Sunday, April 27, 2014

Stock splits, odd lots, and liquidity premia

Earlier this week Apple announced a 7:1 stock split. Each share of Apple, currently trading for around $570, will be worth about $80 after the split goes into effect. Stock split announcements like Apple's are becoming ever more rare, and for good reason. All things staying the same, a stock split could typically be trusted to rejuvenate the size of a share's liquidity premium, and therefore increase the real value of the firm's stock. Thanks to changes in market structure, this stock split liquidity effect no longer exists.

The phenomena of a stock trading in the high triple digits, let alone quadruple digits (Priceline currently trades at $1,150) is a relatively new one for markets. During the decades before this one, a firm would typically announce a stock split once its shares had passed the $100 mark. Anyone reading the finance textbooks of the day—which for the most part taught that splits are irrelevant—would find this constant splitting and re-splitting to be puzzling. Academic finance, however, has tended to omit liquidity which, when combined with odd-lot trade pricing, helped drive these split dynamics.

I first ran into odd lot pricing when, as an 18-year old stock market rookie, I tried to buy 90 shares of some company, the name of which I've long forgotten. My broker told me that I'd have to pay more commission on that 90 shares than if I bought an even 100 shares. Was I fine with that? Cost-conscious individual that I am, I ended up buying 100 shares. What I had learnt was that round lot purchases, any multiple of 100 shares, would be docked at the regular commission rate. Purchasing odd lots, anything between 1 and 99 shares, attracted higher commissions, and therefore higher per share fees. After that I never tried to buy another odd lot.

This creates some interesting dynamics. When a stock has a very high price, odd lot pricing dissuades retail investors from participating in that market. As long as a share (say Microsoft) trades at just $50, small investors can easily bear the $5,000 cost of a round lot of 100 shares. But once Microsoft hits $100, the $10,000 cost of 100 shares starts to get expensive. Buying an odd lot of 50 Microsoft shares is an affordable option, but if odd lot commission rates apply, this significantly reduces the expected profitability of the position. Better for investors to hold off on purchasing $100 Microsoft and find a cheaper stock, say $50 IBM, that allows them to buy an affordable round lot and thereby avoid odd lot commissions.

Odd lot pricing therefore has the effect of pushing retail investor participation towards stocks priced in the low to mid range of the price spectrum. With a larger proportion of buyers and sellers participating in low and mid-priced shares, the ability to trade in and out of those stocks is augmented while the ability to enter and exit high-priced stocks is diminished. Liquidity is a very useful tool to cope with uncertainty—people will typically pay a premium to own it. Thanks to odd lot pricing, liquidity premia will be larger among lower priced stocks than among stocks near the high end of the price spectrum.

Having a large liquidity premium can be beneficial. Earnings staying constant, the wider a firm's liquidity premium is the higher its stock price will be. A richer stock price in turn lowers the firm's cost of capital. It can now issue the same amount of stock at higher prices, thus funding a larger project than would otherwise be the case if the liquidity premium had not been augmented.

The urge to defend liquidity premia explains why through most of stock market history, whenever a stock approached the edge of round-lot affordability, it quickly split. The higher it rose the more its liquidity premium shrunk as its base of retail investors, eager to avoid odd lot commissions, fled to lower-priced stock. By splitting its shares so that they were once again affordable, a firm could re-tempt retail investors into trading the firm's shares, returning it's thinning liquidity premium to historical levels and increasing the real value of each share. Because splitting is costless, a firm that announced a split effectively made its shareholders better off without sacrificing any resources.

Nowadays odd lot commissions are a thing of the past. Historically, odd lot transactions were routed to specialized brokers who made their best efforts to match purchases and sales, taking an eight of a dollar cut for their efforts. Later on, odd lot transactions began to electronically processed on the very same books as round lot orders. By 1991 the New York Stock Exchange's odd lot differential was removed, thanks to the ease with which computers could match odd lot tickets. Discount brokerages now apply flat pricing so that it makes no difference if a retail client purchases 100 or 99 shares.

The death of odd lot pricing has made it affordable for retail investors to invest in high-priced stock. Companies can now let their shares rise up into the high triple or quadruple digits without facing shrinking liquidity premia. I think that this helps explain the fall in stock splits over the last decade (see chart below).  In the 1980s and 90s, it was typical for sixty or so splits to be announced each year.  In 2013, only fourteen stocks in the S&P 500 announced splits, despite the fact that it was an excellent year for equity prices. So far in 2014 only four splits have been announced.

Souce: WSJ

Odd lot pricing's demise also explains the rise in the average price of an S&P 500 stock. The average price has fluctuated between $30 and $50 since 1980. Nowadays it is hitting $70. As firms are slowly discovering, modern stocks stay liquid well into the $1000 range.

Source: WSJ

But there still exists an upward limit to retail affordability. Since stock cannot be purchased in lots less than one share, as the price of a share rises towards $10,000 or so it will once again become difficult for retail investors to participate in that market. Priceline, which at $1100 is the highest price share in the S&P 500, has a long way to go before it hits that level. Until then, expect average share prices to continue rising, and share splits to remain far more muted than in previous decades.

Sunday, April 20, 2014

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.

Sunday, April 13, 2014

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.

Tuesday, April 8, 2014

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 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.

Friday, April 4, 2014

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. VoilĂ , 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.