Beware CAPE, it could be your undoing

The blogosphere has been slowly shifting from worrying about the tepid nature of the current recovery to biting its nails over the timing of the next downturn. Feeding its fears is Robert Shiller's cyclically-adjusted price earnings (CAPE) ratio, the elevated nature of which would seem to indicate that the fun can't go on (see chart below). I think the the CAPE is a crappy measure for measuring valuations and should be largely ignored.

The general idea behind CAPE is that there exists a long-term average price earnings ratio to which stock markets will eventually revert. In the 1970s and early 80s, markets were undervalued on an earnings basis relative to their 16.5x average, so purchases made sense. Now they are overvalued relative to their historical average, so sales would be appropriate.

I have two explanations for why CAPE is a crappy measure for determining the over or undervaluation of equity markets. These are both "money" reasons, meaning that they have a monetary basis. I discussed the first last year in Beyond Buffett: Liquidity Adjusted Equity Valuation. I'll briefly summarize my points from that post before launching my second swipe at CAPE.

In brief, CAPE ignores the changing moneyness of stocks, or their liquidity. Stocks provide owners with a flow of earnings, but they also throw off a non-pecuniary flow of liquidity services. These non-pecuniary services stem from an investor's expectation that they will be able to easily liquidate those shares in secondary markets. For example, should your roof start leaking, your IBM shares can be quickly sold, the proceeds used to hire a contractor to patch the leak. The more liquid the stock, the more easily it can be dispatched to resolve the various unexpected problems that arise in life. Since these uncertainty-shielding services are valuable, people will pay a premium to enjoy them, a liquidity premium developing. Illiquid stocks may take longer to sell, and therefore provide a smaller flow of uncertainty-shielding services, commanding commensurately smaller liquidity premia.

Anyone who uses CAPE as a model is implicitly assuming that investors only purchase a stock so that they can own its expected flow of earnings, not its flow of liquidity services. Put differently, the CAPE model sets the liquidity premium on stock to zero. Thus a user of CAPE will attribute any rise in the CAPE above its long term average to changes in investors' willingness to pay more for each dollar of earnings. But if we bring liquidity into the picture, a rise in CAPE above its long-term average could just as easily be the result of a technological improvements to stock market liquidity. If the typical S&P 500 stock is more liquid than it was a decade ago, then people will pay more to own the liquidity return associated with stock, and the price of the S&P 500 will rise independent of earnings. This doesn't mean that a stock is expensive. It only means that stock "does" more things for the investor than before, and trades at a deservedly higher price.

A strict interpretation of CAPE says that we are currently so far above the market's long term valuation range that we need a market crash to bring things back into line. But if we adopt a liquidity-adjusted view, the idea that there exists a long term average to which price earnings ratios need to fall is silly. Stocks today are not your grandfather's stocks. They have become evermore cash-like and will probably continue to evolve in that direction, a progressively larger liquidity premia over the decades arising as a result. If so, observed price earnings ratios are not destined to revert to mean, but have attained a new and justifiably higher plateau, and will continue to hit higher plateaus in the future.

The second reason I don't like CAPE is its failure to properly account for inflation. Shiller uses earnings as his denominator, but during inflationary periods like the late 1960s, 70, and early 80s, earnings were a terrible measure of the true financial health of a company. Inflation, combined with historical cost accounting, has the effect of creating "phantom" earnings. These phantom earnings are mere artifacts of accounting rules, yet firms have to pay very real taxes on these earnings. As inflation mounts, a firm's artificially accelerating tax bill robs them of the cash they need to fund operations and new projects.

What follows is a short explanation of this effect, but if you prefer a longer one, try my old post A stock portfolio is a bad hedge against inflation.

If inflation doubles, the standard view is that stock is a great inflation hedge since a firm's revenues and costs immediately adjust upwards, the real value of the bottom line staying unchanged. However, historical cost accounting impedes a fluid 1:1 inflation adjustment. First, the cost of goods sold line on a firm's income statement doesn't rise in line with inflation. Inventories are accounted for on a first in, first out basis, which means the prices used to compute costs of goods sold are stale prices, as yet unadjusted for the ravages of inflation. Secondly, the depreciation line item doesn't rise with inflation. Machinery and other equipment are depreciated based on the item's historical (and therefore stale) purchase price, not on the basis of the good's current inflated price.

Since neither cost of goods sold nor depreciation rise during the early stages of an inflation, the firm announces higher real pre-tax profits. However, the rosy picture provided by the accountants obscures the fact that the firm's true economic position has not changed one bit. As inflation accelerates, the effect on the firm's cash flow is neutral. The net quantity of cash flowing into the firm from its clients less the cash flowing out of it to suppliers rise together. If the firm must pay 20% more cash to purchase inventory, that rise is completely compensated by 20% more in cash receipts from clients.

While the firm's net cash inflows from clients less outflows to suppliers remain constant during the inflation, the firm will find itself incurring larger cash outflows due to taxes. Based on the firm's growing accounting profits, the firm faces a higher tax bill than it did prior to the inflation. The growing quantities of cash that leak away to the government as inflation accelerates mean that less cash is available to pay suppliers, expand operations, or add to dividends. Inflation has made shareholders worse off. Taken to the extreme, a wild inflation will force a firm to pay an increasingly large portion of its wealth to the tax man, eventually resulting in the firm's bankruptcy.

So in periods like the late 1960s, 70s, and early 80s, it made absolutely no sense to value companies on the basis of their earnings. This makes a mockery of the CAPE parable. According to CAPE, investors in the 1970s irrationally bid stock down to very low prices relative to earnings. A smart investor should have picked up shares at these low levels in anticipation of a reversion to the long term CAPE ratio, a bet that would eventually payoff in the 1980s bull market.

In reality, since such a large portion of the earnings during that era were phantom, or non-existent earnings, investors placed a large value discount on them, or only purchased stock at very low price to earnings ratios. Stocks weren't being undervalued, they were being properly valued as the terrible inflation hedges that they were.

Contra the CAPE parable, the 1980s bull market was not the eventual payoff to the patient few who invested in low PE stocks. Rather, the bull market has Paul Volker to thank for, as it was his inflation-reducing policies that saved stocks from their own Achilles' heel; the adverse mixture of rising prices and historical cost accounting. Terrible inflation hedges they may be, when the reverse happens—low and falling inflation—stocks become stellar investments, as the 1980s would bear out. As inflation withered, phantom profits disappeared and firms were no longer forced to pay undeservedly high taxes. The large discounts that had been applied to earnings during the inflationary period were steadily removed.

So the CAPE fails because it ignores two monetary phenomena. It does not properly adjust for liquidity, nor does it account for the illusory profits that are created during inflationary periods. Until the quants figure out how to create a CAPE measure that corrects for these monetary effects, throw the CAPE in the toilet.

Gresham's law and credit cards

This is a follow up to my previous post on the monetary effects of credit cards. In this post I'll explore the idea that the use of credit cards in payments is driving a modern Gresham effect, the result of which is a displacement of cash and an inflationary race to the bottom of sorts. This downward spiral resembles the same dynamic set off by coin clippers in the medieval age, the era when Gresham's Law was first enunciated.

First, we need to revisit the idea of Gresham's law, or the idea that the bad money drives out the good. Imagine that it's 1592 and you're a fish monger in a busy market in London. Like everyone else, the unit of account that you use to price your wares is the pound unit of account, further subdividable into twelve shillings and 240 pennies. The actual medium that you and most other merchants have chosen to represent that unit (ie. the medium of account) is the English penny, coined by the Royal Mint from twenty-four grains of silver.

However, not all English pennies are the same! You've been selling fish for most of your career at 1d (d is the sign for the penny unit). But lately you've noticed that a growing number of the pennies you've been receiving have been altered. Small notches have been clipped from these coin's edges. The imprints on them look increasingly worn, and you hear stories about people who "sweat" coins. These ruffians are putting pennies into a sack, shaking them, and removing the small pieces of silver that have been scratched off.

Which means that in a growing minority of your transactions you are receiving the same amount of coin per fish but earning less silver. Clippers and sweaters are stealing the difference. To solve this problem, what you'd really like to do is weigh and assay each penny proffered and charge a unique price based on that coin's silver content. But you don't have the expertise to do this, and in any case, the chaos of the market doesn't offer enough time. Even if you could, accepting coins by weight rather than tale (their face value) is probably punishable by something grisly like getting your finger chopped off.

So instead you raise your prices a bit. By selling fish for 1¼d, you get more pennies than before, but roughly the same amount of silver. What you've done here is switch the medium you use to define the "d" unit of account, or your medium-of-account. You've adopted clipped and sweated shillings as your definition of the penny unit rather than full bodied shillings.

Here's where Gresham's law kicks in. Anyone who has undebased pennies (i.e. good pennies) in their pockets now has to pay 1¼d for your fish rather than 1d. But this is a bad deal for them. Our fish buyer can simply pay with with clipped and sweated pennies that contain less silver, say twenty-three grains of silver... and buy the same quantity of fish. Good pennies containing twenty-four grains of silver are being undervalued in the market place. Owners of these good pennies will choose to hoard them in their pockets and never use anything other than bad pennies to buy things or pay debts.

Where will all the good pennies go? They'll eventually be sent to wherever their silver is not being undervalued. In 1592, people would most likely have melted their good coin down into bullion and shipped this bullion across the Channel to France, only to have it re-minted into French coin and used to buy a larger quantity of fish (or more likely some durable good) than the London market allowed. That is Gresham's Law: when the price of various exchange media are fixed by law or custom, if the true market value of these media diverge, the market will tend to adopt the overvalued medium as their preferred payments option. In short, the bad English pennies drove out the good.

Now it's 2014 and you're a fish monger in a busy market in downtown Toronto. You use the dollar unit of account, the medium that represents this unit being Canadian banknotes.

However, not all dollars are the same! You've been selling fish for $10 for the past few years, but lately you've noticed that the use of credit cards has increased. Furthermore, the credit card networks are charging you ever higher transaction fees, say twenty cents rather than just two cents. This means that people are paying you the same amount of dollars per fish, but after fees you're earning the equivalent of just $9.80 worth of paper dollars in your account.

To solve this deficit, you'd like to charge the transactor a 20c fee, similar to how in 1592 you would have liked to assay each coin and charge a discount to face value based on the coin's actual silver content. By placing a 20c surcharge on credit card transactions, you'd end up with $10 per fish. However, the credit card companies stipulate in their contract with you that card payments can't be surcharged, the penalty being banishment from the card network. (Banishment certainly seems more humane than having your finger cut off.)

So instead you raise your prices a bit, just like you did in 1592. By selling fish for $10.20 you receive more in payment than before, but once the twenty-cent fee kicks in you end up with the same $10 quantity of paper dollars. Just like the medieval fish monger switched from full bodied pennies to clipped pennies, you've switched the medium you use to define the $ unit of account from paper money to credit card money. By doing so, you've preserved your margins.

As it did in 1592, Gresham's law kicks in. All things staying the same, anyone with paper money in their pocket now has to pay $10.20 for a fish rather than $10. But this is a bad deal for them since it undervalues their paper dollars. Better to pay $10.20 in credit card money and get all the associated rewards (air miles, cash back, etc) then pay $10.20 in cash and get no rewards. People will keep their paper dollars in their pockets and only make purchases by credit card.

Where will all the hoarded banknotes be exported? Well, people can't ship them down to the U.S. Americans aren't fond of Canadian dollars. But there will still be places in Canada that don't undervalue banknotes, namely all those retailers who only accept cash. Perhaps there's a competing fishmonger on the other side of town, say Scarborough, who won't accept credit cards and still charges $10 per fish. People will export undervalued banknotes to Scarborough where their dollars earn their full value. Or maybe they'll be exported to Toronto's drug market, or its prostitution market, or anywhere else where cash is still king. At the end of the line is the Bank of Canada, which will always offer to repurchase and shred all of the unwanted old notes that it has issued.

So the point of my little exercise has been to illustrate how 1592 is no different from 2014. Just substitute out the word "coin" with "credit cards" and the same Gresham effects are generated.

In both eras, one of the ways to remedy the displacement of good money by bad money would be to allow the price of the various exchange media to float. In the case of medieval coins, if merchants were allowed to charge varying prices based on the quality of coins proffered, then good coins would once again be properly valued and return into circulation. In the modern case of cash and credit cards, if retailers could charge surcharges on credit card payments, then cash would no longer be undervalued and would return to universal circulation.

In Australia and the U.S., authorities have adopted policies that should relieve these modern Gresham effects. Merchants in both nations are allowed to put surcharges on credit cards transactions. In Canada, surcharges are not allowed, despite efforts by the Competition Bureau to allow them. Gresham's law, it would seem, is still in effect up here.

Left unchecked, the Gresham effects kickstarted by both coin clippers and credit card networks contribute  a race to the bottom of sorts. In 1592, the incentives to clip coin would have been huge since the payor would be able to buy a greater real quantity of goods with a clipped coin than an unclipped coin. In reaction to the appearance of newly clipped coin, merchants would defensively raise their prices. The rest of the populace could only tag along and adopt the newly clipped coin as their standard payment medium. After all, using their good coin in local trade would be madness, since good coin was always and everywhere undervalued. The clippers would attack once more, prices would rise, and once again non-clippers would have to shift their cash holdings into inferior coin. Unless something was done to break out of this downward spiral, there was a tendency for the standard to be perpetually debased and prices to rise forever.

The same dynamic set off by clippers also emerges when credit card networks issue new premium cards that offer better rewards. Say that the networks introduce a "super" card that offers 5% cash back. Early-moving consumers will quickly adopt these cards—after all, they can buy the same quantity of goods at the same price... and get a large cash reward to boot. The higher the reward, the higher the fees a merchant must pay. They now find themselves ponying up 5% of the value of each transaction to the networks. In defense, merchants will belatedly raise their prices.

However, while early movers have adopted 5% cards, the general populace may still only be using cards that allow, say, a measly 1% cash back reward. Their existing cards are now undervalued, since merchants' prices are implicitly being marked up to a 5% card standard. What retailed for $100 now retails for $105. Anyone purchasing $105 worth of goods and getting only $1 cash back incurs a loss of $4. To avoid real losses, the population has no choice but to play catch up and apply for 5% cash back cards. By then, the card networks may be offering 6% cash back cards, which early movers will quickly adopt in order to enjoy the increased purchasing power that these cards afford. Once again merchants will raise prices to defend their margins, adopting a 6% card standard (in other words, their chosen medium-of-account is now 6% cards). But now the 5% cash back cards adopted earlier by the general populace will be undervalued, forcing them to transition to the use of 6% cash back cards. And on and on and on till we have a 100% cash back Visa card standard.

Empirically, we can see this effect over the last decade by the proliferation of premium credit cards, as well is the growing fees that merchants must pay to the card networks.  See this GAO report, especially Figure 3 which I've appended below.

In closing, here's a rare bit of practical advice from the Moneyness blog. If you live in a nation that doesn't allow credit card surcharges (like Canada), and you use cash to pay for most things, YOU ARE LOSING MONEY. Many merchants are implicitly setting prices based on the expectation that credit cards will be used and are pricing in a premium to cover the fees they must pay to the card networks. Either demand a 2-3% cash discount on everything you buy, or get yourself a credit card that yields decent rewards. Save your cash for buying stuff at your local farmer's market or any other cash-only venue where your cash isn't being undervalued. Put differently, if you aren't behaving according to the strictures of Gresham's law, you should be.

Short Squeezes, Bank Runs, and Liquidity Premiums

This is a guest post by Mike Sproul. Many of you may know Mike from his comments on this blog and other economics blogs. I first encountered Mike at the Mises.com website back in 2007 where he would eagerly debate ten or twenty angry Austrians at the same time. Mike was the first to make me wonder why central banks had assets at all. Here is Mike's website. 

On October 26, 2008, Porsche announced that it had raised its ownership stake in Volkswagen to 43%, at the same time that it had acquired options that could increase its stake by a further 31%, to a total ownership stake of 74%. The state of Lower Saxony already owned another 20% stake in VW, so Porsche's announcement meant that only 6% of VW's shares were in “free float”, that is, held by investors who might be interested in selling.

Porsche's buying had inflated the price of VW stock, and investors had been selling VW short, expecting that once Porsche's buying spree ended, VW shares would fall back to realistic levels. Short sellers had borrowed and sold 12.8% of VW’s outstanding stock, but with free float now down to 6%, short sellers owed more shares than were publicly available. If the lenders of those shares all at once demanded repayment of their shares, then there would be 12.8 buy orders for every 6 shares available. In what was called “the mother of all short squeezes” share price rose until the short sellers went broke.

A short squeeze is bad news for financial markets, largely because the fear of short squeezes deters short selling, and thus inhibits the normal arbitrage processes that keep securities correctly priced. If I may make a suggestion to the owners of the world's stock exchanges, there is a simple way to prevent short squeezes from happening on your exchange: Allow cash settlement of all short positions, just like in futures trading. If the most recent selling price of VW was 250 euros, and if short sellers suddenly find no shares available, then allow those short sellers to pay 250 euros in cash (plus some small penalty) to the lenders of the shares, rather than having to return an actual share of VW. This would prevent the stampede to buy VW, and would assure that VW’s price would not skyrocket to crazy levels. (As a measure of short-squeeze mis-pricing, it is worth noting that VW briefly became the world's most valuable company at the height of the short squeeze.)

Short squeezes on stock exchanges are mercifully rare. Unfortunately they are not quite as rare in the banking world, where they go by the name of bank runs. Just as a short squeeze pushes short sellers to hand over more shares of VW than can be obtained on the market, a bank run pushes banks to hand over more currency than can be obtained on the market. And just as short squeezes can be mitigated by allowing cash settlement, so can bank runs be mitigated by allowing banks to settle their obligations in forms other than currency. Clearinghouses and other banking associations can issue loan certificates or scrip for use in clearing checks, or even for public use as currency. Some creativity might be required in the issuance of money substitutes, but in return banks are spared from having to sell their assets at distress prices, while the community is spared from the effects of a bank panic.

What I find most interesting about short squeezes and bank runs is that they are a clear case of market failure, where financial instruments are obviously trading above the value of the assets backing them. During a short squeeze, value is no longer determined by backing, but by the forces of supply and demand. I don't think that economists pay enough attention to this point. The price of financial securities is normally determined by the underlying assets, while the price of commodities is determined by supply and demand. When economics textbooks explain supply and demand, they speak of the supply and demand for apples and oranges or other commodities. They rarely if ever speak of the supply and demand for stocks and bonds, because stocks and bonds are not objects of consumption, and they are not produced using scarce resources. There is no production function and no consumption function, hence there are no supply or demand curves. When we examine a bond that promises to pay $105 in 1 year, we find the price of that bond by dividing 105/(1+R). If R=5% and we tried to sketch supply and demand curves for that bond, we would draw a pair of meaningless curves that were both horizontal at $100. This is what makes short squeezes so strange. The price of VW stock is supposed to be determined by backing, and not by the supply and demand for VW shares. But during a squeeze, supply and demand take over, and stocks trade at a premium relative to their backing. The same might be true of money during a bank run.

This is a problem that JP and I have batted around a bit. I usually argue that arbitrage prevents money from trading at a premium relative to its backing, while JP usually argues that money can trade at a small premium. I can never pin him down on the size of the premium, but he doesn't argue much when I throw around a figure of 5%. Well, here we have VW stock trading at a premium of 500%. Might such a premium be possible for money?

Apparently not. We never see comparably large premiums on currency during bank runs. Gerald Dwyer and Alton Gilbert (Bank Runs and Private Remedies, May/June, 1989) examined American banking panics that occurred between 1857 and 1933, and found that the largest paper currency premium (relative to certified checks) ever observed during bank panics was 5%. The average paper currency premium during bank panics was much lower, only about 1%. Other measures of a currency premium, such as a rise in the value of money relative to goods in general (i.e., deflation), are also in the modest range of 1-5%. Why the enormous gap, from a 1% premium on currency to a 500% premium on VW stock? My best explanation is that banks can get creative in devising alternate forms of payment, while the traders in VW stock simply did not have the time or the legal means to devise alternate forms of payment. Thus the market in VW stock failed catastrophically, while banks facing a run are able to muddle through.

The result of the banks' muddling with money substitutes is that even during stressful events like bank runs, the value of money is, at most, only 5% higher than its fundamental backing value. This makes sense, because any premium over backing value gives an arbitrage opportunity to investors. If the fundamental backing value of each dollar is 1 oz. of silver, and if the dollar somehow trades at 1.05 oz., then the issuer of that dollar earned a free lunch of .05 oz. This free lunch would attract issuers of rival moneys, and rival moneys would keep being created until each dollar traded at its fundamental value of 1 oz.

The idea that money is worth no more than the assets backing it is consistent with finance theory, and with the backing theory of money, but it contradicts the quantity theory of money. The quantity theory asserts that modern fiat money has no backing, that it is not the liability of its issuer, and that its entire value is therefore a monetary premium. Which of the two theories gives a better fit to real-life moneys? When we look around for moneys that fit the quantity theory, that have no backing and are not anyone's liability, we find very little. Just bitcoin and a few orphaned currencies like the Iraqi Swiss Dinar. When we look around for moneys that fit the backing theory, that are the recognized liability of their issuer, and are backed by their issuer's assets, we find every other kind of paper and credit money that has ever existed. I conclude that the backing theory beats the quantity theory.

Rowe v Glasner... round 33!

It's the Roe v Wade of the blogosphere, a battle that never quite gets resolved. Nick Rowe and David Glasner have been having one of their bi-annual debates over the ability of private bankers to create excess deposits. See here, here, and here.

The nub of their conflict seems to resolve revolve around the following points: if we assume that 1) bank deposits and cash are imperfect substitutes for each other, and that 2) bankers simultaneously raise the rate on deposits and increase the quantity of deposits, then 3) an excess supply of deposits and cash will emerge. Nick argues for the last point while David argues against it.

At the risk of only adding noise to what is always an interesting debate, I'm going to chime in. I'm going to focus on the step-by-step process by which events play themselves out, the bricks & mortar if you will. Given the complexity of this process there will no doubt be errors in this post, hopefully readers will flag them.

The thought experiment that Nick and David have been debating involves a simultaneous increase in deposit rates and the quantity of deposits via loans. But I'm going to focus on just an increase in deposit rates first, then bring in the quantity adjustment later.

Let's start out with a full spectrum of assets, including central bank liabilities (cash and reserves), bank deposits, durable assets (i.e. gold, houses, stocks, and bonds) and perishable assets (apples, soap, jeans). All provide varying expected pecuniary returns (i.e. dividends, interest, and capital appreciation) as well as expected non-pecuniary returns (consumption and liquidity), the sum of which adds up to an asset's total return. In equilibrium, every asset offers the same total expected return.

What do we mean when we say that cash and deposits are imperfect substitutes for each other? Like cash, deposits are useful in a wide range of transactions. However, unlike 0% banknotes, deposits yield interest. Given that deposits provide both interest income and broad marketability, people will prefer to only hold the bare minimum of cash that they deem necessary.

What dictates this bare minimum? The marginal unit of cash that an individual holds in their wallet has been specifically accumulated to deal with a unique set of transactions in which deposits simply cannot participate. This unique set of transactions occurs in markets where digital payments are not allowed, say laundromats, farmers' markets, or cash-only diners; or where fees are levied on card payments, like gas stations; or in places where payments must be anonymous, like in the back alley behind city hall.

On the margin, people try to anticipate the chances of engaging in these sorts of cash-only transactions and accumulate what they deem to be an appropriately sized cash inventory. So while an individual's inventory of 0% cash does not provide a pecuniary return, it does provide a non-pecuniary liquidity return arising from its ability to be used in both a broad set of transactions in which it competes with deposits, and a narrower set of transactions in which only it is useful.

Now say that banks have figured out a way to cut costs. Their profits grow, but this only lasts a short time as competition forces them to increase the interest rate they offer on deposits. Given stationary pecuniary yields and non-pecuniary yields on cash, durables, and perishable assets, deposits now offer the best return. An excess demand for superior-yielding deposits and an excess supply of inferior-yielding durable assets, perishable assets, and cash emerges.

A number of adjustments need to occur in order to restore equilibrium. Along the margin of deposits-to- durables and perishables, an effort to simultaneously sell these assets for deposits will result in a fall in the their relative price. Their prices will fall until they stabilize at a low enough level that they are now expected to appreciate at a rate sufficient to equal the return provided by deposits. This resolves the excess demand for deposits along both the deposit-to-durable asset margin and the deposit-to-perishable asset margin.

Things are a little trickier along the deposit-to-cash margin. Given the superior return on deposits, people will now want to hold more deposits. An excess supply of cash develops. Unlike the durable and perishable asset markets, the cash-to-deposit market is inflexible; the price of cash cannot fall relative to deposits in order to restore equilibrium.

What happens instead is a quantity adjustment; people begin to sell cash for deposits at a fixed rate of one-to-one. The market where they go to do this is at a bank. They don't "sell" cash. Rather, they deposit cash at the bank in return for higher-yielding deposits. They continue to deposit cash until the benefits of adding one more unit of deposits to their portfolio, namely the marginal enjoyment provided by their higher pecuniary return, no longer exceeds the foregone benefit of one less unit of cash, namely their ability to participate in prospective cash-only transactions.

Once people have reduced their cash balances to a point at which they are once again indifferent between cash and deposits, equilibrium has once again been restored along the cash-to-deposit margin.

So in short, an increase in deposit rates causes a temporary excess demand for deposits in the deposit-to-cash market as well as the deposit-to-durable and perishable asset markets. These excesses are quickly removed by a fall in the prices of durable and perishable assets, and a quantity substitution of cash for deposits.

I'll bring this back to Rowe v Glasner in a moment, but as an aside it's worth noting that the process doesn't halt here. Having sold deposits for cash, the banks now have more cash than they desire. Their excess balances are trucked over to the central bank where they are converted into reserves, or clearing balances. But banks don't really want these either. Instead, they will all try to spend away their reserves simultaneously on durable assets, or try to lend them in vain to other banks in the interbank market. This pushes prices of durable and perishable assets higher and the interbank rate lower. At this point the central bank, noticing that its target for the interbank interest rate has deviated from its target, steps in and mops up all the excess reserves by conducting open market sales. This pushes the interbank rate back up to target. Voilà, the excess quantity of cash (and reserves) has been removed, first by depositors forcing cash back on banks, and then banks forcing the cash back on the central bank.

Let's circle back to Nick and David's argument. They were considering not just an increase in deposit rates, but a simultaneous increase in deposit rates and the issuance of new deposits. I'd argue that the same process that I've just described applies to this second scenario.

The rise in deposit rates causes durable and perishable asset prices to fall. At the same time, the new deposits are spent into the economy by borrowers. Individuals now hold more deposits than before, but they still own the same quantity of cash, an undesirable situation for them since cash is providing an inferior return relative to deposits. How can they rid themselves of this unwanted cash? If one person sells their horde, the next person will only try to sell it to someone else, and someone else. The cash never leaves the economy.

But here's an out. At some point an individual who is in debt to a bank will come into possession of that cash and will use it to reduce the amount owing. That cash will take the same route back to the central bank described earlier, ultimately meeting its demise in the blades of a paper shredder.

So given an increase in deposit rates and the emission of more deposits, the final resting point is a fall in durable and perishable asset prices, and an increase in the amount of deposits at the expense of the quantity of cash. That leaves us in the same spot as an increase in deposit rates alone.

Where does that place me relative to Nick and David? If it takes a while for unwanted cash to find a debtor who will reflux that cash back to the banks, then we can see the sort of effects that Nick describes. But on the whole, I think I'm more on David's side here. But that's hardly surprising. As Nick usually says, he's arguing against the mainstream view. The odds always were that I'd land in the same bucket as the majority. Anyways, for what it's worth, those were my two-cents.

Before I sign off, let's follow one final tangent. Thanks to higher deposit rates, one of the features of my final resting point is lower durable and perishable asset prices. But after a few months, our central bank will notice that the incoming data is showing that the price of perishable assets has ticked down. The perishable asset category, which includes things like jeans, apples, and soap, is the category of assets the prices of which a modern central banker targets. In an effort to right deflation in the perishable goods market, our central banker will counter by reducing the return on reserves. (He/she can do so by conducting open market purchases and/or by reducing the interest rate corridor). Banks will react by simultaneously trying to offload their inferior-yielding reserves in favour of durable and perishable assets. Prices will rise back to the central bank's target.

So a fall in prices that was kicked off by commercial banks sweetening the return on deposits is ultimately reversed by a central bank reducing the return on central bank liabilities. Tit-for-tat. Here I definitely agree with Nick Rowe—central banks are alpha banks. Commercial banks can only have a passing influence on the price level if a central banker decides to have his or her way.

Liquidity everywhere

A few weeks ago I claimed that the so-called value premium was really just a liquidity premium. The value premium, illustrated best by the HML, or high-minus-low strategy (shorting stocks that have high price-to-book ratios while buying stocks that have low ratios), is one of the more well-known market anomalies. By following this strategy, investors can supposedly do better than their counterparts on a risk-adjusted basis.

My point was simply that stocks with low price-to-book ratios get those low ratios in the first place because they are illiquid relative to stocks with high ratios. Anyone who buys the former while shorting the latter is acting as a liquidity creator for which the HML return is a reward. Fund managers who uses this strategy to drive fund returns aren't necessarily earning alpha, they're earning a fair return for acting like a liquidity-providing bank.

I got some push-back in the comments, on Twitter, and on Reddit from readers, some who were skeptical that the value premium could be a reward for bearing illiquidity, and others who were unhappy with my lack of data. I poked around a bit. Here are two empirical papers that try to describe the value premium as a liquidity phenomena: Time-Varying Liquidity Risk of Value and Growth Stocks (Akbas, Boehmer, Gene, Petkova; 2010), and A Liquidity-Augmented Capital Asset Pricing Model (Liu, 2006). Eat your heart out, folks.

But the main point of this post isn't to beat around the HML bush. My basic strategy in the last post was to take an abnormality and explain it by resorting to an unseen liquidity factor. I'm going to wash and repeat this strategy a few more times today. Liquidity is an invisible vector, or a missing plug variable, that can be used to explain all sorts of puzzles, anomalies, abnormalities, oddities, and weirdness. It's sort of like the Force, it's all around us.

The size premium is a market puzzle whereby small firms outperform large firms on a risk-adjusted basis. Again, we can introduce liquidity to explain at least part of this anomaly. Since the shares of small firms will typically be less liquid than the shares of larger firms, anyone who buys the former and shorts the latter is creating liquidity, an activity for which they should be duly compensated.

Torchio and Surrana (2013) reconcile the size premium with liquidity in this paper, noting that the size premium subsumes a liquidity premium. In the case of the smallest stocks in their study, the majority of the size premium is entirely explained by a lack of liquidity.

Then there's the mother of all pricing puzzles, the equity premium puzzle. Studies show that the return to holding stocks in the S&P 500 is far too high on a risk-adjusted basis relative to the return on U.S. treasury bills. This anomaly seems like a no-brainer to me. You can't compare the pecuniary return on stocks to t-bills because the two asset classes are like apples and oranges to each other. The U.S. Treasury bill is one of the most liquid assets in the world. By comparison, the average stock in the S&P 500 trades by appointment. If t-bills have seemed to underperform equities over the decades, it's only because t-bills provide a compensating stream of liquidity services that equities don't. When all is said and done, there's a good chance that once we account for liquidity returns, the total returns of equities and t-bills balance out.

Nor would I be the first to make this claim. Amihud (2002) [ungated version] tries to resolve the equity premium puzzle with a liquidity explanation, noting that the equity risk premium is

in part a premium for stock illiquidity. This contributes to the explanation of the puzzle that the equity premium is too high. The results mean that stock excess returns reflect not only the higher risk but also the lower liquidity of stock compared to Treasury securities.

Another interesting anomaly is the closed end fund puzzle. Closed end funds issue non-redeemable shares to the public and use the proceeds to invest in assets like stock or real estate. Oddly, shares in closed-end funds often trade at large premiums or discounts to underlying net asset value. Once again, liquidity seems like it could be a decent explanation. If the underlying assets that the fund invests in are highly illiquid, but the share units themselves are highly liquid, then those units provide an extra stream of liquidity services and should therefore trade at a premium to illiquid underlying assets. This premium could turn to a discount as the liquidity profile of underlying assets improves, or the liquidity return provided by share units deteriorates.

A neat paper that uses liquidity to explain the closed end fund puzzle is A Liquidity-Based Theory of Closed-End Funds (Cherkes, Sagi, Stanton; 2007).

Back in the early 1980s, Robert Shiller posited an excess volatility puzzle. The price of equities seem to fluctuate far more than one would expect based on the dividends that they are expected to pay. Let's introduce liquidity once again. Investors value shares not only for the their pecuniary yield (both dividends and price appreciation) but also for their moneyness, or their liquidity. In calculating the price at which a share should trade at, investors must estimate not only the discounted value of dividends thrown off by the firm, but also the discounted value of liquidity services it provides. If share prices seem to volatile relative to dividends, it may be estimates of liquidity services that are driving the results.

Ravikumar and Shao (2010) try to solve Shiller's volatility puzzle by explaining how the dual role of an asset as both a good yielding a flow of dividends, and a medium of exchange, might explain observed excess volatility.

Uncovered interest parity (UIP) is the idea that an investment in t-bills in two different countries should provide the same overall expected rate of return. Say that a Canadian t-bill yields 2% but U.S. t-bills yield 4%. If people are willing to hold low-yielding Canadian debt, UIP says that it must be because the exchange rate is expected to appreciate, providing Canadian debt holders with an extra 2% forex gain to bring their net return in line with the return on U.S. t-bills. UIP says, in short, that low yielding currencies should appreciate over time.

The uncovered interest parity puzzle, or forward premium puzzle, is that UIP is almost always violated; high-yielding currencies tend to appreciate over time rather than falling. A carry trade in which an investor borrows in the currency with the low interest rate and invests in the currency with a high rate is usually profitable.

Liquidity might be able to help explain violations of UIP. If low-yielding t-bills provide a superior stream of liquidity services than higher-yielding bills, then the exchange rate doesn't need to do as much "work" in resolving the lack of interest parity between low- and high-yielding t-bill rates across nations. UIP "violations" might be no more than shadows of an invisible liquidity premia. Carry traders that make their living shorting low-yielding t-bills of one nation and buying high yielding bills in another aren't earning excess returns, they are simply acting as liquidity creators—and getting fairly rewarded for it by liquidity buyers. (See my bit on the on-the-run off-the-run trade in my previous post.)

Linnemann and Schabert (2013) try to explain UIP violations in terms of the liquidity premia on treasuries.

Lastly, there's the credit spread puzzle. A credit spread is the difference between the yield on corporate bonds and risk-free treasuries. Data shows that the credit spread has historically been far too high to be explained by risks like expected default loss. Owners of corporate bonds earn too much, and owners of t-bills earn too little.

The answer to this puzzle is similar to that of the equity premium puzzle. Risk-free treasuries are some of the most liquid securities in the world, corporate bonds are not. Because t-bills provide an extra liquidity return, they don't need to provide as high a yield. If we factor this liquidity return into the equation, then what seems like an anomalously high spread between t-bills and corproate bonds probably isn't so anomalous after all.

There are a number of papers that try to explain the credit spread puzzle by resorting to liquidity. Parraudin and Taylor (2001), for instance, find that a large part of the AAA- to A-grade bond spreads are explained by liquidity.

So yes, I see liquidity premia everywhere, but as this survey of papers shows, so do a lot of people. If you haven't incorporated liquidity into your model of the world, whether that model be CAPM or something more specific to yourself, then both your investing and your way of doing economics will probably suffer.

Dismantling a central bank

In a previous post, I made the point that banknotes aren't Samuelsonian bubble assets, say like a chain letter or a ponzi scheme or bitcoin. Upon the dismantling of a central bank, each note has a senior claim on a central bank's remaining assets. Rather than being mere "oblongs of paper", as Samuelson described them, banknotes occupy the very top of the capital structure hierarchy, above stock and bonds. This quality of being "well backed" might be sufficient for notes to trade at a positive value in the first place, and also help explain subsequent fluctuations in the purchasing power of those notes. In this post I revisit these ideas.

The process of dismantling a central bank would go like this. Imagine that the Reserve Bank of Fiji announces that it will wind up operations next week and recall all notes. Its assets consist entirely of Fijian dollar-denominated bonds. With the eminent end of Fijian dollars, the entire Fijian economy will have to quickly re-denominate existing debts and contracts into a new unit of account, say U.S. dollars. After this redenomination, the Reserve Bank of Fiji now finds itself holding a large quantity of U.S. dollar-denominated debt. It proceeds to sell these bonds, as well as its printing presses and premises, for dollars, and then uses dollars to cancel all Fijian notes. The Reserve Bank of Fiji is no more, and neither are Fijian dollars.

Because the central bank's hypothetical dissolution would result in noteholders ending up with some ultimate quantity of U.S. dollars in their pockets, Fijians can use this terminal value as a basis for computing the present value of Fijian banknotes. They would go about doing this computation in the same that they would with a stock and bond, both of which also have hypothetical terminal values, or liquidation values.

The inestimable Mike Freimuth, who blogs here, pointed out that there is a problem with this. How can Fijian noteholders actually quantify the amount of dollars to which they are entitled upon dissolution? This is easy if the Reserve Bank of Fiji is already on a dollar standard (say it redeems notes for US$1). Once all of the central bank's assets have been sold for U.S. dollars, each noteholder would get US$1 until all Fijian noteholders had been satisfied, upon which less senior stakeholders like bondholders and shareholders would get their portion of the central bank's remaining stash of U.S. dollars.

However, if Fiji is on a floating standard, the task of valuing noteholders' claims gets quite thorny. While fiat notes may have a senior claim on assets upon dissolution, it isn't evident how many actual dollars this entitles noteholders too. And if their quota of remaining assets, or terminal value, is not known at the outset, how can Fijians arrive at a value for notes in the first place?

One answer to Mike's criticism is that Fijian note owners come up with their best estimate of how much dollars the central bank (or a judge) would decide to award them upon a hypothetical dissolution. If the market's collective guess is that no assets would be forthcoming, then Fijian dollars would be worth nothing upon windup. If Fijians on average assume that the sale of bank assets would net $100m, and they think a judge would award them half of that, then each Fijian banknote will earn a prorated share of $50m. If they think that the all assets will be awarded to them, then they'll get a prorated share of $100m.

While these expectations about the terminal value of notes would probably be sufficient to jumpstart the positive value of Fijian dollars in the first place, this isn't a very satisfying explanation for subsequent variations in the price level. After all, the Fijian price level on any given day would be a function of Fijians' many and divergent expectations concerning their as-yet-unstated share of some future pie. As noteholders take potshots at guessing what this unknown size of this slice would be, the Fijian dollar would fluctuate wildly, sort of like a penny stock. Penny stocks owners have wildly fluctuating estimates concerning their ultimate, and unfixed, share of the corporate pie, which is only determined after debtors have had their pickings.

However, the behavior of currencies is not like penny stocks—the former tend to vary only a little in price from day-to-day. To explain price level fluctuations, it would seem that something other than the terminal value of the Reserve Bank of Fiji's assets must be at work.

Here I would like to reiterate my point from an earlier post that once a banknote has been jumpstarted into having a positive value, the dissolution-value of a central bank assets will only have a distant influence on those note's subsequent value. By far the more immediate effect that central bank assets have on the value of notes emerges via their ability to be mobilized in the maintenance of price stability. By selling assets for notes and retiring them (or threatening to do so), a central bank can prevent the value of their notes from flagging. Alternatively, the income earned by those assets provides the central bank with the resources to pay more interest (on reserves at least), a feature that will also ensure price stability.

So it seems to me that any impairment to a central bank's assets will affect the value of notes not so much because it lowers their value come future dissolution, but because it limits the central bank's ability to repurchase notes and pay interest in the present so as to maintain their price target. If a central bank didn't provide a target supported by a repurchase facility, then the value of notes would be dictated by something like their terminal value—and prices would be much more volatile then they are now.

Credit cards as media of account

What is this gas station using as a medium of account? Visa/Mastercard dollars or Federal Reserve dollars?

In this post I'll argue that in many cases, a nation's medium-of-account doesn't consist of base money issued by its central bank, but credit card money created by Visa and Mastercard. This may have some interesting implications for monetary policy. Whoever issues, creates, or manages a nation's medium-of- account determines the general level of prices, and this makes it a monetary superpower.

But before I get to that, let's revisit the meaning of the word medium-of-account.

I've written a number of posts on the idea of medium-of-account because it has always seemed to me like an important concept, although admittedly it's taken me a while to zero-in on a satisfactory understanding of the term. What I like about medium-of-account is that along with the ideas of unit-of-account and moneyness, it allows us to pretty much remove "money" from the list of terminology we use when talking about monetary phenomena. No single word is so widely-used yet so imprecise as money. And because of this, no word has bred as many bitter econblog battles. By splitting apart the various ideas associated with "money" and passing these meanings on to alternative words like medium-of-account, some of this morass can hopefully be unclogged.

Without further ado, here are the definitions. By the way, these aren't mine. I've picked them up from folks like Jurg Niehans, who coined the term medium-of-account; Scott Sumner; and Bill Woolsey—hopefully nothing has been lost in translation.

The unit-of-account is a word or symbol like $, ¥, £. Inherent in the idea of UOA is the subdivision of the unit, so that $1 is comprised of 100 cents. (1)

The thing (or things) that defines that unit is (are) the medium-of-account. When a merchant chooses to sell a painting for $100, for instance, he is selecting the unit in which he prices, say the $, as well as the specific medium that defines the $ unit. This last choice is important because dollars might appear in any number of different mediums, or forms, including Federal Reserve paper money, Federal Reserve deposits, branded private bank deposits, cheques, credit cards, and more.

Isn't it the case that a merchant chooses "all of the above media of account" when choosing to price in dollars? After all, one dollar is just as good as another.

Not necessarily. For instance, we know that in the early to mid-19th century a plethora of dollar-denominated exchange media circulated, much like now. There were dollar coins, which the U.S. Mint coined out of a certain number of grains of silver and/or gold. There were also privately-issued dollar banknotes, these being the most prevalent exchange media since coins rarely circulated. However, when merchants set sticker prices, the medium they had in mind when defining the $ unit was the less-common coin, not the more-prevalent notes. Notes were only accepted by merchants at varying discounts to their face value, despite the fact that most banknotes were branded as "dollars".

For example, if our merchant listed a painting for $100, then it could be purchased with one-hundred one dollar coins, or, alternatively, $102 in banknotes from a certain bank, or $103 from another.

If the value of all banknotes simultaneously inflated, what would happen to prices? Given that the value of the coin had remained constant, the merchant's price as well as the general price level would not have changed during this inflation. All that would adjust would be the varying discounts applied to the whole range of private banknotes. The painting would still be listed at $100, and it could still be purchased with the same quantity of coins, but it might take $110 or $115 worth of notes to purchase it.

However, if the U.S. Mint had chosen to reduce the quantity of gold or silver in a coin, then the merchant would increase his sticker price for the painting to $110 or so. The general price level would inflate.

So a unique feature of the medium of account is that the general price level pivots around the MOA's value. If the owner or issuer of the medium of account, in our example the U.S. Mint, has the wherewithal, it can control these economy-wide price changes by modifying the nature of the media it emits, say by reducing the metal content of coins. Few institutions have this sort of monetary superpower because only a few institutions create media that also happen to be media-of-account. Because 19th century private banks didn't issue media of account, they were not monetary superpowers.

Let's bring this back to the present. What is the modern medium of account? Who controls it and thereby earns the mantle of the U.S.'s reigning monetary superpower? Scott Sumner argues that central bank base money serves as the medium of account. I don't doubt that he's right. But in a large subset of transactions, I'd argue that Visa and Mastercard dollars are the medium of account. And this means that Visa and Mastercard rival (in theory at least) the Fed as monetary superpowers.

To understand why Visa and Mastercard dollars serve as media of account, you need to know a bit about how credit cards work. Merchants who accept credit cards as payment must pay a small percentage of each transaction's value to the credit card networks (comprised of the Visa and Mastercard associations, plus the banks that issue cards and process payments). So if someone buys $1.00 worth of stuff, the merchant might get $0.995, the remaining half cent going to the card network.

The fee that the merchant must pay varies by the quality of card. Basic cards might result in the merchant giving up 0.5% to 1% to the card network while premium cards, those offering better rewards, might bring a fee of 2-4%. Merchant fees have been rising over time, especially as card rewards become more exotic.

Merchants hate seeing credit cards, especially premium cards. They hate them because they are required to pay the card fees but cannot pass these costs off to the customer. Why? Well the best way to pass these costs off would be for the merchant to put a surcharge on each credit card transaction equal to the fee the card network charges the merchant. A surcharge policy would mean that it would cost any customer wishing to buy a $100 painting with Visa or Mastercard $102 or $103.

However, as a condition of using the card networks, merchants are prohibited from discriminating against card users. Surcharges are 'illegal'. Visa and Mastercard can extract these sorts of promises from merchants because they are oligopolies. If you are exiled from their networks for breaking their rules, you're as good dead.

So the upshot is that if a customer buys a $100 painting with cash (or debit), the merchant gets $100; if they buy it with a basic Visa card, the merchant might get $98; but if the customer buys it with a premium card, the merchant will only get $96. I'd hate premium cards too if I only got 96 cents on the dollar.

To get around these rules, merchants who accept cards have come up with an ingenious strategy: change the medium of account. Basically, the unit of account that merchants use, the $, stays the same, but whereas the merchant's original medium of account was Federal Reserve dollars, they now switch over to defining the $ in terms of Visa/Mastercard dollars. In the eyes of a merchant, a credit card dollar is only worth around 97 or 98 cents. Having adopted Visa/Mastercard as his MOA, our merchant will proceed increase his sticker prices by a percent or two across the board. The painting which retailed for $100 is now priced at ~$102. When someone buys the painting with a credit card, two dollars of this amount goes to the card network, leaving the merchant with $100. He earns the same real income as before.

This switch in MOAs allows our merchant to inflate their prices and thereby pass off card fees to their customers without illegally imposing surcharges. Fed cash has ceased to be the MOA, but will still be a popular exchange medium. But now customers who prefer paying in cash must request a cash discount at the merchant's till. Given the $102 sticker price on the painting, they should be able to buy the painting for around ~$100 Fed dollars.

Since Visa and Mastercard now manage the medium of account for a large proportion of American merchants, they have become monetary superpowers and can exercise their own brand of monetary policy. If Visa and Mastercard increase the rewards on their cards, merchants will be docked larger fees. Merchants will react by increasing sticker prices across the board. Thus we get inflation. If rewards are lowered so that the merchant is penalized less, then merchants will lower their sticker prices. This is deflation. These price changes are independent of any action taken by the Federal Reserve.

That's not to say that the Fed would have lost its monetary superpowers. It can still cause inflation or deflation by engaging in open market operations are adjusting the interest rate on reserves. However, in an extreme scenario, we could imagine the Fed's effort to increase prices being offset by Visa and Mastercard's efforts to decrease prices. A monetary battle of sorts could erupt.

I think that a good analogy to help understand this is to return to the 19th century example of dollar coins issued by the U.S. Mint. If gold prices rose, the price level would fall. But if the U.S. Mint were to simultaneously reduce the gold content of dollar coins, the MOA, it could entirely offset this fall and create stable prices. Just like the U.S. Mint can offset any change in the value of gold by increasing or decreasing gold content of coins, Mastercard and Visa as issuers of MOA can (in theory at least) offset any change to the value of Fed dollars by increasing or decreasing the reward content of Visa/Mastercard dollars.

An interesting bit of news worth pointing out is that in 2013, Visa and Mastercard finally allowed U.S. merchants to introduce surcharges on credit card transactions. I'd expect that merchants will slowly start to transition back to using Federal Reserve dollars as their medium of account. We should see the various types of credit cards dollars being priced at varying discounts to Federal Reserve dollars, similar to how banknotes in the 19th century were priced, with each note earning a discount relative to the dollar coin. Premium cards will face large surcharges, and regular cards small surcharges.

This means that in the U.S., Visa and Mastercard have effectively lost their monetary superpowers. They can no longer effect the general price level. In other places like Canada, however, courts have allowed the no-surcharge policy to continue, which means that Visa and Mastercard dollars will continue to be MOA. The card networks will remain as Canadian monetary superpowers.

There's a lot more material that I'd like to add to this already-dense post, but I'll hold off for now. In sum, in this post I'm "kicking the tires" of the basic definitions that folks like Scott Sumner and Bill Woolsey provide us. In applying them to the world around us, it sure seems to me like credit card media-of-account currently coexist with the standard Fed dollar medium-of-account. But I'm curious to see if others agree with my interpretation.

P.S. Here are two interesting tangents I plan on writing about next month:

1) A bimetallic monetary system has two media of account; gold and silver. When the market rate between gold and silver shifts, the system suffers from Gresham's Law. If we have a monetary system that uses Federal Reserve dollars and Visa/Mastercard dollars as the two media of account, what does a modern version of Gresham's Law look like?

2) The Fed gathers price data so it can better target a 2% decline rate in the CPI value of the "dollar". But if some merchants are pricing goods in terms of a different dollar medium of account, isn't the Fed gathering inappropriate data? If credit card networks are pushing up prices via fee increases, the Fed might misinterpret these changes as being Fed-inspired and adopt the wrong monetary policy. How might the Fed adjust its methodology to account for the use of credit card MOA?

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(1) As Tom Brown points out, some economists describe the unit-of-account not just as a sign, but also as a fixed quantity of the medium-of-account. So if the unit of account is the $, and the medium-of-account is gold, than the number of grains of gold that defines the dollar is rolled into the concept of unit-of-account. Alternatively, we can leave the unit-of-account as a mere sign, and refer to the medium-of-account not just gold but a given quantity of gold grains. Thirdly, we could give the quantity of the medium of account that defines the $ an entirely different term, say the "Tom Brown multiple". As long as we remember that there's a sign, the thing that represents that sign, and the quantity of that thing then we can avoid unnecessary semantic debates

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.