Francis Longstaff paper


Francis Longstaff

Working Paper 20589


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October 2014

Francis A. Longstaff is with the UCLA Anderson School and the NBER, and is a consultant to Blackrock. I am grateful for helpful discussions with Maureen Chakraborty and Stephen Schurman. All errors are my responsibility. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

© 2014 by Francis Longstaff. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

Valuing Thinly-Traded Assets
Francis Longstaff
NBER Working Paper No. 20589
October 2014
JEL No. G12,G32


We model illiquidity as a restriction on the stopping rules investors can follow in selling assets, and apply this framework to the valuation of thinly-traded investments. We find that discounts for illiquidity can be surprisingly large, approaching 30 to 50 percent in some cases. Immediacy plays a unique role and is valued much more than ongoing liquidity. We show that investors in illiquid enterprises have strong incentives to increase dividends and other cash payouts, thereby introducing potential agency conflicts. We also find that illiquidity and volatility are fundamentally entangled in their effects on asset prices. This aspect may help explain why some assets are viewed as inherently more liquid than others and why liquidity concerns are heightened during financial crises.

Francis Longstaff
Anderson Graduate School of Management
110 Westwood Plaza, Box 951481
Los Angeles, CA 90095-1481
and NBER


Thinly-traded assets are often defined as investments for which there is no liquid market available. Thus, investors holding illiquid or thinly-traded assets may not be able to sell their positions for extended periods, if ever. At best, investors may only be able to sell in infrequent privately-negotiated transactions. The eco- nomics of these private transactions, however, are complicated since prospective buyers realize that they will inherit the same problem when they later want to resell the assets. Not surprisingly, sales of thinly-traded assets typically occur at prices far lower than would be the case if there was a liquid public market. The valuation of thinly-traded assets is one of the most important unresolved issues in asset pricing. One reason for this is that thinly-traded assets collectively represent a large fraction of the aggregate wealth in the economy. Key examples where investors may face long delays before being able to liquidate holdings include:

– Sole proprietorships.
– Partnerships, limited partnerships.
– Private equity and venture capital.
– Life insurance and annuities.
– Pensions and retirement assets.
– Residential and commercial real estate.
– Private placements of debt and equity.
– Distressed assets and fire sales.
– Compensation in the form of restricted options and shares.
– Investments in education and human capital.
Other examples include transactions that take public firms private such as a leveraged buyouts (LBOs) that result in residual equityholders having much less liquid positions. Many hedge funds have lock up provisions that prohibit investors from withdrawing their capital for months or even years. Investors in initial public offerings (IPOs) are often allocated shares with restrictions on reselling or “flipping” the shares.

Many insightful approaches have been us ed in the asset pricing literature to study the effects of illiquidity on security prices. Important examples include Amihud and Mendelson (1986), Constantinides (1986), Vayanos (1998), Vayanos and Vila (1999), Acharya and Pedersen (2005) and others who model the relation between asset prices and transaction co sts. Duffie, Garleanu, and Pedersen (2005, 2007) study the role that search costs may play in the valuation of securities in illiquid markets. Gromb and Vayanos (2002) and Brunnermeier and Pedersen (2009) consider how the funding constraints faced by market participants can affect market liquidity and security values. Shleifer and Vishny (1992, 2011), Coval and Stafford (2007), and others focus on the effects of financial constraints on security prices in fire sales and forced liquidations. Longstaff (2009) solves for equilibrium security prices in a model when agents can only trade intermittently.

This paper approaches the challenge of valuing illiquid assets from a new perspective. Specifically, we view illiquidity as a restriction on the stopping rules that an investor is allowed to follow in selling the asset. This approach allows us to use an option-theoretic framework to place realistic lower bounds on the values of securities that cannot be traded continuously. Intuitively, these bounds are determined by solving for the value of an option that would compensate an investor for having to follow a buy-and-hold strategy rather than being able to follow an optimal stopping strategy in selling the asset.

There are many reasons why having a lower bound on the value of an illiquid asset could be valuable. For example, the lower bound could serve as a reser- vation price in negotiations between sellers and prospective buyers. Having a lower bound on the value of illiquid assets held by financial institutions can pro- vide guidance to policymakers in making r egulatory capital decisions. The lower bound also establishes limits on the collateral value of illiquid or thinly-traded assets used to secure debt financing or held in margin accounts. Recent changes to generally accepted accounting principles (GAAP) explicitly acknowledge that firms holding illiquid assets may need to base their valuations on unverifiable es- timates. 1 These lower bounds provide us a conservative but much more objective standard for valuing these types of illiquid assets.

The results provide a number of important insights into the potential effects of illiquidity on asset values. First, we show that the value of immediacy in financial markets is much higher than the value of future liquidity. For example, the discount for illiquidity for the first day of illiquidity is 2.4 times that for the second day, 4.2 times that for the fifth day, 6.2 times that for the tenth day, and 20.0 times that for the 100th day. These results suggest that immediacy is viewed as fundamentally different in its nature. This dramatic time asymmetry in the value of liquidity may also help explain the rapidly growing trend towards electronic execution and high-freque ncy trading in many financial markets.
Second, our results confirm that the values of illiquid assets can be heavily discounted in the market. We show that investors could discount the value of illiquid stock by as much as 10, 20, or 30 percent for illiquidity horizons of 1,
1 For example, Statement of Financial Accounting Standards (SFAS) 157 allows for the use of unverifiable inputs in the valuation of a broad category of illiquid assets that are designated as Level 3 investments.

2, or 5 years, respectively. Although our results only provide lower bounds on the values of illiquid assets, the evidence in the empirical literature suggests that these bounds may be realistic approximations of the prices at which various types of thinly-traded securities are sold in privately-negotiated transactions. For example, Amihud, Me ndelson, and Pedersen (2005) report that studies of the pricing of restricted letter stock find average discounts ranging from 20 to 35 percent for illiquidity horizons of one to two years. In addition, Brenner, Eldor, and Hauser (2001) find that thinly-traded currency options are placed privately at roughly a 20 percent discount to fully liquid options.

Third, we find that the effects of illiquidity and volatility on asset prices are fundamentally entangled. Specifically, asset return variances and the degree of asset illiquidity are indistinguishable in their effects on discounts for illiquidity. This makes intuitive sense since investors are more likely to want to sell assets when prices have diverged significantly from their original purchase prices. This divergence, however, can arise both through the passage of time as well as through the volatility of asset prices. Because of this, assets with stable prices such as cash or short-term Treasury bills can be viewed as inherently more liquid than assets such as stocks even when all are readily tradable. This may also help explain why concerns about market liquidity become much more central during financial crises and periods of market stress.

Finally, the results indicate that the effect of illiquidity on asset prices is smaller for investments with higher dividends or cash payouts. An important implication of this is that investors in illiquid assets such as private equity, ven- ture capital, leveraged buyouts, etc. have strong economic incentives to increase payouts. Thus, illiquidity may have the potential to be a fundamental driver of both dividend policy and capital structure decisions for private-held ventures or thinly-traded firms.

The remainder of this paper is as follows. Section 2 reviews the literature on the valuation of illiquid assets. Section 3 describes our approach to modeling illiquidity. Section 4 uses this approach to derive lower bounds on the values of illiquid or thinly-traded assets. Section 5 discusses the asset pricing implications. Section 6 extends the results to assets that pay dividends. Section 7 summarizes the results and makes concluding remarks.


The literature on the effects of illiquidity on asset valuation is too extensive for us to be able to review in detail. Instead, we will simply summarize some of the key themes that have been discussed in this literature. For an in-depth survey of this literature, see the excellent review by Amihud, Mendelson, and Pedersen (2005) on liquidity and asset prices.

Many important papers in this literature focus on the role played by trans- action costs and other financial frictions in determining security prices. Amihud and Mendelson (1986) present a model in which risk-neutral investors consider the effect of future transaction costs in determining current valuations for assets. Constantinides (1986) shows that while transaction costs can have a large effect on trading volume, investors optimally trade in a way that mitigates the effect of transaction costs on prices. Heaton and Lucas (1996) study the effects of transaction costs on asset prices and risk sharing in an incomplete markets set- ting. Vayanos (1998) and Vayanos and Vila (1999) show that transaction costs can increase the value of liquid assets, but can have an ambiguous effect on the values of illiquid assets.

Another important theme in the literature is the role of asymmetric informa- tion. Glosten and Milgrom (1985) model a market maker who provides liquidity and sets bid-ask prices conditional on the sequential arrival of orders from po- tentially informed agents. Brunnermeier and Pedersen (2005) develop a model in which large investors who are forced to sell are exploited via predatory trading by other traders, and show how the resulting illiquidity affects asset valuations.

A number of recent papers recognize that liquidity is time varying and de- velop models in which liquidity risk is priced into asset valuations. Pastor and Stambaugh (2003) consider a model in which marketwide systemic liquidity risk is priced. Acharya and Pedersen (2005) show how time-varying liquidity risk affects current security prices and future expected returns. Gromb and Vayanos (2002) and Brunnermeier and Pedersen (2009) develop models in which changes in the abilities of dealers to fund their inventories translates into variation in the liquidity they can provide, which in turn results in liquidity risk premium being embedded into asset values.

Another recent theme in the literature addresses the effects of search costs or the cost of being present in the market on liquidity and asset prices. Duffie, Garleanu, and Pedersen (2005), Vayanos (2007, 2008), and others consider models in which agents incur costs as they search for other investors willing to trade with them, and show how these costs affect security prices. Huang and Wang (2008a, 2008b) study asset pricing in a market where it is costly for dealers to be continuously present in the market and provide liquidity.

A number of papers in the literature view illiquidity from the perspective of a limitation on the ability of an agent to trade continuously. Lippman and McCall (1986) define liquidity in terms of the expected time to execute trading strate- gies. Longstaff (2001) and Kahl, Liu, and Longstaff (2003) study the welfare effects imposed on investors by liquidity restrictions on assets. Longstaff (2009) presents a general equilibrium asset pricing model in which agents must hold asset positions for a fixed horizon rather than being able to trade continuously.

Finally, several papers approach the valuation of liquidity from an option- theoretic perspective. Copeland and Galai (1983) model limit orders as an option given to informed investors. Chacko, Jurek, and Stafford (2008) value immediacy by modeling limit orders as American options. Ang and Bollen (2010) model the option to withdraw funds from a hedge fund as a real option. Ghaidarov (2014) models the option to sell equity securities as a forward-starting put option.

The papers most similar to this one are Longstaff (1995) and Finnerty (2012) who present models in which investors are assumed to follow specific trading strategies which allows them to derive bounds on illiquid asset values. These papers, however, result in discounts for illiquidity with counterintuitive properties such as exceeding the value of the liquid asset, or not being monotonic in the illiquidity horizon. This paper differs fundamentally from these papers, in that we allow investors to follow optimal stopping strategies in making selling decisions. An important advantage of this is that it leads to bounds that are much more realistic.










We model illiquidity as a restriction on the stopping rules that an investor can follow in selling asset holdings. We use this framework to derive realistic lower bounds on the value of illiquid and thinly-traded investments.

A number of important asset pricing insights emerge from this analysis. For example, we show that immediacy plays a unique role and is much more highly valued than ongoing liquidity. In addition, we show that illiquidity can reduce the value of an asset substantially. For illiquidity horizons on the order of those common in private equity, the discount for illiquidity can be as much as 30 to 50 percent. Although large in magnitude, these discounts are consistent with the empirical evidence on the valuation of thinly-traded assets. Thus, these lower bounds could be useful in determi ning reservation prices and providing conservative valuations in situations where other methods of valuation are not available.

Finally, we find that the discount for illiquidity decreases as the cash flow generated by the underlying asset increases. Thus, investors in private ventures may have strong incentives to increase dividends and other cash flows to reduce the impact of illiquidity on their holdings. This implies that the illiquid nature of investments in partnerships, private equity, venture capital, LBOs, etc. has the potential to introduce agency co nflicts as cash flow policy is impacted.


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