VALUE OF LIQUIDITY IN FINANCIAL MARKETS By VINAY DATAR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1994 ACKNOWLEDGEMENTS My sincere gratitude for the invaluable guidance, encouragement and support of my dissertation committee cannot be sufficiently articulated. This intense effort would not have been possible without the understanding and support from my family and I shall, forever, remain grateful. 11 TABLE OF CONTENTS ACKNOWLEDGMENTS ii ABSTRACT v CHAPTERS L A TUTORIAL ON LIQUIDITY 1 Introduction 1 What is Liquidity? Overview of Literature 3 Why do people demand liquidity? 3 Why is it costly to supply liquidity? 5 Incomplete markets 5 Imperfect markets 7 Market micro-structure 8 Different measures of liquidity 9 Value of Liquidity: A Basic Model 12 The economy 13 Price of the 'liquid' asset 14 Price of the 'illiquid' asset 14 Discussion 18 Summary 21 2. CROSS-SECTION OF STOCK RETURNS REVISITED: LIQUIDITY PREMIA AND ROLE OF SIZE 23 Introduction 23 Data and Methodology 26 Description of data 26 Estimation of beta 28 Proxies for liquidity 28 Returns, Size and Liquidity 30 Size or Volume? Evidence from Test Portfolios 33 Analysis of Residuals 38 in Summary 40 3. IMPACT OF LIQUIDITY ON PREMIA/DISCOUNTS IN CLOSED-END FUNDS 50 Introduction 50 Liquidity and Premia/Discounts 53 How is liquidity related to premia/discounts 53 Testable hypotheses 54 Proxies for liquidity 56 Data and Methodology 56 Data 56 Methodology 58 Discussion of Results 59 Sensitivity Analysis 62 Some Informal Evidence 65 Summary 67 APPENDIX A PROPERTIES OF PORTFOLIOS 79 APPENDIX B TESTABLE HYPOTHESES: AN ALGEBRAIC ILLUSTRATION 85 REFERENCES 88 BIOGRAPHICAL SKETCH 93 IV Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy VALUE OF LIQUIDITY IN FINANCIAL MARKETS By VINAY DATAR APRIL 1994 Chairman: Dr. Robert C. Radcliffe Major Department: Finance, Insurance and Real Estate In ideal markets, asset prices depend purely on fundamentals and asset liquidity is not a concern because buyers (willing to pay the fundamental value) can be readily found. However, when markets are less than ideal, liquidity considerations may affect equilibrium asset prices, reflecting the anticipated frictions in trading. It is difficult to formalize liquidity because it may be influenced by a variety of trading frictions related to various forms of market imperfections or incompleteness. Chapter 1 is a 'tutorial' on liquidity. It briefly reviews different types of trading frictions that may affect liquidity of traded as.sets. Several, albeit noisy, measures of liquidity are outlined. A simple model of liquidity is presented to demonstrate the basic economics of liquidity. If liquidity has value then investors may demand a premium (higher returns) on less liquid assets. Is there any empirical support for such liquidity preinia in asset returns? Chapter 2 examines this question and presents evidence of liquidity premia in the cross-section of stock returns. It is suggested that the well known relationship between firm-size and returns may, in fact, be due to liquidity considerations. Further, the relationship between returns and " liquidity is found to be robust to any potential seasonality in stock returns (i.e., the 'January effect'). Chapter 3 examines the impact of liquidity on the pricing of Closed- End funds. Funds can potentially create value by buying illiquid assets and selling more liquid claims. The claims issued by such funds would be more valuable than the underlying assets and would, therefore, trade at premium relative to the underlying assets. The empirical evidence is consistent with this notion. Specifically, in a cross- sectional study, premia increase (or discounts decrease) as liquidity of a fund increases (as measured by proxies). Overall, the results suggest that liquidity considerations may play an important role in the determination asset prices in financial markets, and may plausibly explain some of the well-known anomalies in financial markets. VI CHAPTER 1 A TUTORIAL ON LIQUIDITY Introduction The notion of asset liquidity lacks a precise formal definition despite its intuitive appeal. Grossman and Miller (1988) express this idea quite succinctly: Keynes once observed that while most of us could surely agree that Queen Victoria was a happier woman but a less successful monarch than Queen Elizabeth I, we would be hard put to restate that notion in precise mathematical terms. Keynes's observation could apply with equal force to the notion of market liquidity, (page 617). Lippman and McCall (1986) observe that academic economists do not have a defmition of liquidity as a measurable concept, although there is a general agreement that liquidity is the 'marketability' of an asset; or the property of an asset that facilitates immediate exchange for cash, without affecting the market price. They define liquidity in terms of the time required to sell an asset to the best bidder (on average). Grossman and Miller (1988) suggest that liquidity is related to the 'price concession' that may be demanded by a potential buyer to participate in an immediate trade. Although a precise metric of liquidity remains elusive in theory, in practice liquidity seems to be important. For example, according to the NYSE (New York 1 2 Stock Exchange) fact book (1990), the dollar volume of trade on U.S exchanges exceeds $ 2 trillion per year, where the total market value of (potentially tradable) listed assets is about $ 3 trillion. This amounts to an yearly turnover rate of about 70%. This suggests that investors do care about the ability to trade, and are willing to pay the attendant transaction costs. Further, the chaotic frenzy on the trading floors suggests a strong sense of urgency to trade. Why might so many traders fall over each other (often times literally), to frantically engage in trade? How might trading, or frictions in trading, affect long run prices? These questions form the central theme of this study; what is the meaning and value of liquidity? Liquidity considerations play no role in traditional asset pricing models; any amount of trade can occur in equilibrium, without affecting prices. This result is natural when markets are perfect. Here, the market value of liquidity is zero, because market participants can supply liquidity at zero cost, if and when liquidity is demanded. Recent literature on liquidity attempts to provide some insights into the impact of trading (and frictions in trading) on asset values. The general suggestion is that less liquid assets have higher expected returns (or lower prices) than more liquid assets.' These higher returns, or liquidity premia, are a compensation demanded by market participants to offset anticipated costs of trading. Liquidity considerations provide valuable insights into asset pricing to the extent that they explain, albeit in part, some well known empirical anomalies: ' This notion is articulated by Amihud and Mendelson (1986) and Constantinides (1986). 3 1) Claims to identical cash tlows may have different prices [ See, e.g., Amihiid and Mendelson (1991), Boudoukh cS: Whitelaw (1991)]. 2) Small firms have higher average returns than large firms [e.g., StoU and Whaley (1983)]. 3) Closed-end funds trade at discounts or premia relative to the market value of underlying assets [See Chapter 3]. This chapter proceeds as follows: The first section describes various motives for trade, sources of potential frictions and prevalent measures of liquidity. The second section presents a simple model that captures the basic economics of liquidity premia. The third section concludes. What Is Liquidity?: Overview of Literature It is helpful to think about liquidity and its value in terms of the supply and demand for liquidity. In particular, let us examine why people might want to trade (demand liquidity); and why it might be costly to supply liquidity. An examination of these aspects might suggest a clue as to the meaning and value of liquidity. Why Do People Demand Liquidity? Fundamentally, individuals would want to trade (i.e. demand liquidity) when private valuation for an extra unit of an asset is different from market valuation. In such situations there are gains to be made from trading, and this suggests a motive for trade. 4 Literature has postulated several reasons for such a differential valuation, where private value may be different from market value. Unforeseen shocks to preferences, endowments, information (about asset quality) and life-cycle trading may lead to personalized values that are different from market value. For example, Amihud and Mendelson (1986), Diamond and Dybvig (1983) and Flannery (1991) consider a situation where individuals are hit by a preference shock; here some agents 'die' early in the sense that such agents care only about current consumption, and they have no value for future consumption. Clearly, these agents would be willing to sell (to the highest bidder) at any non-negative price. In similar spirit, Campbell, Grossman and Wang (1992) introduce change in the degree of risk aversion as a motive for trade; here, personal values are affected because of the change in risk aversion and agents can gain by trading. Admati and Ptleiderer (1988), Glosten and Milgrom (1985) and Kyle (1985) present models with private information as a motive for trade; smart traders have private information about the true value of the asset, and such traders can benefit by trading, as long as the market value is different from the true value. DeLong, Shleifer, Summers and Waldman examine the impact of 'noise'; irrational traders perceive the market value to be too low or too high, and such traders arrive in the market as buyers or sellers. Constantinides (1986) and Grossman and Miller (1988) introduce rebalancing as a motive for trade; individuals trade to allocate optimal amounts of their wealth between risky and risk-free assets. In such situations, the value of an extra unit of risky assets is lower because of risk aversion, and depending on the wealth level there is an optimum amount of risky assets that an