Why the steepest borrowing rate may be the best rate

(This isn't a piece of financial advice. It's more of a fun parable about interest rates.)

So here's an interesting financial riddle. Let's say I want to buy a used car for $1000. 

First, I need a loan. Say that there are two floating rate loans available to me: one that currently costs 3.2% per year, and another that costs 2.3%. Logic dictates that I should take the cheaper 2.3% option, right? But I don't. Instead I take the more expensive one, figuring to myself that the expensive 3.2% loan is actually the cheaper loan.

Why on earth did I do that?

The rates in question are from the website for Aave, a tool for borrowing and lending cryptocurrencies, including stablecoins:

The cost of borrowing two different stablecoins on Aave [source]

If I borrow 1000 Tether stablecoins from Aave to fund my purchase of the $1000 car, it'll cost me 3.2%. But if I borrow 1000 USD Coins, it'll cost me just 2.3%. Those are floating rates, not fixed. (I could also borrow stablecoins on a fixed basis. A fixed-rate Tether loan would cost me 12.26% on Aave, a USD Coin loan 10.69%. Again, it's more expensive to borrow Tether.)

Why would I pay 3.2% to borrow one type of U.S. dollar, Tether, when I can get another type of U.S. dollar, USD Coin, at a cheaper rate? I mean, they're both dollars, right? They each do same thing; that is, they both provide me with the means to buy a $1000 car.

To see why I might prefer the more expensive Tether loan, we need to understand why the rates on Tether and USD Coin differ:

If I borrow 1000 stablecoins to buy a $1000 car, eventually I'll have to buy those 1000 stablecoins back in order to repay my loan. Wouldn't it be nice if, in the interim, the stablecoin I've borrowed loses its peg and falls in value? Because if it were to do so, I'd be able to buy back the 1000 stablecoins on the cheap (say for $400 or $500), pay back my 1000 stablecoin loan, and keep the $1000 car. 

In short, I'd be getting a $1000 automobile for just $400-$500 plus interest.

By contrast, if I were to borrow a more robust stablecoin in order to purchase the car, then that'd reduce the odds of its price being weak when it comes time to repay my loan, thus making the entire transaction more expensive to me. 

A $1000 car would cost me... $1000 plus interest.  

We can imagine that all potential borrowers are perusing Aave's loan list with that exact same thought in mind. Jack wants to finance a house for $250,000 by getting a stablecoin loan on Aave. Jane wants to borrow $100 in stablecoins on Aave to pay off her credit card debt. All three of us would really, really, really, like to borrow a stablecoin that fails, reducing the net cost of our purchase. So we all do our respective research and select what we believe to be the stablecoin with the worst prospects, the one most likely to be worth just 40 or 50 cents when it comes time for us to repay our debt.

The competition between the three of us to borrow the worst stablecoin will cause borrowing rates for the worst stablecoins to rise. Conversely, borrowing rates on the stablecoins with the best prospects will fall.

And that's what I suspect is happening on Aave. Tether is seen as the riskier stablecoin. And so from the perspective of the borrowing public, a Tether loan is superior to a USD Coin loan. Jack, Jill, and myself are all scrambling for the privilege of borrowing Tether, in the process pushing the cost of borrowing Tether 0.9% above the cost of borrowing USD Coin.

Now we can get back to the original riddle. Even though the rate to borrow Tether is higher than the rate to borrow USD Coin, it may be worthwhile for me to go with the a Tether loan if I think that the odds of Tether failing justify the higher financing cost.

We can even go a bit further and say that the 0.9% premium on a Tether loan is the market's best estimate of the odds of Tether losing its peg relative to USD Coin losing its peg. So for all those would-be stablecoin analysts out there, keep your eye on Aave's USD Coin-Tether spread. It's a good indicator of stablecoin risk.

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P.S: The difference between the cost of borrowing Tether and USD Coin could also be due to the liquidity premium on Tether being larger than the liquidity premium on USD Coin. I'm not going to get into that possibility in this post, but if you're curious ask me about it in the comments. 

P.P.S: Does this same logic apply to borrowing from banks? Would I rather borrow from a bank that's about to fail rather than a solid respectable bank?

P.P.P.S: Some Dune dashboards tracking he Tether-to-USD rate premium: here and here.

Is the Fed breaking the law by paying too much interest?

George Selgin had an interesting post describing how the Fed appears to be breaking the law by paying too much interest to reserve-holders. This is an idea that's cropped up on the blogosphere before, here is David Glasner, for instance.

I agree with George that the the letter of the law is being broken. That's unfortunate. As Section 19(b)(12)(A) of the Federal Reserve Act stipulates, the Fed can only pay interest "at a rate or rates not to exceed the general level of short-term interest rates." With three month treasury bills currently around 0.33% and the fed funds rate at 0.4%, the current interest rate on reserves (IOR) of 0.5% exceeds the legal maximum.

Unlike George, I don't think the Fed deserves criticism over this. If the letter of the law is being broken, the spirit of the law surely isn't.

If there is a spirit residing in the law governing IOR, it's the ghost of Milton Friedman. Since the Fed's inception in 1913, IOR had been effectively set at 0%, far below the general level of short term interest rates. This has acted as a tax on bankers. They have been forced to hold an asset—reserves—that provides a below-market return. Friedman's big idea was to remove this distortionary tax by bringing IOR up to the same level as other short term interest rates. Banks would now be earning the same rate as everyone else. The Fed would only get the authority to set a positive rate on reserves in 2008, long after most modern central banks like the Bank of Canada had implemented Friedman's idea.

Friedman wanted to remove the tax, but he didn't want to introduce a subsidy in its place. To prevent central bank subsidization of banks, the Federal Reserve Act is explicit that IOR should not exceed other short-term interest rates.

In practice, how might the Fed set IOR in a way that subsidizes banks? This is more complicated than it seems. If the Fed sets IOR at 1%, arbitrage dictates that all other short term rates will converge to that same level. After all, why would a financial institution buy a safe short term fixed income product for anything less than 1% if the central bank is fixing the yield of a competing product, reserves, at 1%?

Short-term yields won't converge exactly to IOR. Some will trade a hair above IOR, others a bit below. This is because each short-term fixed income product has its own set of peculiarities and these get built into their yield. For instance, buying federal funds is riskier than parking money at the Fed; in the latter transaction the Fed is your counterparty while in the former it's a bank, So the fed funds rate should trade a bit above IOR. But we wouldn't say that a higher fed funds rate is a sign of a below-market return on reserves, or that this spread represents an implicit tax on reserve owners. The fed funds rate exceeds IOR only because that is how the market has chosen to appraise the risk of owning fed funds.

Conversely, because a treasury bill is ofttimes less risky then parking money at the Fed, its yield should regularly dip below IOR. When it does, no one would say that the Fed is providing an unfair subsidy to reserve holders by paying IOR in excess of the treasury bill rate. The lower treasury bill rate is simply the free market's way of accounting for the superior risk profile of treasury bills relative to reserves.

Nowadays, with IOR at 0.5% and treasury bills yielding 0.33%, the Fed is clearly contradicting the wording of the Federal Reserve Act. IOR has been set at a rate that "exceeds the general level of short-term interest rates." But this by no means implies that the Fed is breaking the spirit of the law. The spirit of the law only tells the Fed not to pay subsidies to banks. As I explained above, the yield differential may simply reflect the market's assessment of the unique risks of various short-term fixed income products, not  a policy of paying subsidies.

To get the ghost of Milton Friedman rolling in his grave, here is how to structure IOR so that it offers a subsidy to banks. The Fed would have to set up a tiered reserve system where a bank's first tier of reserves earns a higher rate than the next tier. To begin with, assume that Fed officials deem that a 0.5% fed funds rate is consistent with a 2% inflation target. The Fed offers to pays interest of 100% on required reserves (I'm exaggerating to make my point) while offering just 0.5% on excess reserves. Banks will hold required reserves up to the maximum and reap an incredibly 100% yearly return. All reserves above that ceiling will either be parked at the Fed to earn 0.5% or lent out in the fed funds market.

Thanks to arbitrage, the 0.5% rate on excess reserves ripples through to other short term rates. Because a bank can always leave excess reserves at the Fed and earn an easy 0.5%, a borrower will have to bid up the fed funds rate and t-bill rates to at least 0.5% in order to coax the marginal lender away from the Fed.

And that's how the Fed would subsidize banks. The "general level" of rates as implied by the rate on fed funds and treasury bills hovers at 0.5% while banks are earning a stunning 100% on a portion of their reserve holdings. It's highway robbery! Milton Friedman would be furious; the distortionary tax he so disliked has been replaced with a distortionary subsidy.

By the way, if you really want to know what tiering and central bank subsidies to banks look like, this is the exact same mechanism the Bank of Japan and Swiss National Bank have introduced to help banks deal with negative interest rates. See here and here.  

So the bit of legalese that says that IOR should not exceed the "general level of short-term interest rates" is really just a poorly chosen set of words meant to describe a very specific idea, namely, a prohibition against setting a tiered reserve policy where the first tier, required reserves, earns more than the second, excess reserves, the ensuing subsidy flowing through to banks.

At the end of the day, what accounts for the current divergence between IOR and the other short term rates? Because the Fed has not set up a tiered reserve policy, there is simply no way that the divergence reflects a subsidization of banks. There is only one remaining explanation. Peculiar developments in the microstructure of the fed funds and t-bills markets have led traders to discount these rates relative to IOR.

So you can rest easy, Milton.

The peculiarities bedeviling the fed funds market are explained by Stephen Williamson here. There are several large entities, the GSEs, that can keep reserves at the Fed but are legally prevented from earning IOR. Anxious to get a better return, they invest in the fed funds market market, but only a limited number of banks have the balance sheet capacity to accept these funds. This oligopoly is able to extract a pound of flesh from the GSEs by lowballing the return they offer, the result being that the fed funds rate lies below IOR.

As for treasury bills, they are unique because, unlike reserves held at the Fed, they are accepted as collateral by a whole assortment of financial intermediaries. Put differently, treasury bills are a better money than reserves. Because the government is loath to issue too many of them, the supply of treasury bills has been kept artificially scarce so that they trade at a premium, a liquidity premium.

George ends his post by appealing to his readers to sue the Fed. I don't think think a lawsuit will bring much justice. If there are to be any legal battles to be fought, better to petition Congress to adjust the wording of the Federal Reserve Act so that it better fits the spirit of the law. We don't want the law to misidentify a situation involving IOR in excess of the "general level of interest rates" as necessarily implying subsidization when microstructure is actually at fault. While Milton Friedman had a lot of reasons to criticize the Fed, this probably wouldn't be one of them.

Slow money

Would it make sense for firms to try to slow down their equity structure?

Equity markets are made of two classes of participants. The minority consists of long-term investors who, like Ulysses, have 'tied themselves to the mast' and would rather fix things when a company runs into problems than sell out. The majority is made of up rootless speculators and nihilistic indexers who cut and run the moment the necessity arises.

Because their holding period is forever, the long-term investor class does all the hard work of monitoring a company and agitating for change. Keeping management honest is the only recourse they have to protecting their wealth. Speculators and indexers are free loaders, enjoying the same upside as investors without having to contribute to any of the costs of stewardship.

How might long-term investors be compensated for the extra expenses they incur in tending the garden?

One method would be for a firm's management to institute a slow/fast share structure. The equity world is currently dominated by the fast stuff, shares that can be bought and sold in a few milliseconds. A slow share is a regular share that, after having been acquired, must be "deposited" for, say, two years. During the lock down period the shareholder enjoys the same cash dividends as a fast share but they cannot sell. Only when the term is up can the slow share be converted back into a fast share and be got rid of. The illiquidity of slow shares is counterbalanced by a carrot; management makes a promise that anyone who converts into slow shares gets to enjoy the benefit of an extra share down the road i.e. a stock dividend. So a shareholder with 100 fast shares who pledges to lock them in for two years will end up with 101 fast shares once the lock-up period is over.

The investor class, which until now has received no compensation for their hard work, will quickly choose to slow down all their shares and enjoy the biennial stock dividend. Feckless speculators and indexers, unwilling to stay tied down for two years, will keep their fast shares and forgo the dividend. After all, the S&P's constituents could change at any moment, so an ETF/index fund needs to be able to cut and run. And a speculator's trend of choice could reverse at any moment.

By the way, ETFs and index funds aren't the only asset type that I include in the fast money category. Also qualifying are the huge population of funds that claim to be "active" but are actually "closet" indexers, as well as all those funds that say they are engaging in 'investing' but are really just speculators. Given the possibility of sudden redemption requests, they need the flexibility that liquid fast shares provide.

As the slow/fast share structure goes mainstream, the benchmark to which market participants are compared, the S&P 500 Index, will evolve into two flavours, the Fast S&P 500 and the Slow S&P 500, the former including the fast shares of the 500 index members while the latter includes only the slow. The Slow S&P will, by definition, show better returns than the Fast S&P, since slow shares enjoy stock dividends at the expense of fast shares. Nihilistic indexers and rootless speculators will choose to benchmark themselves to the lagging Fast S&P. Active investors with a genuine long-term bias, most of whom will choose to own slow shares, will compare themselves to the better-performing Slow S&P.

Mass adoption of fast/slow share structure could change the complexion of the very combative active vs passive investing debate. Passive investors have typically outperformed active investors after fees, largely because they have been able to freeload off of the stewardship of long-term investors. With a new structure in place, buyers of passive indexed products would—by definition—begin to underperform the average long-term active investor. This is because the dual share structure obliges the passive class to compensate long-term investors for their efforts.

I suspect that the adoption of a fast/slow share structure would increase the size of the investor class. After all, with a long-term investing mentality now being rewarded, those on the margin between the investing class and the mass of speculators/indexers will elect to slow down their shares. Once they have lost the ability to cut & run, the only way to protect their wealth will be through constant surveillance of management and a more activist stance. This is a good thing since long-term shareholders are better stewards of capital than short-term ones. In general, share prices should rise.

On the other hand, as more shares are locked down, market liquidity will suffer. Will the increase in stock prices due to improved stewardship outweigh the drop in prices due to a much narrower liquidity premium? If I had to guess, I'd say yes. Which means that even feckless indexers and speculators should support the subsidization of long-term investors.

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Addendum: This isn't a new idea. Read all about loyalty-driven securities here.
Disclaimer: I consider myself to be 50% speculator, 25% indexer, 25% investor. But I'm trying my best to boost the last category.

Why big fat Greek bank premiums?

National Bank of Greece depository receipt certificate (source)

If you're like me and you like to: 1) explore anomalies in markets; and 2) mix equity analysis with monetary analysis, then you'll like this post. A sneak peak: by the end, we'll be able to use equity markets to figure out the unofficial exchange rate between a Greek euro and non-Greek euro.

For the last few weeks shares of Greek banks have diverged dramatically from their overlying depository receipts (see chart below). A bit of background first. A depository receipt is much like an exchange-traded fund, except where an ETF holds a bundle of different stocks, a depository receipt represents just one stock. That stock is usually listed on an out-of-the-way market (like Greece), whereas the depository receipt trades on a major exchange like New York. Investors interested in owning a foreign stock can avoid currency conversion costs and foreign settlement problems and instead purchase the New York-listed depository receipt hassle-free.

In general, the parent security and its offspring should trade in line with each other. Recently, however, the US-listed depository receipts of the National Bank of Greece and Alpha Bank have risen to a massive premium relative to their Greek-listed parents. For instance, in mid-August investors could have bought National Bank's New-York listed depository receipt for €0.73. However, the Greek-listed stock was trading for just €0.60. For some reason, investors are paying 30% more for a security that provides the exact same stream of earnings. We've got a gross violation of the law of one price.*

This is especially interesting given that a redemption/creation mechanism for depository receipts links the price of parent and offspring via arbitrage. In the same way that an investor deposits cash at a bank and gets a bank deposit, an investor can buy a National Bank of Greece share listed in Athens and 'deposit' that share at a custodian, receiving in return a newly-created New York-listed depository receipt. If either security can be bought for less than the other, an arbitrage opportunity arises. For instance, in mid-August one might (in theory) have bought Greek-listed National Bank of Greece shares for €0.60, converted them into New York-listed depository receipts, sold the depository receipts for €0.73, wired the proceeds from New York to Greece, and repurchased Greek-listed National Bank of Greece shares for €0.60. Rinse and repeat. (This works the other way, too. In the same way that a bank deposit can be converted into cash, investors can purchase a depository receipt and redeem it for underlying equity.)

The effect is that as investors clamour to harvest arbitrage gains, any premium or discount between a New York-listed depository receipts and its Greek parent equity should quickly fall towards zero. Why hasn't this been the case in Greece of late?

There are several explanations for persistent premia/discounts between depository receipts and their underlying shares. The first is liquidity differences. If the depository receipt is more liquid than the underlying equity, then investors will be willing to pay a bit more for the depository receipt. In the case of National Bank of Greece, the depository receipt tends to attract higher trading volumes than the underlying Athens-listed shares, which probably explains why the receipts have tended to trade at a premium.

Premiums or discounts can also occur when the redemption/creation mechanism is inhibited. Depository receipts for Taipei-listed Taiwan Semi Conductor rose to an incredible 60% premium to the shares in the late 1990s and early 2000s. The reason for this premium can be traced to the fact that Taiwan restricts foreign ownership of local companies. This effectively prevented the closing of the premium via purchases of local shares for conversion into depository receipts. These premia evaporated when Taiwan removed foreign ownership restrictions in 2003. (Here is a good summary).

In a 2006 paper, Saxena found that the New York-traded depository receipts of a handful of Indian stocks, including Infosys, Wipro, State Bank of India, MTNL, ICICI Bank, HDFC Bank and Satyam Computers, habitually traded at substantial premium to the underlying Indian-listed equity. Infosys's premium (which reached 60% in 2002) had existed since its U.S. listing in 1999. However, German, South Korean, and Hong Kong-listed companies with New York-listed depository receipts showed negligible premia.

Why was this? Saxena found that Indian depository receipts suffered from limited two-way fungibility. Depository receipts could be freely converted into Indian-listed shares, but Indian-listed shares could only be converted into depository receipts to the extent that there was available 'head room'. The amount of headroom in turn depended on the extent of past conversion of depository receipts into shares. Since headroom in the above shares had been all used up, when American investors flocked to buy depository receipts, thus driving them to a premium relative to the Indian-listed equity, there was no way for arbitrageurs to close the difference.

In the case of Greece, the imposition of capital controls on June 29 seems to have inhibited the redemption/creation mechanism. The Athens stock exchange was closed the same day (the New York-listed receipts continued to trade), but when it reopened on August 3, capital controls remained in place. Since reopening, a wedge has appeared between the prices of National Bank of Greece's depository receipts and its underlying shares, implying that there has been much more demand for the former than the latter. Typically, arbitrageurs would close this gap, buying the underlying Athens-listed shares and turning them into new deposit receipts. Presumably the Greek authorities have asked that banking intermediaries cease allowing the conversion of Greek shares into receipts, so arbitrage has not been possible.

That ended on August 27, 2015. According to a press release for BNY Mellon, clarification requested from Greek authorities regarding conversions of depository receipts had finally been received and, as a result, deposit receipt books would be re-opened for issuance and cancellation. With the ability to arbitrage receipts and the underlying shares once again available, the National Bank of Greece depository receipt premium collapsed from around 30% to 10% when markets opened on August 28. It has been shrinking ever since and now lies within its historical range.

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That explains the anomaly and its disappearance. But that's not the end of the story. Going forward, watching the relative price of National Bank of Greece's depository receipts and its share price may provide valuable insights.

In permitting depository receipt redemption and creation, the Greek government has effectively removed capital controls. Currently, Greeks cannot withdraw more than €420 in cash per week from their bank accounts and are not permitted to transfer more than €500 per month to a foreign account. Businesses must go through tedious application processes to get access to their funds. However, with the depository receipt window open, businesses and individuals can simply spend all their bank deposits on Athens-listed National Bank of Greece, convert the shares into depository receipts, sell them in New York for dollars, and convert the funds back to euros. Voila, capital controls evaded.

This loop hole doesn't seem very fair to me. After all, only the financial elite will be aware of the depository receipt escape, with widows, orphans, and the rest oblivious that capital controls have been effectively lifted. Loosening up the depository receipt window only make sense if it is twinned with similar effort to help the broad public, say a higher ceiling on cash withdrawals.

Depending how tightly Greece's capital controls bind, Athens-listed National Bank of Greece shares might actually lose their traditional discount and rise to a premium relative to New York-listed depository receipts (in euro terms). If depository receipts are the best route to evade capital controls, then those desperate to get their money out of Greece will be willing to pay a 'fee' for that privilege. By purchasing National Bank of Greece shares in Athens for, say 0.65 euro, and converting them into depository receipts that trade for just 0.60 euros, investors effectively lose 0.05 euros. The size of that fee, the premium, will equal the cost of the next best alternative for evading capital controls. If controls are leaky, the premium will be small. If they aren't, it could be quite wide.

A number of studies have found that during the Argentinean corralito, Buenos Aires-listed shares rose to a huge premium relative to their New York-listed depository receipts. Brechner, for instance, finds that the premium reached over 40% in January 2002. This gap represented the amount that Argentinians were willing to pay to use depository receipts as a vehicle for moving their wealth from frozen Argentinean bank deposits into liquid U.S bank deposits. When share conversions were restricted in March 2002, that premium disappeared.

Greece seems on its way to being mended. Capital controls should be loosened soon, and people no longer seem anxious about an imminent drachma conversion. So if a premium on local National Bank of Greece shares were to develop, I doubt it would be large like the sort of premia that prevailed in Argentina. However, if things were to get worse, we might see a large gap develop.

In closing, now that depository receipt conversion has been reopened but capital controls remain in place, the exchange rate between Athens-listed National Bank of Greece shares and New York-listed depository receipts serves as the "black market" rate between Greek euros and non-Greek euros. After Hugo Chavez imposed capital controls in 2003, Venezuelans used the rate between Caracas-traded CA Nacional Telefonos de Venezuela (CAN TV) shares relative to New York-listed depository receipts as a shadow rate for the Venezuelan bolivar, until CANTV was nationalized in 2007. Likewise burdened by capital controls, Zimbabweans used the exchange rate between Old Mutual shares listed on the Zimbabwe Stock Exchange and those listed in London as the implicit Zimbabwe dollar exchange rate. It even had a name: the OMIR, or Old Mutual Implied Rate.

So watch the National Bank of Greece equity-to-depository receipt rate closely. It's conveying information about Greek euros.


* More accurately, the depository receipts were trading for US$0.83. To calculate their euro price, I use the 9:30-10:30 price of New York-listed National Bank of Greece depository receipts and converted them into euros at the prevailing dollar-to-euro exchange rate.

No Eureka moment when it comes to measuring liquidity

Measuring liquidity is a pain in the ass.

The value of a good, say an apple, is easy to calculate; just look at the market price for apples. Unfortunately, doing the same for liquidity is much more difficult because liquidity lacks its own unique marketplace. Liquidity is like a remora, it never exists on its own, choosing instead to attach itself to another good or asset. For instance, a bond provides an investor with both an investment return in the form of interest and a consumption return in the form of a flow of liquidity services. Since the price of this combined Frankenstein reflects the value that an investor attributes to both returns, we can't easily disentangle the value of the one from the other.

Here's a symmetrical (and equally valid) way to think about this. If liquidity is a good then illiquidity is a bad, where a bad is anything with negative value to a consumer. This bad doesn't exist on its own but, like a virus, infects other goods and assets. While all goods and assets are plagued by a certain degree of illiquidity, determining the price of of this nuisance—the amount that people will pay to rid themselves of an asset's illiquidity—is difficult because the price of the compound entity combines both a flow of illiquidity disservices as well a flow of positive investment returns.

The only technique we currently have to back out liquidity valuations (or illiquidity penalties) from market data is to find the price or yield differential between two similar instruments, this gap indicating the value that the market ascribes to liquidity (or the negative value of illiquidity). Think identical twin studies in the life sciences. To get a clean differential, the two financial instruments must be "twins," issued by the same entity and having the same maturity. That way any differential between them can't be attributed to credit or term risk, the lone remaining factor—liquidity (or illiquidity)—being the culprit.

The best example is the on-the-run vs off-the-run Treasury spread, the difference in yield between newly-issued 10-year Treasuries and 30-year Treasuries that have 10 years left till maturity. The credit quality and term of these two issues is precisely similar, yet the yield of a newly-issued 10-year Treasury is typically 10 basis points below that of an "off-the-run" equivalent. This gap represents the extra bit of value that investors will pay to enjoy an on-the-run Treasury's liquidity (or, alternatively, the negative value of the illiquid "bad" embedded in an off-the-run Treasury). Assuming that a new bond worth $1000 has a 1.9% yield while an equivalent off-the run issues yields 2.0%, investors are valuing the extra bit of liquidity provided by the on-the-run issue at around $1 per year for each $1000 that they invest.

The first problem with this technique will be familiar to anyone who has tried to conduct studies using twins separated at birth; its very difficult to find twin assets. The second problem is that even if we succeed in locating twin assets, a comparison of them will only reveal the degree to which investors prefer, say, an on-the-run bond's liquidity to that of an off-the-run bond. In other words, it provides us with a relative value. But if we want to find the absolute value that investors place on an on-the-run issue's liquidity (or the absolute disvalue that they place on an off-the-run issue's liquidity), we're left empty-handed. Sean Connery may be cooler than Johnny Depp, but what if we want to calculate Sean Connery's total amount of coolness?

Here's an out. Unlike human identical twins, financial twin assets can be easily manufactured. Create a market in which identical duplicates of existing assets trade. This solves the first of these two problems; rarity.

As for the relative value problem, we can solve it by manufacturing these twin assets in a way that allows us to measure absolute liquidity (or absolute illiquidity). Just create an infinitely liquid twin. An infinitely liquid good can be traded frictionlessly and instantaneously for any other good. The premium at which the manufactured twin trades above the original asset represents the penalty applied to the illiquid original. We thus have a measure of absolute illiquidity; specifically, we have backed out the total amount of compensation that investors require for bearing the illiquid "bad" bound up in a given asset.

In practice, what would these infinitely liquid twins look like? Imagine that a risk-free institution, say a government-backed bank, creates deposits that are denominated and redeemable in Microsoft shares. The bank would pay interest at the same rate that Microsoft pays dividends. Since the purchasing power of these deposits would fluctuate in line with the price of underlying Microsoft shares, the Microsoft deposit would be an exact replica of a Microsoft share. One difference remains: Microsoft shares trade on just one market—the stock market—whereas Microsoft deposits, like bank deposits, have the potential to trade in all markets. Imagine buying an ice cream cone with 0.055 Microsoft deposits. The premium at which Microsoft deposit will trade is an absolute measure of the penalty investors expect to incur for enduring the illiquid "bad" attached to Microsoft shares. Problem solved, right? We've go a clean measure of illiquidity.

Not quite. While infinite liquidity is a nice idea, it's impossible to create. Bank deposits are highly liquid, but not infinitely liquid. Just try purchasing something at a garage sale with a bank card. Second, even if a bank begins to offer Microsoft deposits, there's no guarantee that merchants who already accept dollar-denominated deposits will accept Microsoft-denominated deposits. The upshot is that Microsoft deposits won't be able to serve as an ideal benchmark since they themselves are destined to be tarred by the same illiquidity as Microsoft shares.

We need a cleaner foil against which to compare Microsoft shares. Fortunately, there's an alternative to manufacturing an infinitely liquid twin—just fabricate its exact opposite, a perfectly illiquid twin. A term deposit is a great example of a perfectly illiquid asset; its owner keeps the instrument in their possession until it reaches maturity. During the interim they cannot trade it to anyone else. The difference in price between the original asset and its completely illiquid twin is a measure of the absolute value that investors ascribe to the liquidity embedded in the original asset.

In practice, imagine that our risk-free banks creates 1-year Microsoft term deposits. One deposit represents an irrevocable commitment to earn Microsoft dividends over the course of a year, the deposit maturing in one year with the paying-out of a Microsoft share. Investors facing the choice between purchasing a Microsoft term deposit and an actual Microsoft share will earn the same dividends and capital gains, but will have to weigh the disadvantages of being locked into the deposit versus the benefits of easily liquidating the exchange-traded share. As such, investors will probably only purchase Microsoft term deposits at a slight discount to the price of a fully-negotiable Microsoft share. After all, if you're going to commit yourself to owning Microsoft for one full year, you need to be compensated for your pains. This discount represents the absolute value of a Microsoft share's liquidity.

Voilà, we've unbundled the value attributed to an asset's flow of liquidity returns from its value as a pure financial IOU. We can do this for all sorts of assets. But it's a pain in the ass to do, since it requires the creation of an as-yet non-existent class of financial assets.*

Why bother decomposing an asset's financial return from its liquidity return? Assets provide both an investment return and a consumption good in the form of liquidity, but no one is entirely sure how to apportion prices among the two. Liquidity is static, it muddies many of the supposedly clear signals we get from market prices. Unbundling the liquidity return from the investment return could make the world a much more efficient place. People would be able to see how much they are paying for each of these two returns, thus potentially improving the way that they choose to allocate their resources. What was once static becomes just another signal.

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PS: Apologies to long-time readers, who will have already read much of the above points in previous posts. I'm hoping a restatement may provide a different approach to thinking about liquidity.

PPS: The post resolves the problem mentioned in the last three paragraphs of Liquidity as Static.

*Interestingly, a limited market in twins already exists. In addition to providing chequing accounts, banks also provide term deposits. The yield differential between the two represents the absolute value of the liquidity services provided by a chequing deposit. The majority of assets, however, have not yet been twinned---think equities, bonds, bills, mortgage-backed securities, derivatives, and more.

Is the U.S. dollar in the midst of the longest Wile E. Coyote moment ever?

It would be wrong to blame the economics blogosphere's failure to foresee the 2008 credit crisis on complacency. Better to say that bloggers were distracted. Instead of sifting through sub-prime and CDO data, they were grappling with an entirely different threat, the impending Wile E. Coyote moment in the U.S. dollar. The perpetual racking-up of ever larger debts by the U.S. to the rest of the world for the sake of funding current consumption, and the eventual dollar collapse that this implied, was believed to be tripping point numero uno at the time. Look no further than Paul Krugman, who in September 2007 (in just his fourth blog post) had this to say:

The argument I and others have made is that the U.S. trade deficit is, fundamentally, not sustainable in the long run, which means that sooner or later the dollar has to decline a lot. But international investors have been buying U.S. bonds at real interest rates barely higher than those offered in euros or yen — in effect, they've been betting that the dollar won’t ever decline.

So, according to the story, one of these days there will be a Wile E. Coyote moment for the dollar: the moment when the cartoon character, who has run off a cliff, looks down and realizes that he’s standing on thin air – and plunges. In this case, investors suddenly realize that Stein’s Law applies — “If something cannot go on forever, it will stop” – and they realize they need to get out of dollars, causing the currency to plunge. Maybe the dollar’s Wile E. Coyote moment has arrived – although, again, I've been wrong about this so far. 

He wasn't alone in this belief.* As we all know, the U.S. did eventually run off a cliff—but it wasn't the cliff that everyone expected. Instead of a dollar crisis, we had a financial and banking crisis. As for the dollar, it has since raced to its highest point in more than a decade.

Since 2008 the ensuing slow recovery has dominated the blogosphere. And now we are hearing about an impending secular stagnation, a new macroeconomic dystopia that has been manufactured by many of the same folks who contributed to the debate surrounding the econ blogosphere's first great macroeconomic bogeyman, U.S. dollar imbalances.

Before allowing the sec stag story to scare our pants off, shouldn't we be asking what happened to the first bogeyman? Given the econ blogosphere's silence on the topic of U.S. dollar imbalances, one could be forgiven for assuming that these imbalances had been resolved. But they haven't. Sure, the U.S.'s current account deficits aren't as high as before. But the stock measure of U.S. indebtedness, its net international investment position (NIIP), continues to fall to increasingly negative levels. Ten years ago, when bloggers were focused on the issue, the U.S. owed $2 trillion more than foreigners owed it, about 15-20% of GDP. The NIIP now clocks in at 39% of GDP, or $7 trillion. See chart below. So if anything, the stock measures that worried so many economists in 2005 have only gotten worse.

What I have troubles understanding is why folks like Larry Summers are having so much success selling the world on their newest bogeyman—secular stagnation—when they have never properly atoned for the bland ending to their first story. Why has growing U.S. international indebtedness never led to a U.S. dollar collapse as predicted? What mistakes did these prognosticators make? Or should we think of the the dollar's Wile E.Coyote moment as just an extended one—for the last ten years the greenback has been hanging in air, not realizing that it's been slated for a collapse.  Reading through old blog posts and articles written circa 2006, the dollar's blithe disregard of its eventual demise was often met by invocations of Stein's law: "If something cannot go on forever, it will stop" or Rudi Dornbusch’s first corollary of Stein’s Law: “Something that can’t go on forever, can go on much longer than you think it will.” It could be that the doomsayers still invoke these quotations, but surely there's a statute of limitations on invocations of Wile E. Coyote.

If the creators of the first bogeyman are just the victims of awful timing, then the net stock data on which they initially based their initial pessimism has only worsened. This means that they should be doubling down on their warnings of impending dollar doom. Instead, we get a steady stream of warnings over a totally different macroeconomic disaster; secular stagnation.

The other side to the story is that maybe we aren't in the midst of the longest Wile E. Coyote moment ever. Maybe the U.S. dollar bears were wrong about imbalances all along.

The fact that foreigners are willing to perpetually buy U.S. financial assets and fund a reckless U.S. consumption binge seems, on the surface, to be a violation of the eternal rule of quid pro quo—an even exchange of one thing for another. In return for a mere promise of distant consumption, Americans are getting valuable foreign labour and goods. 

But what if something is missing to this story? Consider that a financial asset isn't a mere IOU. Rather, it is an IOU twinned with a durable consumption good. This very special good is called liquidity. Workers in the financial industry incur a significant amount of time and energy in fabricating this component. They expend this effort because people will pay good money to consume liquidity. Just like having a fire extinguisher or a revolver on hand provides a measure of relief, the possession of liquidity provides its owner with a stream of comfort.

Unfortunately, liquidity is never sold as a stand-alone product. Like a room with a view—you can't buy the view without also getting the room—people who want to own liquidity must simultaneously buy the attached financial asset.

It just so happens that the Yankees are the world's leading manufacturer of liquidity premia. This means that foreigners may be gobbling up such incredible amounts of American financial assets not because they have an urge for U.S. IOUs per se, but because they desire to consume the liquidity premia that go along with those IOUs. The U.S.'s NIIP, which is supposed to include only financial assets, is effectively being contaminated by consumption goods. Specifically, some portion of U.S.'s liabilities to the rest of the world is actually comprised of accumulated exports of liquidity premia. Rather than classifying these liquidity services as a stock of financial assets/liabilities, they should be reclassified as a flow of liquidity services and moved to the current account side of the U.S.'s balance of payments, along with the rest of the U.S.'s goods & services exports. This would have the effect of making the U.S.'s NIIP much less abysmal then it appears. Rather than Americans living beyond their means, this allows us to tell a story in which foreign goods and services are being bartered for liquidity premia which, like machines or wheat or apple pie, require the toil and sweat of American laborers to produce. This isn't an extravagant privilege, it's honest quid pro quo.**

We can argue about the size of the liquidity premia that the U.S. exports. On the one hand, these premia may outweigh the value of goods & services that the U.S. imports, indicating that rather than being profligate, Americans are tightwads. Or this number may be relatively small, indicating that while Americans are less spendthrift than is commonly assume, they still aren't models of prudence.

I'm not sure if the creators of the blogosphere's first great bogeyman would agree with any of this, since not only have they gone silent on the topic—they've switched to talking about a new bad guy.*** Interestingly, if exports of liquidity premia explain why the U.S.'s negative NIIP is not a catastrophe in the making but a stable equilibrium, those same liquidity premia can explain some of the stylized symptoms of so-called secular stagnation—namely persistently falling interest rates. 

Liquidity is static, it interferes with many of the supposedly clear signals we get from data. If liquidity led economists astray in the last decade by creating what seemed to be ominously extreme dollar stock imbalances, it may be leading them astray this decade by creating what seem to be ominously low real interest rates. The last thing we want is a repeat of the previous decade in which economists missed out on the big one because they were so focused on what, in hind sight, seems to have been a bogus threat.

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*Here is DeLong. It was one of Brad Setser's favorite topics. Non-bloggers including Rogoff and Summers also questioned the ability of the U.S. to generate perpetual current account deficits.
** The idea that the U.S. is exporting something unseen in the official data isn't a new idea. In this 2006 paper, Ricardo Hausmann and Federico Sturzenegger were one of the first to discuss the idea of "dark matter." This stuff is comprised of U.S. exports of expertise and knowledge, liquidity services, and insurance services. Ricardo and Hausmann believed that dark matter increased the value of U.S. assets held overseas, but it seems to me that dark matter, namely liquidity premia, does the opposite: it decreases the value of U.S. liabilities to foreigners.
*** At the time, Krugman, Setser, DeLong, and Hamilton criticized the dark matter idea. Buiter, publishing through Goldman Sachs, also criticized the idea here. 

Liquidity as static

In his first blog skirmish, Ben Bernanke took on Larry Summers' secular stagnation thesis, generating a slew of commentary by other bloggers. If the economy is in stagnation, the econ-blogosphere surely isn't.

I thought that Stephen Williamson had a good meta-criticism of the entire debate. Both Bernanke and Summers present the incredibly low yields on Treasury inflation protected securities (TIPS) as evidence of paltry real returns on capital. But as Williamson points out, their chosen signal is beset by static.

Government debt instruments like TIPS are useful as media of exchange, specifically as collateral, goes Williamson's argument. Those who own these instruments therefore enjoy a stream of liquidity services that gets embodied in their price as a liquidity premium. Rising TIPS prices (and falling yields) could therefore be entirely unrelated to returns on capital and wholly a function of widening liquidity premia. Bernanke and Summers can't make broad assumptions about returns on capital on the basis of market-driven yields without knowing something about these invisible premia. (Assiduous readers may remember that I've used a version of the liquidity premium argument to try to explain the three decade long bond bull market, as well as the odd twin bull markets in bond and equity prices.)

Riffing on Williamson, liquidity premia are a universal form of static that muddy not only bond rates but many of the supposedly clear signals we get from market prices. Equity investors, for instance, need to be careful about using price earnings ratios to infer anything about stock market valuations. The operating assumption behind something like Robert Shiller's cyclically adjusted PE (CAPE) measure is that rational investors apply a consistent multiple to stock earnings over time. When CAPE travels out of its historical average, investors are getting silly and stocks are over- or undervalued.

But not so fast. Since a stock's price embodies a varying liquidity premium, a rise in equity prices relative to earnings may be a function of changes in liquidity premia, not investor irrationality. Until we can independently price these liquidity services, CAPE is useless as a signal of over- or undervaluation, a point I've made before. Hush, all you Shiller CAPE acolytes.

Liquidity also interferes with another signal dear to economists and finance types alike; expectations surrounding future inflation. The most popular measure of inflation expectations is distilled by subtracting the nominal yield on 10-year Treasuries from the equivalent yield on 10-year TIPS. The residual is supposed to represent the value of inflation protection offered by TIPS. But it is a widely known fact that this measure is corrupted by the inferior liquidity in TIPS markets. See commentary here, here, and here. The upshot is that a widening in TIPS spreads—which is widely assumed to be an indicator of rising inflation expectations—could be due to a degeneration  improvement in the liquidity of TIPS relative to the liquidity of straight Treasuries.

Interestingly, the Cleveland Fed publishes a measure of inflation expectations that tries to "address the shortcomings" of rates derived from TIPS by turning to data from a different source: inflation swaps markets. In an inflation swap, one party pays the other a fixed rate on a nominal amount of cash while the other returns a floating rate linked to the CPI. Given the market price of this swap, we can extract the market's prediction for inflation. According to the people who compile the Cleveland Fed estimate, inflation swaps are less prone to changes in liquidity than TIPS yields, thus providing a true signal of inflation expectations.

But how can that be? Surely the prices of swaps and other derivatives are not established independently of market liquidity. After all, like stocks and bonds, derivatives are characterized by bid-ask spreads, buyers strikes, and runs. Sometimes they are easy to buy or sell, sometimes difficult. When I first thought about this, it wasn't immediately apparent to me what liquidity premia in derivative markets would look like. With bond and equity markets, its easy to determine the shape and direction of the premium. Since liquidity is valuable, buyers compete to own liquid stocks and bonds while sellers must be compensated for doing without them. A premium on top of a security's fundamental value develops to balance the market.

Derivatives are different. Take a call option, where the writer of the option, the seller, provides the purchaser of the option the right to buy some underlying security at a certain price. In theory, the more liquid the option, the higher the price the purchaser should be willing to pay for the option. After all, a liquid option can be sold much easier than an illiquid one, a benefit to the owner. But what about the seller? I risk repeating myself here, but a seller of a stock or bond will require a *higher* price if they are to part with a more liquid the security. However, in the case of the option, the writer (or seller) will be willing to accept a *lower* and inferior price on a liquid option. After all, the writer will face more difficulties backing out of their commitment (by re-selling the option) if it is illiquid than if it is liquid.

This creates a pricing conundrum. As liquidity improves, the option writer will be willing to sell for less and the purchaser willing to buy for more. Put differently, the value that the writer attributes to the option's liquidity and the concomitant liquidity premium this creates drives the option price down, while the value the purchaser attributes to that same liquidity engenders a liquidity premium that drives the option price up. What is the net effect?

I stumbled on a paper which provides an answer of sorts (pdf | RePEc). Drawing on data from OTC options markets, the authors finds that illiquid interest rate options trade at higher prices relative to more liquid options. This effect goes in the opposite direction to what is observed for stocks and bonds, where richer liquidity means a higher price. The authors' hypothesis is that the liquidity premium of an option is set by those investors who, on the margin, are most concerned over liquidity. Given the peculiarities of OTC option markets, this marginal investor will usually be the option writer (or seller), typically a dealer who is interested in reversing their trades and holding as little inventory as possible, thus instilling a preference for liquidity. Buyers, on the other hand, tend to be corporations who are willing to buy and hold for the long term and are therefore less concerned with a fast getaway. The net result is that for otherwise identical call options, the overriding urgency of dealers drives the price of the more liquid option down and illiquid one up.

Anyone who has dabbled in futures markets may see the similarity in the story just recounted to a much older idea, the theory of normal backwardation. The intuition behind normal backwardation is that a futures contract, much like a call option, has two counterparties, both of whom need to be rewarded with a decent expected return in order to encourage them to enter into what is otherwise a very risky bet. If both require this return, then how does an appropriate "risk premium" get embodied in a single futures price?

None other than John Maynard Keynes hypothesized that the two counterparties to a futures trade are not entirely symmetrical. Hedgers, say farmers (who are normally short futures), simply want a guaranteed market for their goods come harvest and are willing to provide speculators with the extra return necessary to induce them to enter into a long futures position. Farmers create this inducement by setting the current price of a futures contract a little bit below the expected spot price upon delivery, thus providing speculators with a promise of extra capital returns, or a risk premium. That's why Keynes said that futures markets are normally backwardated.

Options writers who desire the comforts of liquidity are playing the same game as farmers who desire a guaranteed price. They are inducing counterparties to take the other side of the deal, in this case the liquid one, by pricing liquid options more advantageously than illiquid but otherwise identical options. And while I don't know the peculiarities of the various counterparties to an inflation swap, I don't see why the same logic that applies to options wouldn't apply to swaps.

So returning to the main thread of this post, just as the signals given off by TIPS spreads are beset by interference arising from liquidity phenomena, the signals given off by inflation swaps are also corrupted. A widening in inflation swap spreads could be due to changing liquidity preference among a certain class of swap counterparties, not to any underlying change in inflation expectations. Its not a clear cut world.

What about the most holy of signals given off by derivative markets: the odds of default as implied by credit default swap spreads? A CDS is supposed to indicate the pure credit risk premium on an underlying security. But if the marginal counterparty on one side of a credit default swap deal is typically more interested in liquidity than the other counterparty, then CDS prices will include a liquidity component. According to the paper behind the following links ( pdf | RePEc ), it is the sellers of credit default swaps, not the buyers, who typically earn compensation for liquidity, the theory being that sellers are long-term players with more wealth than buyers. The paper's conclusion is that CDS spreads cannot be used as frictionless measures of default risk.

Liquidity is like static, it blurs the picture. The clarity of the indicators mentioned in this post—Bernanke & Summers' real interest rates, stock market price earnings ratios, inflation expectations implied by both TIPS and swap markets, and finally the odds of default implied in corporate default swap spreads—are all contaminated by liquidity premia that vary in size over time. Models created by both economists and financial analysts contain abstract variables that map to these external data sources. I doubt that this data is irrevocably damaged by liquidity, but it may be warped enough that we should be wary about drawing strong conclusions from models that depend on them as input.

Before I slide too far into economic nihilism, there may be a way to resuscitate the purity of these indicators. If we can calculate the precise size of liquidity premia in the various markets mentioned above, then we can clean up the real signals these markets give off by removing the liquidity static.

One way to go about calculating the size of a liquidity premium is by polling the owners of a given security how much they must be compensated for doing without the benefits of that security's liquidity for a period of time. Symmetrically, a potential owner of that security's liquidity is queried to determine how much they are willing to pay to own those services. The price at which these two meet represents the pure liquidity premium. Problem solved. We can now get a pure real interest rate, a precise measure of inflation expectations, a true measure of credit default odds, or a liquidity-adjusted price-to-earnings multiple.

Unfortunately, its not that easy. The only way to properly discover the price at which a buyer and seller of a particular instrument's liquidity services will meet is by fashioning a financial contract between them,  a financial derivative. These derivatives will trade in a market for liquidity or 'moneyness' that might look something like this. And therein lies the paradox. Much like the option and CDS of our previous example, this new derivative will itself be characterized by its own liquidity premium, thus impairing its ability to provide a clean measure of the original instrument's liquidity premium. We could fashion a second derivative contract to measure the liquidity premium of the first derivative contract, but that too will be compromised by its own liquidity premium, taking us down into an infinite loop of imprecision.

So... back to economic nihilism. Either that or a more healthy skepticism of those who confidently declare the economy to be in stagnation or the stock market to be a bubble. After all, there's a lot of static out there.

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Note: David Beckworth has also written about the difficulties of using bond yields as indicators of secular stagnation. (1)(2)(3). And now Nick Rowe has a post on secular stagnation and liquidity.

The bond-stock conundrum

Here's a conundrum. Many commentators have been trying to puzzle out why stocks have been continually hitting new highs at the same time that bond yields have been hitting new lows. See here, here, here, and here. On the surface, equity markets and bond markets seem to be saying two different things about the future. Stronger equities indicate a bright future while rising bond prices (and falling yields) portend a bleak one. Since these two predictions can't both be right, either the bond market or the stock market is terribly wrong. It's the I'm with stupid theory of the bond and equity bull markets.

I hope to show in this post that investor stupidity isn't the only way to explain today's concurrent bull market pattern. Improvements in financial market liquidity and declining expectations surrounding the pace of consumer price inflation can both account for why stocks and equities are moving higher together. More on these two factors later.

1. I'm with stupid

The I'm with stupid view goes something like this...

If investors expect strong real growth for the next few decades, a new bond issue has to provide a competitive coupon in order to attract capital. Soon after the bond is issued, economic growth stagnates and the economy's expected real rate of return falls. The bond's coupon, originally rated for a much healthier economy, has become too good for the new slow-growth environment. The price of the bond has to rise relative to its face value (thus counterbalancing the juicy coupon with a guaranteed capital loss) so that its overall rate of return falls to a level commensurate with the economy's lower real rate of return. That's why rising bond prices are often a sign of a bleaker future.

As for equities, that same decline in the real rate of return will result in a fall in prices. A stock is a claim on whatever profits remain after interest, and lower real growth means a smaller remainder. No wonder then that a number of investment commentators believe that the modern rise of stock and bond prices requires one set of investors to be acting irrationally; after all, things can't be simultaneously better and worse off in the future. Either that or arbitrage between the two markets is simply impossible, say because large actors like the Fed are rigging the market. Whatever the case, concurrent bull markets implies a giant market inefficiency, as Diego Espinosa has described it.

Massive inefficiency isn't a very satisfying theory for the twin rises in bond and stock markets. Thankfully, we don't need to resort to changes in real growth rates to explain securities price changes. Let's explore two other factors that could be driving the concurrent bull market pattern:

2. Falling inflationary expectations and concurrent bull markets

Assume that the real growth rate is constant over time but inflation expectations decline. The real value of all flows of coupon payments from existing bonds are suddenly more valuable, causing a one-time jump in bond prices. If inflation expectations consistently fall over time, then a bull trend in bond prices will emerge. This is standard stuff.

And stocks? What many people don't realize is that those same declining inflation expectations will set off a bull market in equities as well. The general view is that a firm's bottom line waxes or wanes at the same pace as inflation, the result being that real stock returns are invariant to inflation. Corporate shares are supposed to be hedges against inflation.

This is (almost always) wrong, a point I've made before (here and here). Let me take another stab at it. In short, thanks to the interaction between historical cost accounting and the way taxes are collected, rising inflation expectations will boost a firm's real future tax burden, reducing real cash flows and therefore stock prices. Falling expectations about inflation act like a tax cut, increasing real cash flows and stock prices.

For folks who want to work through the logic, what follows is a numerical example. Take a very simple firm which incorporates itself, buys inventory and a machine with the cash raised, operates for four years, and dissolves itself. At the end of each year it pays out all the cash it has earned to its shareholders. At the outset, the company buys 40 unfinished widgets for $60 each. Over the course of its life, it expects to process 10 widgets a year and sell the finished product at a real price of $100. In order to process the unfinished widgets, it buys a widget upgrader for $500. The upgrader is used up, or depreciated, at a rate of $125 year so that it will be useless after year four. Since the company will have also depleted its inventory of unfinished widgets by that time, it has nothing left over after the fourth year.

The first table shows the anticipated cash flows that will be paid to shareholders after taxes have been rendered to the tax authority, assuming 0% inflation over the course of four years. The cash amounts to an even $876.25 a year.

Let's boost the expected inflation rate to 1% (see table below). The real value of cash flows starts out at $876.25 in year one but steadily declines, hitting $866.66 by year four. Shareholder get less real cash flows than they did in a stable inflation environment.

On the other hand, if we ratchet down expected inflation to -1%, the real value of cash flows starts out at $876.50 in the first year but climbs to $886.24 by the end of year four. Shareholders enjoy a larger real flow cash payments than they did in either the stable or the rising expected inflation environments. If cash dividends are immediately spent on consumption, this means that shareholders enjoy the greatest flow of consumption when inflation expectations are falling.

A reduction in expected inflation will cause a one-time jump in our company's share price. If these reductions in expected inflation occur consistently over time, we get a series of jumps in the company's share price, or a bull market.

The core intuition behind this result is that under historical cost accounting, a company's cost of goods sold and its depreciation expenses are both fixed in time. Cost of goods sold is valued on a first-in-first out basis, which means the price of the oldest good is used to value unit costs (in our case, $60), while depreciation is calculated as a fixed percentage of a machine's original purchase price. When inflation is stable, this is unimportant. But once expected inflation rises, the firm's costs grow stale and can no longer keep up with its anticipated revenues, the result being artificially higher pre-tax accounting profits and a larger tax bill. These bloated future tax bills drain cash from the firm, resulting in lower expected cash payouts to shareholders over the life of the firm.

When expected inflation falls, the firm's anticipated revenues shrink relative to its costs, the result being lower future pre-tax profits and a lighter tax bill. Less cash filters out of the firm, leaving more cash in the kitty for shareholders to enjoy at the end of each year.

The table below shows how our firm's real tax bill varies across each of these scenarios:

So a reduction in expected inflation is (almost always) good for equity prices as it amounts to a tax cut. Why have I inserted a caveat? When a company is indebted, lower-than-expected inflation will increase the real burden of that debt. If its debt load is heavy, the debt effect may outweigh the combined effects of cost of goods sold and depreciation. One reason why falling inflation expectations in Japan during the 1990s and 2000s didn't result in an equity boom is that Japanese companies tend to be far more indebted than companies in the rest of the world. (This may also explain why Japanese stocks outperformed U.S. stocks during the inflationary 1970s.) For most of the world's markets a reduction in expectations surrounding the rate of inflation is an ideal situation for equities.*

What do we know about the actual shape of inflation expectations? In general people have been marking their expectations downwards since the early 1980s, a trend that has been amplified since the credit crisis as central banks around the developed world have consistently undershot their inflation targets. We thus have the underpinnings for a concurrent bull market in stocks and bonds, driven by falling inflation expectations.

3. Liquidity and the concurrent bull market pattern

Let's move on to our second factor. Assuming that the real growth rate and expected inflation both stay constant, we can also generate concurrent bull markets in stocks and bonds by simultaneously improving their liquidity. Innovations in market infrastructure over the years have made it easier to buy and sell financial assets. Investors can increasingly use financial assets as media of exchange, swapping them directly for other financial assets rather than having to go through deposits as an intervening medium. Think buzz words like re-hypothecation and collateral chains.

As financial assets become more liquid, a larger portion of their overall return comes in the form of a non-pecuniary liquidity yield. All things staying the same, investors must cough up a larger premium in order to enjoy this liquidity-augmented return, resulting in a one time jump in asset prices. Consistent improvements to liquidity will result in a step-wise asset bull market.

I've written here about the ongoing liquidity enhancements in equity markets, and speculated here that thirty-year bull market is bonds is (partly) a function of improved bond liquidity. In the same vein, Frances Coppola once penned an article noting that when everything becomes highly liquid, the yield curve is flat, reducing returns across all classes of financial assets (a flattening of the yield curve implies a jump in the price of long term bonds).

While I think that liquidity-improving innovations in market technology and declining inflation expectations can explain a good chunk of the stock bull market, I don't think they can't quite explain as much of the secular rise in bond prices. After all, market interest rates haven't just plunged. In many cases both nominal and real bond interest rates have gone negative.

We can salvage this problem by resorting to another liquidity-based explanation for why bond investors are willing to accept negative returns. Government bonds provide a unique range of liquidity services in their role as a financial media of exchange, a role that cannot be replicated by central bank reserves or any other medium of exchange. Reserves, after all, can only be held by banks, and corporate bonds aren't safe enough to serve as universally-accepted collateral. However, governments have gone into austerity mode, reducing the flow rate of bonds coming onto the market. At the same time, central banks are buying up and removing government bonds from circulation. As a result, the supply of unique liquidity services provided by bonds is growing increasingly scarce, forcing investors to bid up the price of these services. Liquidity premia are high. So a negative real return on bonds may be a reflection of the the hidden fee that bond investors are willing to pay to own a government bond's flow of liquidity returns. I've written about this here.

In sum, the I'm with stupid theory, with its implication of massive inefficiencies, shouldn't be our only theory for concurrent bull markets. Asset prices move for many reasons, not just changes in expected real growth. Bond and equity investors may be reacting non-stupidly to shifting liquidity patterns and declining inflation expectations, the result being a steady bidding up of the prices of both assets.

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*If you are interested in the difference between Japan and the rest of the world, here are some papers worth investigating: 

The Taxation of Income from Capital in Japan, Kikutani and Tachibanaki (pdf)
The Cost of Capital in the U.S. and Japan: A Comparison, Ando and Auerbach (pdf)
Are Japanes Stock Prices to High. French and Poterba (pdf)

Sign Wars

Does a lowering of a central bank's interest rates create inflation or deflation? Dubbed the 'Sign Wars' by Nick Rowe, this has been a recurring debate in the economics blogosphere since at least as far back as 2010.

The conventional view of interest rate policy is that if a central bank keeps its interest rate too low, the inflation rate will steadily spiral higher. Imagine a cylinder resting on a flat plane. Tilt the plane in one direction —a motif to explain a change in interest rates—and the cylinder, or the price level, will perpetually roll in the opposite direction, at least until the plane's tilt (i.e. the interest rate) has been shifted enough in a compensatory way to halt the cylinder's roll. Without a counter-balancing shift, we get hyperinflation in one direction, or hyperdeflation in the other.

The heretical view, dubbed the Neo-Fisherian view by Noah Smith (and having nothing to do with Irving Fisher), is that in response to a tilt in the plane, the cylinder rolls... but uphill. Specifically, if the interest rate is set too low, the inflation rate will jump either instantaneously or more slowly. But after that, a steady deflation will set in, even without the help of a counter-balancing shift in the interest rate. We get neither hyperinflation nor hyperdeflation. (John Cochrane provides a great introduction to this viewpoint).

Many pixels have already been displayed on this subject, about the only value I can add is to translate a jargon-heavy academic debate into a more finance-friendly way of thinking. Let's approach the problem as an exercise in security analysis.

First, we'll have to take a detour through the bond market, then we'll return to money. Consider what happens if IBM announces that its 10-year bond will forever cease to pay interest, or a coupon. The price of the bond will quickly plunge. But not forever, nor to zero. At some much lower price, value investors will bid for the bond because they expect its price to appreciate at a rate that is competitive with other assets in the economy. These expectations will be motivated by the fact that despite the lack of coupon payments, the bond still has some residual value; specifically, IBM promises a return of principal on the bond's tenth year.

Now there's nothing controversial in what I just said, but note that we've arrived at the 'heretical' result here. A sudden setting of the interest rate at zero results in a rapid dose of inflation (a fall in the bond's purchasing power) as investors bid down the bond's price, followed by deflation (a steady expected rise in its value over the next ten years until payout) as its residual value kicks in. The bond's price does not "roll" forever down the tilted plane.

Now let's imagine an IBM-issued perpetual bond. A perpetual bond has no maturity date which means that the investor never gets their principle back. Perpetuals are not make-believe financial instruments. The most famous example of perpetual debt is the British consol. A number of these bonds float around to this day after having been issued to help pay for WWI. When our IBM perpetual bond ceases to pay interest its price will quickly plunge, just like a normal bond. But it's price won't fall to zero. At some very low level, value investors will line up to buy the bond because its price is expected to rise at a competitive rate. What drives this expectation? Though the bond promises neither a return of principal nor interest payments, it still offers a fixed residual claim on a firm's assets come bankruptcy, windup, or a takeover. This gives value investors a focal point on which they can price the instrument.

So with a non-interest paying perpetual bond, we still get the heretical result. In response to a plunge in rates, we eventually get long term deflation, or a rise in the perpetual's price, but only after an initial steep fall.  As before, the bond's price does not fall forever.

Now let's bring this back to money. Think of a central bank liability as a highly-liquid perpetual bond (a point I've made before). If a central banker decides to set the interest rate on central bank liabilities at zero forever, then the purchasing power of those liabilities will rapidly decline, much like how the cylinder rolls down the plane in the standard view. However, once investors see a profit opportunity in holding those liabilities due to some remaining residual value, that downward movement will be halted... and then it will start to roll uphill. Once again we get the heretical result.

The residual claim that tempts fundamental investors to step in and anchor the price of a 0% yielding central bank liability could be some perceived fixed claim on a central bank's assets upon the bank's future dissolution, the same feature that anchored our IBM perpetual. Or it could be a promise on the part of the government to buy those liabilities back in the future with some real quantity of resources.

However, if central bank liabilities don't offer any residual value whatsoever, then we get the conventional result. The moment that the central bank ceases to pay interest, the purchasing power of a central bank liability declines...forever. Absent some residual claim, no value investor will ever step in and set a floor. In the same way, should an IBM perpetual bond cease to pay interest and it also had all its residual claims on IBM's assets stripped away, value investors would never touch it, no matter how low it fell.

So does central bank money boast a residual claim on the issuer? Or does it lack this residual claim? The option you choose results in a heretical result or a conventional result.

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What does the data tell us, specifically the many cases of hyperinflation? As David Beckworth has pointed out, the conventional explanation has no difficulties explaining the Weimar hyperinflation; the Reichsbank kept the interest rate on marks fixed at very low levels between 1921 and 1923 so that the price level spiraled ever upwards. Heretics seem to have difficulties with Weimar—the deflation they predict never set in.

Here's one way to get a heretical explanation of the Wiemar inflation. Let's return to our analogy with bonds. What would it take for the price of an IBM perpetual bond to collapse over a period of several years, even as its coupon rate remained constant? For that to happen, the quality of the bond's perceived residual value would have to be consistently deteriorating. Say IBM management invested in a series of increasingly dumb ventures, or it faced a string of unbeatable new competitors entering its markets. Each hit to potential residual value would cause fundamental investors to mark down IBM's bond price, even though the bond's coupon remained fixed.

Now assuming that German marks were like IBM perpetual bonds, it could be that from 1921 to 1923, investors consistently downgraded the value of the residual fixed claim that marks had upon the Reichsbank's assets. Alternatively, perhaps the market consistently reduced its appraisal of the government's ability to buy marks back with real resources. Either assumption would have created a consistent decline in the purchasing power of marks while the interest rate paid on marks stayed constant.

Compounding each hit to residual value would have been a decline in the mark's liquidity premium. When the price of a highly-liquid item begins to fluctuate, people ditch that item for competing liquid items with more stable values. With less people dealing in that item, it becomes less liquid, which reduces the liquidity premium it previously enjoyed. This causes the item's purchasing power to fall even more, forcing people to once again turn to alternatives, thus making it less liquid and igniting another round of cuts to its liquidity premium and therefore its price, etcetera etcetera. In Weimar's case, marks would have been increasingly replaced by dollars and notgeld.

So consistent declines in the mark's perceived residual value, twinned with a shrinking in its liquidity premium, might have been capable of creating a Weimar-like inflation, all while the Reichsbank kept its interest rate constant.

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That's not to say that central bank liabilities do have a residual value and that the heretical result is necessarily the right one. Both possibilities make sense, and both can explain hyperinflations. But to determine which is right, we need to go in and do some gritty security analysis to isolate whether central bank money possesses a fixed residual claim on either central bank assets or future government resources. Parsing the fine print in central bank acts and government documents to tease out this data is the task of lawyers, bankers, historians, fixed income analysts, and accountants. And they would have to do a separate analysis for each of the world's 150 or so central banks and currencies, since each central bank has its own unique constituting documents. In the end we might find that some currencies are conventional and others are heretic, so that some central banks should be running conventional monetary policies, and others heretic policies. 

In closing, a few links. I've taken a shot at a security analysis of central bank liabilities in a number of posts (here | here | here), but I don't think that's the final word. And if you're curious how the Weimar inflation ended, go here.