Valuing a Liquidity Discount

Ren-Raw Chen is a professor in the Finance Area of the Graduate School of Business Administration at Fordham University in New York, NY. [email protected] This article is motivated by the fact that the majority of securities in the financial markets are not frequently traded and hence a discount can be applied to properly ref lect such a deprived privilege. First, only a small fraction of corporate bonds are actively traded. Institutional investors hold the majority of these bonds until maturity. Similarly, term loans that assume a large part of the liabilities of a corporation are transacted extremely rarely. It is also important to note that nearly twothirds of the $14.2 trillion in mortgage-backed securities are highly illiquid. Finally, the most prominent example of illiquid securities is a recent contract that allows for easy and convenient transfer of credit risk—credit default swaps, which reached over $60 trillion in 2007 and now stay at a level of roughly $40 trillion. Most of these contracts are illiquid. For such contracts that are not easily transactable, a discount must be placed on the price. In this article, we show within a simple equilibrium-modeling framework that such a discount can be exceptionally large. Putting our analysis in the perspective of a quadratic utility setting, we discover that strikingly large discounts must be placed on security prices for even very reasonable levels of risk preference. In the recent financial crisis, we have witnessed unprecedented compressions of asset prices so extreme that professionals and regulators have started to question, and have proposed to abandon, marking to market. The advocates of abandoning marking to market argue that prices have started to deviate from economic fundamentals. Among countless other examples during the crisis, the most noticeable was Bear Stearns’ stock price, which went from $30 on March 14, 2008 (Friday), to $10 on March 17, 2008 (Monday). Over that weekend, the stock price of Bear Stearns went down by two-thirds, even though the economic fundamentals of Bear Stearns could not have possibly changed so substantially. To explain such a large drop in price even though no fundamentals changed, we propose a liquidity discount model that demonstrates economically how such large drops in prices, with no changes in fundamentals, are possible. Our model also helps salvage the long tradition of marking to market that Wall Street has prided itself on. With our model, price discount due to illiquidity can be computed and consequently the “fair value” of a security can be restored.