Using restricted stock studies to measure liquidity

I like to say that everything is money, which is just another way of saying that all goods are liquid to some degree or other. Whether it be a house, a banknote, or ice cream, each of these items carries a liquidity premium. How large are these liquidity premia? It's difficult to get good measurements, but there are a few venues that offer a glimpse of this rare beast. One of them is equity markets. More specifically, we can use restricted stock studies to tease out liquidity premia.

Imagine that your shares in Microsoft, normally so easily exchanged on various stock markets like the New York Stock exchange or NASDAQ, were restricted for a period of time in a way that prevented you from trading them. Apart from this impairment, your illiquid Microsoft shares are exactly like any other Microsoft share: they provide you with a dividend, voting power, and a contingent claim on firm assets should Microsoft decide to wind up the business. The price you'd be willing to pay to own these rather unique shares would reflect their lack of liquidity. Or, put differently, the difference between the price of regular Microsoft shares and restricted Microsoft shares would precisely represent the value that you ascribe to the liquidity of regular Microsoft shares, or their liquidity premium.

Luckily for us, the practice of placing restricted stock, or unregistered stock, with investors provides an opportunity to measure this  difference. When you buy a blue chip stock on the NYSE you're purchasing registered stock—the issuer has registered the original offering of securities with the SEC. This is an expensive and time consuming process involving all sorts of lawyers and fees. If the issuer wishes to avoid these fees, it can choose to forgo registration and issue what are called unregistered shares, as long as the issue is presented to private accredited investors and not to the general public. However, securities law stipulates that investors who receive unregistered stock must accept a number of restrictions, all of which limit the liquidity of unregistered stock. In general, laws proscribe a holding period over which the owner of restricted stock cannot sell in public markets. After the holding period expires, unregistered securities can be sold in public transactions but only by complying with certain “dribble out,” or volume limit, provisions that may impede a stockholder from liquidating a position sufficiently fast. (For instance, an owner of restricted stock might not be able to sell more than x% of the stocks monthly trading volume).

Restricted stock studies measure the difference between the price at which a company has issued restricted stock and the publicly-traded price of that same company's non-restricted, or registered, stock . This difference represents the liquidity premium on the firm's registered stock; the very same liquidity that restricted stock owner forgo.

The chart below provides a partial listing of restricted stock studies and the average discount to market value displayed by restricted stock in each:

Source

The earliest restricted stock studies show a ~30% difference between the price of restricted stock and its publicly-traded equivalent. This implies that the liquidity premium over the combination of the holding period (initially set at two years) and dribbling out period on an average stock amounted to about 30 cents per each dollar of stock. That number doesn't include the value of liquidity after the holding period has expired and dribbling out rules have ceased to have a significant effect; if the entire lifespan of a stock were incorporated, we can imagine that 40-50 cents of each dollar worth of a typical stock might be due to liquidity. That's quite a lot!

As the chart shows, over time studies have found that the measured gap between the price of restricted shares and regular publicly-traded shares has steadily shrunk. This is due in part to changes in SEC rules concerning the sales of restricted shares. Owners of restricted shares initially faced a 2-year holding period, but this was reduced to 1-year in 1997 and then six months in 2008. Non affiliate owners (those who are not insiders and don't own controlling blocks of stock) initially faced an indefinite dribbling out period (ie. volume limitations) but this was reduced to 3 years of volume limitations in 1983, 2 years in 1997, and just six months in 2008. In 1990, something called the “tacking” rule was changed. Prior to this amendment, any sale of unregistered stock, even in privately negotiated transactions, would result in the required holding period restarting, a large inconvenience to the buyer. The 1990 amendment allowed non-affiliate purchasers to “tack” the previous owners’ holding period to their own holding period. Because all of these rule changes improved the liquidity of restricted shares, over time investors have needed less of an inducement to hold restricted stock relative to regular shares—thus the downward trend in average discount size.

Why so many restricted stock studies? In the field of business appraisal, evaluators are often called upon to estimate the values of illiquid assets in estates and divorce proceedings, typically small privately held company shares. One way to go about this is to apply an earnings multiple from a comparable publicly- traded companies trade to the privately held firm's earnings. But this assumes an "as if marketable" value for what is actually a very illiquid asset. A discount for lack of marketability (DLOM) must be applied to correct for this problem. A DLOM is the amount an appraiser deducts from the value of an ownership interest to reflect the relative absence of marketability. It will often be the single largest value adjustment than an appraiser will have to make. The results must be defensible in a court of law, necessitating a well structured argument backed by data. Restricted stock studies offer a way for an appraiser at a reasonable DLOM. Of course, an owner of an asset may want as large a discount as possible, usually for tax reasons. They therefore will be tempted to use a study with the highest discount, perhaps an older study that assumes 2-year holding periods, even though six month holding periods now prevail. The IRS has made efforts to shift the profession to using smaller DLOMs, for obvious reasons.

A major weakness of restricted stock studies is the assumption that the entire price gap between a restricted stock price and its publicly traded counterpart can be traced to the liquidity factor. But this isn't necessarily the case. Companies will often artificially underprice private offerings as a way to pay for services rendered (say to suppliers), to reward insiders, or to curry favor. This is the barter function of stock. We need to separate the portion of a restricted share discount that arises for liquidity reasons from that which arises due to this barter function. One way to do so is to compare the prices at which private offerings of restricted stock are carried out relative to private offerings of regular stock. Since both forms of private stock issuance are equally likely to be used for barter, the barter function can be canceled out, thereby leaving liquidity as the only explanation for the gap between the prices of restricted and non-restricted private stock issues.

Wruck (1989) found that the difference in average discounts between the restricted share offerings in her study and registered share offerings was 17.6%, while the difference in median discounts was 10.4%.  Bajaj et al found that private issues of registered shares were conducted at average discounts of 14.04% to their publicly traded price, while the average discount on placements of unregistered shares were conducted at 28.13% to their public price, 14.09% higher than the average discount on registered placements. This puts stock liquidity premiums at about 10-15 cents on the dollar, far below levels found in other studies.

Nevertheless, the fact that around 10 cents of each $1 worth of Microsoft stock can be attributed to the value that the market ascribes to one or two years of liquidity is still a significant number. And remember that restricted stock studies don't measure the long-term liquidity factor, only the value of liquidity foregone over the holding period and a dribbling out period. If the studies did isolate longer term measures of liquidity, we might find that 15-20 cents of each $1 of Microsoft stock is comprised of liquidity value.

All of this means that a share of Microsoft isn't a mere financial asset—a portion of any Microsoft share is providing its owner with a stream of consumable services, much like one's lawyer or neighborhood policeman or pair of shoes provides a service. If some sort of shock were to reduce the liquidity that Microsoft provides, then everyone would be made worse off. (All the more reason to adopt liquidity-adjusted equity analysis). Of course, all of this applies just as well to other securities like bonds and derivatives. And it also applies to consumer and capital goods, houses, land, and collectibles. Everything carries a degree of liquidity, and if we could compare the price of that asset to some illiquid copy of itself (restricted houses, restricted land, restricted paintings) then we'd have a pretty good idea for how much value the market ascribes to that liquidity.

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Other links worth exploring:

Blogs
Using Illiquidity Premiums on the Risk Free Asset to Measure Illiquidity Discounts by Joshua B. Angell

Papers
Revisiting the Illiquidity Discount for Private Companies by Robert Comment
Determining Discounts for Lack of Marketability: A Companion Guide to The FMV Restricted Stock Study
The Discount for Lack of Marketability by Reilly and Rotkowski
Market Discounts and Shareholder Gains for Placing Equity Privately by Hertzel and Smith (RePEc)

Fedwire transactions and PT vs PY

Milton Friedman's alleged license plate, showing the equation of exchange

The excruciatingly large revisions that U.S. first quarter GDP growth underwent from the BEA's advance estimate (+0.1%, April 30, 2014) to its preliminary estimate (-1.0%, May 29, 2014) and then its final estimate (-2.9%, June 25m, 2014) left me scratching my head. Isn't there a more timely and accurate measure of spending in an economy?

One interesting set of data I like to follow is the Fedwire Fund Service's monthly, quarterly, and yearly statistics. Fedwire, a real time gross settlement interbank payment mechanism run by the Federal Reserve*, is probably the most important financial utility in the U.S., if not the world. Member banks initiate Fedwire payments on their own behalf or on behalf of their clients using the Fedwire common currency: Fed-issued reserves. Whenever you wire a payment to another bank in order to settle a purchase, you're using Fedwire. Since a large percentage of U.S. spending is transacted via Fedwire, why not use this transactions data as a proxy for U.S. spending?

Some might say that using Fedwire data is an old-fashioned approach to measuring spending. Irving Fisher wrote out one of the earliest versions of the equation of exchange, MV=PT, where T measures the "volume of trade" or "real expenditure" and P is the price at which this trade is conducted. Combined together, PT amounts to the sum of all exchanges in an economy. More specifically, Fisher's T included all exchanges of goods where his chosen meaning for a good was broadly defined as any sort of wealth or property. That's a pretty wide net, including everything from lettuce to publicly-traded equities to land.

Practically speaking, Fisher wrote that it was "utterly impossible to secure data for all exchanges" and therefore his statistical approximation of T was limited to the quantities of trade in 44 articles of internal commerce (including pig iron, rice, hogs, boots & shoes), 23 articles of import and 25 of export, sales of equities, railroad freight carried, and letters through the post office. This mishmash of items included everything from wholesale goods to securities to and consumption goods. Using Fedwire transactions to track total spending is very much in the spirit of Fisher, since any sort of transaction can be conducted through the interbank payments system, including financial transactions.

Nowadays we are no longer taught the Fisherian transactions version of the equation of exchange MV=PT but rather the income approach, or MV=PY. What is the difference between the two? Y is a much smaller number than T. This is because it represents GDP, or only those goods and services that are qualified as final, where "final" indicates items bought by a final user. T, on the other hand, includes not only the set of final goods and services Y but also all spending on second hand goods, stocks and bonds, existing homes, transfer payments, and more. Whereas GDP measures final goods in order to avoid double counting, T measures final and intermediate goods, thus counting the same good twice, thrice, or even more if the good changes hands more often than that.

A good illustration of the difference in size between Y and T is to chart them. The total yearly value of Fedwire transactions, which are about as good a measure of PT that we have (but by no means perfect), exceeds nominal GDP (or PY) by a factor of 40 or so, as the chart below shows. Specifically, nominal GDP came in at $17 trillion or so in 2013 whereas the total value of Fedwire transactions clocked in at $713 trillion.

So why do we focus these days on PY and not Fisher's PT? We can find some clues by progressing a little further through the history of economic thought to John Keynes (is it a travesty to omit his middle name?). In his Treatise on Money, Keynes was unimpressed with Fisher's cash transactions standard, as he referred to it, because PT failed to capture the most important human activities:

Human effort and human consumption are the ultimate matters from which alone economic transactions are capable of deriving any significant; and all other forms of expenditure only acquire importance from their having some relationship, sooner or later, to the efforts of producers or to the expenditure of consumers.

Keynes proposed to "break away from the traditional method" of tabulating the total quantity of money "irrespective of the purposes on which it was employed" and focus instead on the narrow range of trade in current consumption and investment output. Keynes's PY measure (the actual variables he chose was PO where O is current output) would be a "more powerful instrument of analysis than their predecessor, when we are considering what kind of monetary and business events will produce what kind of consequences."

And later down the line, Milton Friedman, who renewed the quantity theory tradition in the 1950s and 60s, had this to say about the shift from PT to PY:

Despite the large amount of empirical work done on the transactions equations, notably by Irving Fisher and Carl Snyder ( Fisher 1911 pp 280-318, Fisher 1919, Snyder 1934), the ambiguity of the concept of "transactions" and the "general price level", particularly those arising from the mixture of current and capital transactions—were never satisfactorily resolved. The more recent development of national income accounting has stressed income transactions rather than gross transactions and has explicitly and satisfactorily dealt with the conceptual and statistical problems of distinguishing between changes in prices and changes in quantities. As a result, the quantity theory has more recently tended to be expressed in terms of income rather than of transactions

So there are  evidently problems with PT, but what are the advantages? Assuming we use Fedwire transactions as the proxy for PT (and again, Fedwire is by no means a perfect measure of T, as I'll go on to show later) the data is immediate and unambiguous. It doesn't require hordes of government statisticians to laboriously compile, recompile, and check, but arises from the regular functioning of Fedwire payments mechanism. There are no revisions to the data after the fact. And rather than being limited to periods of time of a month or a quarter, there's no reason we couldn't see Fedwire data on a weekly, daily, or even real time level of granularity if the Fed chose to publish it.

Even Keynes granted the advantages of PT data when he wrote that the "figures are available promptly without the necessity for any special calculation." In Volume II of his Treatise, he took U.S. "bank clearings" data (presumably Fedwire data), and tried to remove those transactions arising from financial activity by excluding New York City, the nation's chief financial centre, thus arriving at a measure of final spending that came closer to PY.

What are the other advantages of PT? While PT counts second-hand and existing sales, might that not be a good thing? Nick Rowe, writing in favour of PT, once made the point that it's "not just new stuff that is harder to sell in a recession; it's old stuff too. New cars and old cars. New houses and old houses. New paintings and old paintings. New furniture and antique furniture. New machine tools and old machine tools. New land and old land." As for the inclusion of financial transactions, anyone who thinks asset price inflation or deflation is an important property of the economy (Austrians and Austrian fellow travelers no doubt) may prefer PT over PY since the latter is mute on the subject.

I'd be interested to hear in the comments the relative merits and demerits of PY and PT. Why don't the CNBC talking heads ever mention Fedwire, whereas they can spend hours debating GDP? Why target nominal GDP, or PY, when we can target PT?

For now, let's explore the Fedwire data a bit more. In the figure below I've charted the total value of Fedwire transactions (PT) for each quarter going back to 1992. I've overlaid nominal GDP (PY) on top of that and set the initial value of each to 100 for the sake of comparison.

It's evident that the relative value of Fedwire transactions has been growing faster than nominal GDP. However, the financial crisis put a far bigger dent in PT than it did PY. Only in the last two quarters has PT been able to break to new levels whereas nominal GDP surpassed its 2008 peak by the second quarter of 2010. Is the financial sector dragging down PT? Or maybe people are spending less on used goods and/or existing homes?

Fedwire data is further split into price and quantity data. Below I've plotted the number of transactions, or T, completed on Fedwire each quarter. On top of that I've overlaid real GDP, or Y. The initial value of real GDP has been set to 16.6 million, or the number of transactions completed on Fedwire in 1992.

After growing at a relatively fast rate until 2007, the number of transactions T being carried out on Fedwire continues to stagnate below peak levels. In fact, last quarter represented the lowest number of transactions since the first quarter of 2012, a decline that coincided with the atrocious first quarter GDP numbers.

Finally, below I've plotted the average value of Fedwire transfer by quarter. On top of that I've overlaid the GDP deflator. To make comparison easier, I've taken the liberty of setting the initial value of the deflator at the 1992 opening value for Fedwire transaction size.

As the chart shows, the average size of Fedwire transfers really took off in 2007, peaked in late 2008 then stagnated until 2013, and has since re-accelerated upwards. In fact, we can attribute the entire rise in the quarterly value of transactions on Fedwire (the second chart) to the growth in transaction size, not the quantity of transactions. Fedwire data is telling us that inflation of the PT sort has finally reemerged.

A few technical notes on the Fedwire data before signing off. As I've already mentioned, Fedwire provides a less-than complete measure of PT. To begin with, it doesn't include cash transactions (GDP does, or at least those that have been reported). This gap arises for the obvious reason that cash transactions aren't conducted over Fedwire. Nor do cheque transactions appear on Fedwire, or at least they do so only indirectly. Check payments are netted against each other and canceled, with only the final amounts owed being settled between banks via Fedwire, these settlements representing just a tiny fraction of the total value of payments that have been conducted by check over any period of time.

The same goes for securities transactions. Fedwire data underestimates the true amount of financial transactions because trades are usually netted against each other by an exchange's clearing house prior to final settlement via Fedwire. The transfer of reserves that enables the system to settle represents a small percent of the total value of trades that have actually occurred.

Another limitation is that Fedwire data doesn't include wire payments that occur on competing payment systems. Fedwire isn't a monopoly, after all, and competes with CHIPS. I believe that once all CHIPS payments have been cleared, final settlement occurs via a transfer of reserves on Fedwire, but this final transfer is a fraction of the size of total CHIPS payments. And finally, payments that occur between customers of the same bank are not represented in the Fedwire data. This is because these sorts of payments can be conducted by a transfer of book entries on the bank's own balance sheet rather than requiring a transfer of reserves.

I'm sure I'm missing other reasons for why Fedwire data undershoots PT, feel free to point them out in the comments. Do Fedwire's limitations cripple its value as an indicator PT? I think there's still some value in looking at these numbers, as long as we're aware of how they might come up short.

Some links:
1. Canadian Large Value Transfer System Data, the Canadian equivalent to Fedwire
2. A paper exploring UK CHAPS data,the British equivalent to Fedwire: Income and Transactions Velocities in the UK

* 'Real time' means that payments are immediate and not subject to delay, while 'gross settlement' indicates that payments are not grouped together for processing but submitted individually upon being entered. Fedwire gets its name from the beginning of the last century, when payments were carried out over the wires, or the telegraph system. 

To recapitulate...

I'm going on holiday and don't have enough time to write anything new. At the risk of being repetitive, here's a recapitulation of what is one of this blog's major themes: the idea of moneyness. Most of the component parts are spread out over a couple of dozen posts written over many months—here I'll try and piece the whole quilt together in one spot.

Money vs moneyness

The initial point comes from one of my first posts (as well as a later one). There are two ways of thinking about monetary phenomena. The standard way is to draw a line between all things in an economy that are "money" and all those things which are not. Deposits typically go in the money bin, widgets go in the non-money bin, dollar bills go in the money bin, labour goes in the non-money bin and so forth.

The second approach, the one this blog takes, begins with the idea that all things in an economy are money-like. The line we are interested in here is the extent to which the value of each thing is determined by its money-like qualities, or its moneyness, versus the degree to which its value is determined by its non-money like qualities, say its ability to be consumed. We might say that deposits have more moneyness than labour, and labour is more money-like than a second-hand speedo and so forth.

(This second approach isn't without precedent, see Keynes, Hayek, and Friedman.)

Why is moneyness a valuable attribute?

It's all in this post, but here's a quick recap. The greater an item's degree of moneyness, the easier it is for its owner to mobilize that item in trade should some unanticipated eventuality arise. This quality of being easily liquidated provides the owner of that asset with a flow of uncertainty-alleviating services over time, or insurance.

Because moneyness, like insurance, is a valuable property, people must choose on the margin whether to sacrifice moneyness for either consumption or interest. In deciding whether to trade an item with high moneyness for a consumption good with low moneyness, an individual must weigh the present value of the flow of uncertainty-shielding services provided by the former against the one-time zing provided by the latter. In considering a potential exchange between an item with high moneyness and an illiquid interest-yielding asset, the tradeoff is between uncertainty-shielding services and an ongoing pecuniary return.

The supply of moneyness

Moneyness is a valuable good, but it also must be produced at a cost.

Certain characteristics of a good allow it to become more money-like, including durability, verifiability, fungibility, and portability. Network effects may promote an item's degree of moneyness.

The moneyness of an object can be improved by manufacturing these characteristics. Gold, for instance, is rendered more money-like by incurring coinage costs in order to promote verifiability. Adding copper to a gold coin increases its durability. Network effects can be harnessed through marketing. As long as the expected returns of boosting an object's moneyness are higher than the costs, liquidity providers will happily bear the costs.

Whereas only banks and central banks create money, the cast of characteristics involved in supplying moneyness is quite varied. Investor relations teams manufacture it as do hedge fund managers like Cliff Asness and roll-ups like Valeant Pharmaceuticals.

Difficulties in measuring moneyness

It's all here. To summarize, people often use bid-ask spreads and the frequency distributions of various assets in trade as a way to measure an asset's moneyness. But this comes up short. Bid-ask spreads and frequency distributions are objective measures of liquidity. We want to know the price that the market ascribes to things like tight bid ask spreads, not the bid ask spread itself. Moneyness, like value, is a subjective quality, not an objective one.

The other problem is that the value of a good is usually derived from not only its moneyness, but also its 1) consumability and 2) its ability to yield pecuniary returns (like interest and capital gains). Stripping out the moneyness component from these others poses some thorny problems.

Here's how to do it

As I pointed out in this post, the trick is to poll people about how much they expect to be compensated if they are to forgo the ability to sell an asset for some a period of time, say one year, while still enjoying the pecuniary and consumption yields provided by that asset. The question goes something like this:

"How much would I have to pay you in order for you to relinquish all rights to trade away your holdings of asset x for one year?"

The price that an individual lists represents the value they ascribe to that asset's moneyness stripped of its other valuable attributes. It represents how much value they put on that asset's foregone bid-ask spread and other objective liquidity data.

On a larger scale, we want to create a moneyness market

The previous paragraph solves for each individual's assessment of moneyness, but we want to know the value that the market as a whole ascribes to a given asset's moneyness. In this post, I imagined what these markets would look like. We'd want to create a financial product that requires investors to set a price on how much they need to be paid if they are to relinquish the right to trade away asset x for a period of time. Buyers and sellers of these rights would establish a market price for the moneyness of all sorts of assets.

A few practical uses of moneyness and moneyness markets

Right now, equity analysts include an equity's moneyness in their valuation metrics, which is a big mistake. I go into this in plenty of detail here and here. If an analyst wants to accurately value an equity's price relative to its earnings, they need to have a measure of moneyness. That way they can strip out that part of an equity's price that is due to its moneyness and compare the non-monetary residual to earnings. A moneyness market would provide them with the missing data.

To properly value bonds and housing, we should probably do the same. See here and here.

And as I wrote here, financial assets like stocks are 2-in-1 deals meaning that you've got to buy an asset's moneyness along with its pecuniary return. Investors may prefer to have the one without the other. A moneyness market allows investors to split off and sell (or buy) each component separately, resulting in a more optimal allocation of moneyness and pecuniary returns.

Moneyness and monetary policy

Monetary policy is more of a sideline, but here are a few posts on the subject. A central bank issues liabilities with a high degree of moneyness. By increasing the quantity of outstanding liabilities, a central bank can reduce the marginal value that people are willing to pay for that moneyness, thereby lowering the purchasing power of central bank liabilities and increasing the price level. By tightening the supply of liabilities, it increases their marginal value, boosting their purchasing power and lowering the price level.

So in short, a central bank manipulates the moneyness of its own liabilities.

However, once it reduces the moneyness of its liabilities to zero across all time frames, a central bank can't create more inflation. This is the zero-lower bound from a moneyness perspective, which I go into here.

And in the future

I'm hoping to write a few posts on liquidity crisis and moneyness markets, and how moneyness markets can displace central banks as lenders of last resort (or at the very least help central banks improve).