanation for the rise in land prices are the various versions of the secular stagnation thesis advocated by folks like Paul Krugman and Larry Summers. According to Krugman, if the natural rate of interest has become persistently negative—i.e. new capital projects are expected to yield a negative return—then investors will look to existing durable assets like gold or land that yield no less than a 0% return. The prices of these goods will be bid upwards, bubble-like. Or, as Summers puts it, if the return on capital is below the economy's growth rate, then intrinsically valueless ponzi assets may be recruited as stores of value to bridge the distance between an individual's present and the future. (Krugman and Summers's ideas are a bit hard to follow, but Nick Rowe has a bunch of helpful posts on these ideas).

In short, these theories explain the paradoxical conjunction of bubbles with a sluggish economy and low inflation.

I think that a better explanation for the rise in real land prices is the emergence of large liquidity premium on land. This premium isn't an irrational "bubble" phenomenon. Rather, over the last decade or two finance and real estate professionals have put in large amounts of time, sweat, and tears to improve the underlying infrastructure that facilitates the transfer of residential land. A few of these improvements include the optimization of the mortgage lending process by the adoption of automated underwriting systems, the development of mortgage scoring, higher loan-to-value ratios on mortgage loans, and the creation of the mortgage-backed securities market.

All these improvements mean that your parcel of land is not like your grandfather's parcel—it can be sold off, parceled up, rented out, collateralized, and re-hypothecated faster than ever. In short, land has become more like cash. Whereas in the past the purchase of a house made you dramatically less liquid, these days that same house impairs your liquidity position much less.

Like any other asset owner, land owners expect to enjoy three services: a pecuniary return such as capital appreciation, a non-pecuniary consumption yield, and liquidity services. In a world in which arbitrage ensures that all assets provide roughly the same return, any improvement in the liquidity services provided by land reduces the amount of capital appreciation people expect to earn on their land parcel (we'll assume the consumption return is constant). This reduction in expected capital appreciation comes about via a rise in land prices now relative to their expected future price. So the steady improvements in the liquidity services thrown off by land have created a stepwise rise in land prices. This rise might appear to be a bubble, but it's only the market's warm response to the finance industry's consistent upgrades to the mechanisms that facilitate transfers of land.

If you believe John Maynard Keynes, what we're seeing now is just a reversion to ancient times. In Chapter 17 of his General Theory, Keynes wrote: "It may be that in certain historic environments the possession of land has been characterized by a high liquidity-premium in the minds of owners of wealth..." He goes on to note that the high liquidity premiums formerly attaching to the ownership of land are now attached to money. It may be the case that in modern times these liquidity premia are detaching from traditional forms of money like deposits and returning to land, the evidence being the rise of land prices and decline in traditional deposit banking.

When a market bursts, the stagnation thesis has it that people have spontaneously switched from one bubble to a new one, or that the underlying features of the economy (i.e the negative natural interest rate) have changed. If land price increases are being driven by improvements in liquidity services rather than low-to-negative rates of return and resulting bubble-seeking behavior, than snap-backs may occur when the underlying architecture supporting that liquidity fails. Alternatively, different networks of finance professionals may be working hard to build up their own asset's liquidity, thus competing away the liquidity premium of the incumbent asset.

Here's an interesting data point: While almost every western nation experienced a housing price boom between the mid 1990s and 2008, Germany somehow missed the boat.

From the Economist's very useful housing price chart tool.

Was Germany somehow exempt from the stagnation that other Western nation's face? Perhaps Germans selected a different bubble asset than land? Or did the underlying mechanics governing the liquidity of the German market for residential land stay constant whereas those of most nation's improved?

We know that while MBS markets were deepening all over the world, German law did not permit MBS issuance until 1997, putting it far behind the mortgage slicing & dicing eight-ball. Rather, German residential real estate finance continued to be underpinned the centuries old pfandrief, or covered bond. While  the originator of an MBS can parcel away mortgages into a bankrupt-remote entity, the assets underlying a pfandriefe are required by law to stay on the issuer's balance sheet. The mortgages comprising MBS often have up to 100% loan-to-value ratios, but German law requires that pfandbriefe be backed by mortgage loans with a maximum of 60% of the home's "lending value" (lending value is more conservative than market value), which in practice means that Germans often have to put up 60-70% cash to buy a home. Such high requirements would surely stifle the liquidity of residential land, especially compared to places like Canada where permitted LTVs went from 80% to 100% in the space of ten years.

So while Keynes's liquidity premium may have migrated back to land in much of the western world, this doesn't seem to be the case in Germany. There are surely advantages to having avoided a rise in housing prices. On the other other hand, owning a liquid house rather than an illiquid one is a boon—it provides an individual with a fluid asset for dealing with an uncertain future. From this perspective, any attempt to stifle some asset's liquidity by limiting the finance industry's ability to innovate reduces the range of coping mechanisms that  a society is presented with.

P.S. I already wrote versions of this post. Here are these ideas applied to equity markets, here they are applied to bond markets. Same idea, different day, different market.

Who signs a country's banknotes?

2010 Bank of England note signed by Andrew Bailey, former Chief Cashier of the Bank.

A few years ago, Peter Stella and Åke Lönnberg conducted a study that classified national banknotes by the signatories on that note's face. They found some interesting results. Of the world's 177 banknotes with signatures (10 had no signature whatsoever), the majority (119) were signed by central bank officials only. Just four countries issue notes upon which the sole signature was that of an official in the finance ministry: Singapore, Bhutan, Samoa, and (drum roll) the United States.

Stella and Lönnberg hypothesize that the signature(s) on a banknote indicate the degree to which the issuing central bank's is financially integrated with its government. The lack of a signature from a nation's finance ministry might be a symbol of a more independent relationship between the two, the central bank's balance sheet being somewhat hived off from the government's balance sheet and vice versa. The presence of a finance minister's signature would indicate the reverse, that both the treasury and central bank's balance sheets might be best thought of as one amalgamated entity.

The nature of this arrangement is significant because if something disastrous were to happen to an independent central bank's financial health, say its assets were destroyed and all hope of profits dashed for eternity, the central banker should not necessarily expect support from his/her government. Lacking in resources, monetary policy could go off the rails. (Why would it go off the rails? Here I go into more detail).

On the other hand, should it be established by law that a government is to backstop its central bank, that same disaster would pose a smaller threat to monetary policy since the nation's finance minister, his John Hancock affixed to the nation's notes, would presumably come to the central bank's rescue.

These ideas are similar to Chris Sims's classification of type F and type E central banks (alternative link). One of the features of type F banks (like the Fed) is that "there is no doubt that potential central bank balance sheet problems are nothing more than a type of fiscal liability for the treasury." On the other hand, with type E banks (like the ECB) "it is not obvious that a treasury would automatically see central bank balance sheet problems as its own liability."

So is it the case that the Federal Reserve is actually more fused with the U.S. Treasury than other central banks are? One reading of the Federal Reserve Act might indicate yes. Section 16.1 stipulates that Federal Reserve notes are ultimately obligations of the US government:

Federal reserve notes, to be issued at the discretion of the Board of Governors of the Federal Reserve System for the purpose of making advances to Federal reserve banks through the Federal reserve agents as hereinafter set forth and for no other purpose, are hereby authorized. The said notes shall be obligations of the United States and shall be receivable by all national and member banks and Federal reserve banks and for all taxes, customs, and other public dues.

The language in the above phrase would seem to indicate that should the Fed find itself incapable of exercising monetary policy (Stella and Lönnberg  use the term policy insolvency), the US government is obliged to step in and make good on the Fed's promises, however those promises might be construed. The fact that Treasury Secretary Jacob Lew's signature appears on all paper notes, as does that of U.S. Treasurer Rosa Gumataotao Rios, can perhaps be taken as an indication of this guarantee.

Bank of Canada notes, on the other hand, are signed by the Governor of the BoC and his deputy. Finance Minister Flaherty's signature is nowhere in sight. This jives well with a quick reading of the Bank of Canada Act, which stipulates that though notes are a first claim on the assets of the Bank of Canada, the government itself accepts no ultimate obligation to make good on banknotes. In theory, should the Bank of Canada cease to earn a profit from now to eternity, Canadian monetary policy could go haywire—American monetary policy, backstopped by the Treasury, less so.

Other central banks go even further in formalizing this separation. In Lithuania, for instance, the law states that: "The State of Lithuania shall not be liable for the obligations of the Bank of Lithuania, and the Bank of Lithuania shall not be liable for the obligations of the State of Lithuania." Should Leituvos Bankas hit a rough patch, so will its monetary policy.

Stella and Lönnberg correlate the rise of independent central banking with a movement away from the printing of finance minister signatures on notes. For instance, the sole signature on Euro banknotes is that of the President of the ECB, Mario Draghi. Two of the currencies replaced by the Euro, the Irish punt and the Luxembourg franc, which had carried signatures of finance department officials, no longer exist, symbolic evidence of the Euro project's dedication to central bank independence.

Sims uses the ECB as an exemplar of type E central banks because "the very fact that there is a host of fiscal authorities that would have to coordinate in order to provide backup were the ECB to develop balance sheet problems suggests that such backup is at least more uncertain than in the US." For evidence, he points to the fact that the Fed carries just 1.9% of its balance sheet in capital and reserves while the ECB holds 6.7%.

Stella and Lönnberg hint at the prevalence of a "rather singular U.S. view of central bank and treasury relations." My interpretation of this is that most conversations about central banking are inherently conversations about the the world's dominant monetary superpower, the Federal Reserve. This is surely evident in the blogosphere, where we mostly talk as-if we were Bernanke, not Carney or Poloz or Ingves (Lars Christensen is a rare counter-example who is fluent in multiple "languages"). In the same way that all Americans only understand English while all foreigners are conversant in English and their native tongue, non-American commentators like me can't talk solely in terms of our own central bank (in my case the Bank of Canada) lest we fall out of the conversation. The Fed becomes our focal point.

Yet among central banks, the Fed is an odd duck, since the wording in the Federal Reserve Act and the signature on its notes would indicate a more well-integrated financial relationship between central bank and treasury than most. The upshot is that popular conceptions of the central banking nexus will often be wrong as they will be couched in terms of the U.S.'s integrated viewpoint, whereas most of the world's central banks are not structured in the same way as the U.S. A deterioration of the Fed's balance sheet would likely be neutral with respect to monetary policy, but for many of the world's nations this simply isn't the case.

On a totally unrelated side note, I found it interesting that Bank of England notes stand out as being signed by the Chief cashier of the Bank, not the governor. When the BoE opened its doors for business in 1694, the banknotes it issued were written on blank sheets of paper, often for unusual quantities (standardized round numbers were not introduced till the 1700s). The bank's directors and its governor, usually well-established bankers who simultaneously ran their family business, were not responsible for the BoE's day-to-day operations, this being devolved to the bank's cashiers who were given the repetitive task of signing each note by hand. Even when the ability to print signatures directly on to notes was developed in the 1800s, the practice of affixing the cashier's signature continued, despite the fact that mechanical process would make it easy for the higher-ranked governor to get his name on each note.

So while Mark Carney's route from the BoC to the BoE got him a higher salary, more prestige, and posher digs, in one respect his standing has deteriorated: there are no longer millions of bits of paper circulating with his name on them. Chief cashier Chris Salmon has that distinction.

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PS: You should try and read all of Peter Stella's papers. They are excellent. He blogs here.

Different goods are differently liquid

An evaporation in liquidity. September 13, 2012, at 12:25:27 to ~12:32 PM, eMini contract. From Nanex.

Steve Roth, who blogs at Asymptosis, recently posted a thoughtful critique of the idea of moneyness over at Cullen Roche's blog. (We've had a series of exchanges before on these questions). Even if my response can't sway Roth it should provide new readers of this blog with a rough overview of where I've been going with the idea of moneyness.

Let's start with definitions. Moneyness is a fancy word for liquidity. In short, it refers to the ease with which we expect to be able to trade something away for another item of value. Our expectations about liquidity are conditioned by an item's historical liquidity and modified by anything that we think could change it in the future, including new market mechanisms that might promote (or demote) that item's liquidity. All valuable goods & assets have varying levels of liquidity, or moneyness. Some will be easier to market when the need arises, others will require more effort.

Roth's first criticism, published on his blog last year, is that the

“moneyness” concept... seems to hinge on a single axis of “liquidity,” when in fact different units of exchange are differently liquid.

He goes on to give more detail at Roche's blog:

Suppose you have $10k in quarters. You can buy all the Snickers bars you want; there's a very liquid exchange market (quarters for snickers bars) out there. (Though need to tromp around to buy $10K worth of Snickers bars does seem to make it less “liquid”…)

But can you buy a car with those quarters? How about treasury bonds? No. Those quarters are completely illiquid relative to cars and treasury bonds.

Now think about treasury bonds. They're completely illiquid relative to both snickers bars and, but extremely liquid relative to fed bank deposits (reserve balances) — if you have 

I don't think I have to stretch this explanation out. Think about fed reserves/deposits — they’re (il)liquid relative to what other goods/assets?

So every financial asset — in fact every real good as well — has multiple liquidities, relative to every other asset/good.

I agree with Roth. Even the most liquid items are only tradeable along a few margins, or routes. The godfather of liquidity, a US dollar chequing deposit, can get you groceries or a car, but can't buy shares in IBM. A deposit at a brokerage can buy you IBM, but it can't get you a bag of groceries or a car. Roth's well turned phrase is worth repeating here, that different goods are "differently liquid", a point that I echo in Long Chains of Monetary Barter.

However, this doesn't mean that we can't arrive at a single combined measure for all of a good's different liquidities. All we need ask an individual is 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?" 

What we are extracting here is the individual's reservation price for x's liquidity. In this setup, the individual is allowed to continue to enjoy all the various pecuniary and non-pecuniary returns provided by x during a one year period, save for one return—its liquidity return. We are asking the individual to forgo each and every one of the good's multiple liquidities, or, put differently, the various margins along which x usually trades.

Whatever compensation the individual requires for giving up the right to trade away x along all routes is an indication of the foregone value that they ascribe to each of x's multiple liquidities. By dividing this price by x's total price, we can estimate what proportion of x's overall valuation our individual attributes to the liquidity component.

I think that this meets Roth's criticism, since in effect we are asking an individual to forgo each of an asset's multiple liquidities, all at once. We can go ahead and ask that individual the same question for each asset they own: how much would you have to be paid to forgo the combined multiple liquidities of a? and b? c? In the end, we'll have a list of all the individual's assets, along with the percentage contribution that each asset's liquidity provides to its total value. Having standardized our measurement of liquidity, we can now construct our individual's scale of moneyness for the coming year, ranked from least liquid to most liquid, the most liquid being that good who's liquidity contributes the largest chunk to its total value.

The upshot: the existence of multiple liquidities shouldn't prevent an individual from making private liquidity comparisons across different goods.

Which leads into Roth's next criticism, that estimates of liquidity differ across individuals. This presumably (Roth doesn't go into detail) hampers the effort to strip out a single measure of moneyness:

the liquidity of many assets depends on who you are. If you're a bank, your treasury bill is more liquid than if you're an individual, cause the bank can trade it for reserves and the individual can't. 

Again, I agree with Roth. Viewed from the eyes of a drug dealer, a chequing deposit is surely much less liquid than cash, while from the eyes of a typical nine-to-fiver, the opposite would be the case.

However, the charge of subjectivity shouldn't preclude us from extracting a market price for liquidity. After all, markets provide prices for diverse consumption goods like wheelchairs, which though an integral part of the life of an eighty-year old, from the perspective of a healthy twenty year old might be worthless. Milk is off-limits for the large portion of the population that is lactose intolerant while being popular with the rest—but markets are still capable of spitting out one price for milk. A particular good's liquidity, like a wheelchair or a carton of milk, is a consumption good the utility of which varies from individual to individual, yet in a competitive market these varying preferences should nevertheless interact together to create one market clearing price for these goods.

What follows is basic microeconomics. We can construct an individual's demand curve for x's liquidity by querying how much he or she would be willing to pay for those services at various prices. If we do this for all individuals and all assets, we can construct market demand curves for each asset's liquidity. Given a set of supply curves (supply is a totally different post), we can then submit this data to a Walrasian calculator to determine the market prices for these liquidities. These prices can be used to calculate the contribution made by liquidity to each asset's total market price, and from there we can proceed to construct the market's scale of moneyness, the asset with the most moneyness being that asset whose price is made up of the largest liquidity contribution.

The upshot is that the many differing personal scales of moneyness that Roth draws attention to can be reconciled by a market-wide moneyness scale. I hope that adequately answers Roth's points. One issue worth mentioning here is that we rarely get an opportunity to see living-breathing liquidity prices. As Nick Edmonds, who blogs here (and who should be on your reading list), points out:

I'm not sure that it is possible to extract out a market clearing price specifically for liquidity services, because it's assets that are traded not services. Each asset comes with a bundle of features yielding utility or disutility, not just the liquidity aspect.

Put differently, the difference between liquidity and a wheelchair is that liquidity doesn't stand alone as its own good but rather coexists as a service attached to an already produced good. Decomposing that service and its respective price from the rest is tricky.

Let me point out that fixed income markets do often provide accurate decompositions of the market price for liquidity. For instance, assume that FDIC-insured banks are offering chequing accounts yielding 0% and 1-year fixed term deposits yielding 2%. If we were to ask the market: "How much would I have to pay you in order for you to relinquish all rights to trade away your holdings of chequing accounts for one year?" ... the answer is 2%. So 2/100ths of the value of each chequing dollar is comprised of a 1-year liquidity return.

I've also spent some time trying to isolate the price of liquidity in equity markets, this post provides some detail.

But my best answer to Edmond's point is that this is a case of missing markets. We really don't have accurate prices for moneyness yet. One of the goals of this blog is to think about what these markets would look like, how you'd build them, and what they'd be useful for.

Banknotes: IOUs or not?

The building that housed the original Swedish Riksbank, the earliest European issuer of banknotes

In my previous post on bitcoin, I noted offhandedly that I don't consider modern central bank-issued banknotes to be fiat but classify them as liabilities of the issuing bank. By fiat, I mean unbacked, intrinsically valueless, inconvertible, unenforced bits of paper. In the comments section, monetary operations whiz ATR (who blogs here) challenged me to clarify the nature of the IOU attached to paper currency, and whether that IOU had any value.

It would be cheating to point out that the world's 160+ central banks all list banknotes as a liability on their balance sheet. The deeper reason that I prefer to classify banknotes as liabilities (i.e. IOUs, promises, claims, or obligations) rather than fiat bits of paper is the "fine print". The best place to find the clauses governing the IOU nature of banknotes isn't on their face, but rather in the various acts and legal documents that govern a given central bank.

Section 16.4 of the Federal Reserve Act, for instance, specifies that:

Federal Reserve notes issued to any such bank shall, upon delivery... become a first and paramount lien on all the assets of such bank.

In the notes to the 2012 audited financial statements of the Federal Reserve system, section 3(k), it says:

To satisfy the obligation to provide sufficient collateral for outstanding Federal Reserve notes, the Reserve Banks have entered into an agreement that provides for certain assets of the Reserve Banks to be jointly pledged as collateral for the Federal Reserve notes issued to all Reserve Banks. In the event that this collateral is insufficient, the Federal Reserve Act provides that Federal Reserve notes become a first and paramount lien on all the assets of the Reserve Banks.

If we look at the Bank of Canada Act, Section 25 (1),

The Bank has the sole right to issue notes and those notes shall be a first charge on the assets of the Bank. 

Section 34.1 of the same Act says that:

...in no case shall the affairs of the Bank be wound up unless Parliament so provides, but if provision is made for winding up the Bank the notes of the Bank outstanding are the first charge on the assets.

So in the case of the two central banks that I'm most familiar with, banknotes are ultimately claims on whatever stuff the central bank happens to have in its vaults. This means that on the occasion of the winding down of the Fed or the BoC, note holders are entitled to receive real assets, in the same way that a bond holder or stock holder would have a claim on a company's property, plant, & other assets upon the dissolution of that company. Banknote holders have an added bonus of being senior to other claimants, since notes provide a "first claim" in the case of the BoC, and a "first and paramount lien" in the case of the Fed.

Now the idea of shutting down either of these central banks sounds like either science fiction or a free banker's wet dream. What about the long period between then and now? Here are a few other indications of the IOU nature of banknotes. When a central bank chops some zeros off of its existing inflating notes, it doesn't leave its old issue stranded. Holders are entitled to bring their legacy notes in for conversion. Nor do central banks try to wiggle out of their obligation to redeem mutilated currency. When a note gets so worn that it becomes unusable, the central bank will replace it with a crisp new note. Lastly, when central banks merge (as in the case of the Euro) or are succeeded by another central bank (e.g. the Central Bank of Russia replacing Gosbank), holders of orphaned notes are given a window during which they can convert into new currency.

If central banks had no liability whatsoever for their note issue, then redenominations, mutilations, and successions would result in large capital losses to stranded note owners. That they don't would seem to indicate the opposite.

However, in the long waiting period until ultimate dissolution, the most important interim IOU provided by central banks is the promise of stability. The corollary of this in the old days was the obligation to redeem notes with some fixed amount of gold, or, during Bretton Woods, some quantity of dollars. Nowadays, central banks promise to ensure that the value of notes doesn't fall more than x% against a CPI basket. They guarantee to buy back IOUs in a sufficient quantity with the assets held in their vaults if the x% limit is exceeded, to the extent that a central banker might conceivably buy back and cancel every single IOU to enforce their promise.

Some central banks like the Reserve Bank of New Zealand encode this promise into their constituting act, along with stipulated penalties in case of non compliance. Other central banks provide this guarantee more informally, either in the form of accepted practice, tradition, or repeated verbal promises. Take the ECB, for instance, which uses the small quota of characters available on its Twitter account to state that its "main task is to maintain the euro's purchasing power."

Are these good liabilities? Not really. The promise of a payout upon central bank dissolution is a distant promise. In the meantime, the obligation to maintain price stability is subject to all sorts of political pressures to weaken the price target, as well as being held hostage to the skills of the central banker in hitting his/her target. Other central bank policy goals including employment and growth targets may interfere with the sanctity of the price stability IOU. The dubious nature of central bank IOUs isn't a new phenomena. Even in the gold standard/Bretton Woods days banknotes were constantly being devalued or rendered inconvertible.

Bad IOUs central banknotes may be, but IOUs they are nonetheless.