Wednesday, April 8, 2015

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.

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.


  1. I would put this, Until we can independently price these liquidity services, the idea a stock's price embodies a varying liquidity premium is speculative at best.

    1. It's uncontroversial that stocks have liquidity premia --- the question is how big.

  2. "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 in the liquidity of TIPS relative to the liquidity of straight Treasuries."

    I think that should be "...improvement in the liquidity of TIPS..."

  3. Interesting post, thanks. Will the situation improve once we have functioning inflation prediction markets? Or would these derivatives be subject to liquidity premia effects as well (probably that would be the case)?

    1. It's very possible that the signals generated by prediction markets could be corrupted by liquidity premia. A contract generated by a prediction market is similar to a swap or an insurance contract. If the peculiarities of prediction markets are such that one set of traders concerned with liquidity usually take one side of a trade, then they will need to pay the other side for that liquidity by altering the contract's price, irrespective of their views of the prediction's outcome.

    2. See:

  4. Regarding markets for liquidity premia,

    Like the story that Steven Hawking told in the opening paragraphs of 'A Brief History of Time' :

    "It's turtles all the way down"

  5. One link from this post led to another led to another led to this:

    Maybe the price difference between stocks XYZ.A and XYZ.B can be used as a close proxy for the liquidity premium?

    1. Gaurav - Stay tuned. I plan on writing about this in an upcoming post.

  6. Sorry.

    These arguments make little sense. Liquidity analyses emerged historically to explain the willingness to hold cash.

    Cash can be thought of as having an opportunity cost, which determines the quantity demanded. The function it provides would therefore have to compensate for this opportunity cost (I am even skeptical of this because its easy for me to see cash use going to zero and therefore no stores of value whose return is strictly dominated by other like risk instruments, in which case the "historical" case in which a liquidity description is needed would disappear)

    But in your format, a 1 year treasury bond and a 2 year treasury bond would have different expected returns owing to their different liquidity. To me that makes no sense. 2 year bonds might have higher expected returns than 1 year bonds rolled over at the end of year 1, because 2 year bonds are slightly more volatile, even if they have the same liquidity (although of course there is substantial disagreement about this).

    So now lets do a thought experiment. Lets say that bonds rally owing to the liquidity premium, what does that mean? As I read Steve Williamson it means they rally such that their expected return--I guess now including term premium as one variable and liquidity as another is negative if financed at the overnight rate. Meaning once we account for the term premium, the expected return should be negative, or maybe zero. Im not sure. What is it in your case, positive? zero?

    Remember, there is a puzzle to explain in bond returns--it is not why there returns are so low, its why the forward curve almost always overstates the actual path of short rates. Thats the real puzzle. Why isnt that arbed away considering long position in government bonds can be financed at high leverage--even in highly adverse market conditions precisely owing to the "liqudity" factor (meaning the collateral value of treasuries is very high in these moments). It would seem all that is required to arb away this difference is capital. Also notice right away that the same is not true of other risky assets where financing is state dependent in the direction we would expect.