Thursday, July 31, 2014

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 stockthe 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:


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 sharesthus 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 asseta 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.

Other links worth exploring:

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

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)


  1. Fantastic survey, thank you for this.

    1. This post actually brought something very fundamental to light which I hadn't really thought to distinguish before. There are two kinds of liquidity returns: One is the liquidity premium one receives for holding a non-marketable asset. The second is outlined here, a liquidity return based off an assets marketability rising over the course of time. I think these two are deserving of different names.

    2. "One is the liquidity premium one receives for holding a non-marketable asset. "

      Do you mean a return to compensate for the asset's lack of marketability? Strictly speaking, a non-marketable asset has no liquidity premium.

    3. *The monetary premium one receives in the place of a liquidity premium. pardon.

    4. I am trying to juxtapose this to the monetary return one receives from an asset whose liquidity premium has risen.

  2. I never knew about this. Well done JP!

    When I first saw that graph, my first thought was that it correlates with nominal interest rates. But then I read your bit about the rules changing over time.

    1. Glad you like it. You're right, the graph correlates with interest rates (and inflation). There could an element of both in the discount, although for the time reason I can't puzzle out why that might be.

    2. High inflation and/or nominal interest rates mean high opportunity cost of holding money. If the cost of holding the most liquid asset goes up, that will spillover and increase demand for the next most liquid asset, and so on down the line. It steepens the whole liquidity premium curve.

    3. Simpler way of saying the same thing. The closer you are to being satiated in liquidity, the less you care about the difference between slightly more and slightly less liquid versions of the same asset.

    4. Aha, I see what you mean. The liquidity premium curve --- I like that. But does it steepen the curve or just shift it?

  3. "...all goods are liquid to some degree or other. Whether it be a house, a banknote, or ice cream..."

    I've noticed that ice cream's liquidity increases as the temperature rises.

  4. Too busy with personal stuff to continue our previous discussion on payments systems and fiat money, but here are some recent links that might interest you and other readers on the crypto-currency, finance, and payment fronts.

    Jed McCaleb's new Ripple rival, Stellar:

    Stripe founders want to make online payments as easy as embedding Youtube videos (also backing Stellar):

    Overstock investigating ways to issue a cryptosecurity via blockchain:

    This stuff is moving at warp speed and makes my head spin. There's a lot of hype that will fizzle out to nothing, but it's still a pretty exciting time.

    Peer-to-peer lending and crowdfunding are also interesting developments that have, imo, already gained more real-world traction than cryptocurrencies. Any opinion on whether they will become a big deal and democratize the financial industry?

    1. I haven't yet been able to figure out the difference between Stellar and Ripple.

    2. The main differences seem to be the target markets and overall perception. Ripple is going for the "suit" approach--targeting financial institutions and explicitly counting on XRP appreciation for profit. Stellar has a punk rock ethos--direct to the people, 95% STR giveaways, non-profit. Positioning and perception matter a lot (I mean, is there really any difference btw Coke and Pepsi, or Walmart and Target?); a lot of the BTC community felt like Ripple was a scam, but the response to Stellar seems to be more favorable.

      Ultimately, I think the competition will legitimize the pre-mined alt-coin category, which is for the best. Mining is wasteful, and I expect in 1-2 years most of the biggest coins at coinmarketcap (save BTC) will use either pre-mining or proof-of-stake. So dump LTC now!

    3. On a similar note, I think marketing gets short shrift in the monetary econ blogosphere, probably because most people aren't used to thinking about competitive monies. But it deserves more attention. For example, I think market monetarists would make a lot more political headway if they endorsed Glasner's compensated dollar plan at the end of his book and called it "the new gold standard." Even though the redemption asset doesn't have to be gold, just adding the word gold makes the plan instantly attractive to a lot of Republicans, who are the natural political allies for MM (Sumner's opinions notwithstanding). Gold is comprehensible; for most, NGDP futures are not (frankly, the median voter cannot differentiate btw NGDP and real GDP; believe me, I've tried to explain it in barroom discussions).

      In cryptocurrency, marketing and product innovation will lead to monies that can do more and more things (smart contracts, new financial products, etc). "Edible euros," so to speak.

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  6. I proofed all information can have major functions of currency.
    Your speaking "everything is money" means that too or not?
    I want to know your opinion precisely because, I want to check my proof is OK or not OK.
    You defining money and currency deferent or not?
    It is the first time to read this blog.
    I am not native speaker, so difficult to understand which order is easy to understand?

    1. Keisuke: Yes, everything is to some extent money, in that everything is liquid to some degree or other. Here is a good introduction:

      I reply here, some question.

    3. Keisuke, I looked over your blogposts. They are difficult for me to understand. In my opinion information can be traded, so information can be money to some degree or other.

  7. I thought, you are tougher debater. And expected answer my question.
    I cannot find tough debater here too.