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Unformatted text preview: 35 Liquidity risk: current research and practice Allan M. Malz RiskMetrics Group [email protected] This article presents a survey of current thinking and practice regarding liquidity risk. We place the notion of liquidity risk as understood by risk managers in financial institutions in the broader context of liquidity as understood by treasury managers, institutional investors and traders, and central bankers. The article also presents and discusses critically two widespread approaches to measuring liquidity risk for individual securities, and discusses the problems that arise in attempting to quantify liquidity risk for a portfolio. Liquidity risk is a large and confusing subject. Most financial institutions have committed or are preparing to commit significant resources to managing liquidity risk. But there are no clear standards regarding the definition of the problem these firms’ efforts are meant to solve, let alone the risk measures themselves. This paper is an effort to describe and evaluate current practice in addressing liquidity risk. This current practice is ill defined. Whether you love it or hate it, value at risk (VaR) can at least be taken as a point of departure in thinking about market risk measurement. There is no such standard point of departure for liquidity risk. Nonetheless, where liquidity risk is measured at all, it is usually via variations on two types of statistic. The first attempts to measure transaction cost risk and is based on bid-ask spreads, while the second attempts to capture the risk of depressing the market price by selling, and is based on trade volume or outstanding stocks. We will describe the mechanics and rationale of these typical measures and assess their validity and relevance to liquidity risk. A large part of the difficulty that practitioners have had in addressing liquidity risk is that it is not clear what problem that they are trying to solve: executing trades efficiently, securing access to funding, and protecting against extreme events are some of the issues that lurk in the background when liquidity risk is discussed. We will attempt to sort out these definitions, and distinguish the types of liquidity risk that naturally fall to the risk management function, as opposed to the trading or treasury functions, of a financial institution. 36 Liquidity risk: current research and practice This paper focuses just on current practice. We find that, under normal circumstances, liquidity risk can be expected to be a small part of intermediaries’ total risk, and that at least some aspects of it can be at least approximately measured by some of the statistics described here. However, at times of financial stress, liquidity risk can become a far more important part of total risk. Precisely at these times, standard liquidity risk measures are likely to be quite misleading. Monitoring liquidity risk should therefore be considered a part of preparing for financial stress and should focus on stress testing and warning signals. We will describe such warning signals in future work. 1 What is liquidity risk? The term “liquidity risk” is used to cover a wide range of issues: Quality of transactions, assets or markets Liquidity most often refers to individual assets or transactions. An asset is said to be liquid if it is “near” or a good substitute for cash. Liquid assets can be readily transformed into other assets should new opportunities present themselves. When used to describe a market, liquidity refers to the ability to maintain a position and unwind in an orderly fashion without excessive transactions costs and without excessive price deterioration. From the standpoint of a market participant, the essential questions concerning liquidity are, how much of the asset can I purchase or sell, how quickly, and at what cost? This aspect is often called asset liquidity. Balance sheet and funding This use of the term “liquidity” refers to whether the on- or off-balance sheet assets and liabilities of market participants permit them to maintain their portfolios or continue operations. It encompasses the first meaning, but adds to it the issue of the terms on which credit is granted. This aspect is often called funding liquidity (as in Counterparty Risk Management Policy Group (1999) and Managed Funds Association (2003)). For traders and investors, the question is the capacity to maintain a leveraged position in the face of a decline in their perceived credit quality or of the value of posted collateral. Traders and investors are generally short-term borrowers, so their capacity to maintain long-term positions and their flexibility when circumstances or expectations change is limited. In banking and insurance, the issue is the institution’s solvency. Traditional banking, in which the bank issues short-term obligations such as deposits and grants longer-term credits, is exposed to liquidity impasses. In extreme cases—“runs”—the bank may become insolvent. Quality of financial system as a whole Much of financial supervision and regulation is oriented at least in part toward reducing the risk of a general impairment of the financial system. In What is liquidity risk? situations of severe financial stress, the ability of the financial system to allocate credit, support markets in financial assets, and even administer payments and settle financial transactions, may be impaired. The risk of stress this severe is called “systemic risk,” and often thought of as a function of economy-wide liquidity. The meaning of liquidity most directly relevant to risk managers is the first, since it bears most directly on the cost of executing transactions and thus of entering into and exiting positions. However, the distinctions are often blurred, as in a statement by the Basel Committee that encompasses the first as well as the second meaning: “Banks should evaluate the adequacy of capital given their own liquidity profile as well as the liquidity of the markets in which they operate.”1 1.1 The border territories Liquidity risk is a somewhat disorderly subject: it is difficult to define its scope clearly. One reason is that “classical” economic and financial theory is based on the idea of perfect markets, that is, markets that clear continuously and without cost. The standard metaphor for this type of market is the Walrasian auctioneer, named for a late-19th century economist. In Walras’ metaphor, market clearing is accomplished by a sequence of auctions, at discrete points in time, in which transactions actually take place only when the market-clearing prices of all goods have been found. Once the metaphor is abandoned and we analyze the market-clearing mechanism itself, there are few guidelines, the simplicity of competitive theory is lost, and the empirical data, which we will describe in Section 2 below, is either sparse or ambiguous. Variations in price due to fluctuations in liquidity occur simultaneously with changes in the equilibrium price and with the price discovery process. Another reason for this disorderliness is that liquidity risk intersects with several other topics in finance. It is helpful in understanding liquidity risk to be aware of these “border territories” and the way in which they overlap with risk issues: 1 Bank for International Settlements (2001), 7. 37 38 Liquidity risk: current research and practice Organization of markets Financial markets are organized in a number of different ways that have their origins in the types of assets traded, the available technological means of “producing” market-clearing service, and the coincidences of historical developments.2 Market microstructure is the systematic and theoretical study of market-clearing mechanisms. Its major concerns are the impact of market organization on asset price returns and their behavior, and how market organization is and ought to be shaped by the cost of acquiring information and competitive imperfections in the market-clearing mechanisms.3 Optimal trade execution identifies the best markets, pace, trade size, and time profile for establishing or unwinding a position. Good execution and reducing transaction costs is important for all market participants, but is particularly important for those trading frequently on small differences among market prices or between market and model prices. Optimal execution differs from liquidity risk in the time frame involved; the former is focused primarily on intraday asset price movements, while liquidity risk measurement is oriented more toward end-of-day risk reporting and thus price movements over at least one or more days. Quantitative trade guidance based on intraday data is difficult to formulate partly because intraday data is scarce and difficult to work with. Most of the research in this area4 incorporates liquidity risk along with the market risk of the assets involved into a portfolio optimization framework. The key liquidity parameters are the cost of trading immediately in larger size, and the adverse price impact of trading more intensively. The focus is on optimization techniques, so these key liquidity parameters, as well as the weight placed on immediacy and price slippage are posited, rather than estimated. In practice, large security trades are not often simply dumped onto the market, but are nursed through execution by splitting them up among a number of different market types. For example, a portion being brought. Optimal execution models are not yet capable of taking this level of institutional detail into account. Asset-liability management (ALM) refers to the problem of matching the cash flows and values of assets and liabilities on the balance sheets of financial intermediaries. It is an important part of liquidity risk in the sense of balance sheet management set out above. It is related to liquidity 2 Material on how particular markets are organized and function can be found, among very many examples, in Blume (2002) for U.S. stock markets, Williams (1986) for futures markets, and Cross (1998) for foreign exchange markets. 3 This is a vast literature that extends back at least to Demsetz (1968), to whom is due the still-current paradigm of modeling securities markets using flow supply and demand curves as well as the idea that the bid-ask spread compensates dealers for providing the ability to market participants to trade immediately. See Biais, Glosten and Spatt (2002), Madhavan (2000) and Madhavan (2002) for comprehensive surveys. 4 See for example Almgren and Chriss (2000/2001) and Lo, Petrov and Wierzbicki (2003). What is liquidity risk? in the first sense because cash required to meet obligations of the firm can be realized by liquidating positions as well as from their regular cash flows. Financial regulation Liquidity of financial institutions is an important part of prudential regulation and supervision. Standards are generally not set out explicitly in great detail, and enforcement is left in large part to on-site examination. Discussion of liquidity risk in supervisory documentation generally focuses on balance sheet and funding risk, and treats the quality of markets in that context.5 Financial crises, as noted, are often termed liquidity crises.6 Crises originate and can be triggered in many ways, but impairment of liquidity is a universal feature once a crisis begins. Much of the concern about liquidity risk, to the extent that it goes beyond ALM, revolves around crises and extreme events. One aspect of liquidity risk during crises that has received considerable attention, particularly with hedge funds in mind, is the sequencing of trades. Imagine a highly leveraged trader with a thin capital layer and a range of more and less liquid positions. In a crisis, the trader may be obliged to liquidate positions in order to meet margin calls and the general contraction of the credit being extended to him. The choice is to liquidate more liquid positions earlier, reducing liquidity losses and the attrition of capital early on but amplifying liquidity risk if the crisis wears on, or liquidate less liquid positions early, taking an immediate liquidity loss but reducing ongoing liquidity risk. Duffie and Ziegler (2003) provide an example of this situation in which it is optimal to liquidate less liquid positions earlier. Credit risk Borrowers’ liquidity difficulties in both the transactions and funding senses become credit risks for their counterparties. Asset and funding liquidity-induced credit problems are an important transmission mechanism that generates systemic risk. Following the 1998 financial crisis, Counterparty Risk Management Policy Group (1999) examined the nexus of credit, liquidity and systemic risk, and focused on ways in which market practices might exacerbate the feedback mechanisms during periods of stress. We will encounter all of these topics—and can treat none of them thoroughly—in this survey. 5 See the discussions of liquidity risk in central bank supervisory manuals, particularly Board of Governors of the Federal Reserve System ((1998) and (2003)) and Deutsche Bundesbank (1999). 6 See, for example, Group of Ten (1996). The Johnson group report on the 1998 financial crisis (Bank for International Settlements (1999a)) attributed it primarily to liquidity problems and an increase in risk aversion. 39 40 Liquidity risk: current research and practice 1.2 Why is there liquidity risk? In order to design and evaluate liquidity risk measures it is necessary to understand where liquidity risk originates. A standard set of characteristics of market liquidity, focusing primarily on asset liquidity, helps to understand the causes of illiquidity and connects well with the available market data:7 Tightness refers to the cost of a round-trip transaction, and is typically measured by the bid-ask spread and brokers’ commissions. Depth describes how large an order it takes to move the market adversely. Resiliency describes the length of time for which a lumpy order moves the market away from the equilibrium price. The latter two characteristics of markets are closely related to immediacy, the speed with which a market participant can execute a transaction. Amihud and Mendelson (1986) show that wider bid-ask spreads are associated with higher returns, indicating that the market places a premium on securities with greater immediacy. In other words, liquidity is a priced risk factor. Liquidity risk arises from market “imperfections” that work against these characteristics. Market imperfections are ultimately due to the cost of searching for a counterparty and the market institutions that assist in search; they fall into four categories: Cost of trade processing Facilitating transactions, like any economic activity, has fixed and variable costs of processing, clearing and settling trades, apart from the cost of finding a counterparty and providing immediacy. These costs are tied partly to the state of technology, and partly to the organization of markets. They are not likely to vary over reasonably long periods of time. While processing may be a significant part of transaction costs, it is unlikely to contribute materially to liquidity risk. The obvious exception is natural or man-made disasters that affect the trading infrastructure. Inventory management by dealers The role of dealers is to provide trade immediacy to other market participants, including other dealers. In order to provide this service, dealers must be prepared to estimate the equilibrium or market-clearing price, and to hold long or short 7 See Kyle (1985) and Bank for International Settlements (1999b). The markets and the data inventories of the asset. Holding inventories exposes dealers to price risk, for which they must be compensated by price concessions. The dealers’ inventory risk is fundamentally a volatility exposure and is analogous to short-term option risk.8 Adverse selection Some traders may be better informed than others, that is, better situated to forecast the equilibrium price. Dealers and market participants cannot distinguish perfectly between offers to trade arising from the counterparty’s wish to reallocate into or out of cash (so-called “liquidity” or “noise traders”) from those who recognize that the prevailing price is wrong (so-called “information traders”). A dealer cannot be sure for which of these reasons he is being shown a trade and needs to be compensated through the bid-ask spread. He does however, have privileged access to the flow of trading activity. An influential formulation of this aspect of liquidity, by Kyle (1985), relates the adverse price impact of an order of a given size to two key parameters: it is positively related to uncertainty about the equilibrium price (i.e., the amount of private information the informed traders possess) and negatively related to the variability in the quantity brought to market by noise traders. In other words, the coefficient of adverse price impact, often called “Kyle’s λ,” is proportional to the likelihood the counterparty knows something the dealer does not. Glosten and Milgrom (1985) study the effect of adverse selection in a dealer-driven market, focusing on the impact on dealers’ quotes rather than on the immediately market-clearing price. They show that if dealers are more likely to be asked for a quote by a market participant with privileged information, bid-ask spreads will be wider. Differences of opinion Investors generally disagree about the “correct” price of an asset, or about how to interpret new information, or even about whether new information is important in assessing current prices. Investors who agree have less reason to trade with one another than investors who disagree. When agreement predominates, for example, when important and surprising information is first made public, or during times of financial stress, it is more difficult to find a counterparty.9 2 The markets and the data Liquidity is bound up with particular market clearing and price discovery mechanisms. In order to understand liquidity risk and approaches to measuring it, we need to understand something about 8 Early formal models include Stoll (1978). 9 Harris and Raviv (1993) model differences of opinion on the importance (rather than the interpretation) of new information. 41 42 Liquidity risk: current research and practice different types of market institutions. As noted, this is a vast subject in its own right. From here onward, we will be focusing on liquidity in the first sense set forward in Section 1 above. Conceptually, there are three key distinctions to be borne in mind. However, these conceptually distinct elements are combined in different ways in actual market institutions: Market-clearing mechanism or the technique by which the equilibrium price is established. Order-driven systems come closest to the perfectly competitive auction model. In this type of market clearing, market participants transmit orders to an aggregation facility, such as a broker, specialist, or electronic trading system. In some cases, a call auction is held in which the price is gradually adjusted until the volumes of bids and offers forthcoming at that price are equated. More typically, a continuous auction is conducted in which the best bids and offers are matched, where possible, throughout the trading session. In a quote-driven system, certain intermediaries, who may be dealers, market makers, or specialists, have the obligation to publicly post two-way prices or quotes and to buy or sell the asset at those prices within known transaction size limits. These intermediaries must be prepared to hold long or short inventories of the asset and typically trade heavily among themselves in order to redistribute the inventories and reduce them overall. Formal organization distinguishes between securities, commodity and derivatives exchanges that are formally organized and those that are less so, that is, over-the-counter (OTC) markets. Exchanges are more heavily regulated than OTC markets and provide greater transparency and better clearing systems. In particular, counterparty credit risk can be reduced to a minimum on exchanges by some combination of margining and clearing houses. Both types of organization accommodate electronic trading systems. Most quote-driven markets are OTC and vice versa. Type of agency distinguishes whether the intermediaries can or must trade for their own accounts in the normal course of business. Dealers make two-way prices for standard-size deals to a well-defined group of other dealers and brokers. A dealer must make prices while “on duty.” Because dealers take ownership of, i.e. take long or short positions in, the securities they deal, they profit or protect themselves by moving their quotes. In an OTC market, dealers post prices and seek transactions on an electronic information system and the telephone, going “out” to the market. In an organized exchange, the market comes to the dealer at his trading post. The markets and the data Brokers do not take ownership of securities, but keep ordered lists of orders received from the public. Lists of limit orders are ordered, separately for bids and offers, by price and time entered. Market orders are ordered by time entered only. In practice, none of these distinction can be made too sharply, since real-world trading institutions mix and match all these features. Examples are: • Increasingly, the larger stock exchanges are combinations of market clearing mechanisms. For example, the New York Stock Exchange (NYSE), is primarily an order-driven organized exchange. However, when imbalances arise, the principal brokers, called specialists, are obliged to act temporarily as dealers and absorb inventory. The trading mechanism is primarily on the continuous auction model, except at the opening, when a call auction is conducted. Although floor trading predominates, a significant share of block trades (≥ 10, 000 shares) are traded OTC (the “upstairs market”) and brought to the floor only to be executed at the arranged prices. Most orders are routed to the NYSE floor via an electronic routing system, the Super Designated Order Turnaround System (SuperDOT), but are executed by specialists. • Some exchange-traded derivatives have trading mechanisms that are similar to OTC, so the exchange is primarily providing a locus of liquidity and settlement services. • Electronic trading systems add an organized exchange functionality to some OTC markets, such as foreign exchange. The microstructural diversity of markets makes it much harder to gather a particular type of liquidity information that might lend itself to measurement uniformly across equity markets. To summarize the main types of data required and their availability in different markets: Bid and offer spreads The difference between bid and asking prices, expressed in currency units, basis points, or a percent of the midprice, the average of the bid and ask. In order to be valid, the spread must be based on a simultaneous bid and ask price and must be on either side of the equilibrium price. These are naturally more readily available in quote-driven markets, since a quote constitutes exactly such a simultaneous bid-ask pair. This includes foreign exchange and money markets. 43 44 Liquidity risk: current research and practice Even in quote-driven markets, however, transactions may occur at prices within the the bid-ask spread. The quoted bid-ask spread may then not accurately reflect the effective spread and true cost of transacting.10 In order-driven markets, there are choices to make as to what constitutes a simultaneous bid-ask pair. If the criterion is that the bid and ask prices were entered into the market at the same time, they will not generally both be the best bid and ask and hence will not flank the market-clearing midprice. If the criterion is best bid and ask prices, they will generally not have been entered simultaneously. In consequence, it is often more difficult to obtain bid and ask prices in order-driven markets, which includes most organized securities and derivatives exchanges. Transaction volume The amount of trading in the asset, expressed either in terms of the money value of transactions, or as the number of asset units changing hands. Transactions volumes are available for exchange-traded assets, and for electronic trading systems. Volumes for OTC markets are not usually available publicly. Amount outstanding The available stock of the asset, expressed in money value or as the number of asset units. For securities, this is unambiguous: a known amount of shares or par value are issued. For futures and exchange-traded options, this is the number of contracts in which a long and short position have been established. For foreign exchange, the amounts outstanding are national money supplies. For commodities, physical quantities are generally rather difficult to establish, especially where quality grades are traded as distinct assets. As important as the total amount outstanding of a security, but far more difficult to measure, is the distribution of asset stocks among market participants. Market participants holding a large fraction of asset stock take great pains to conceal their positions. In a few cases, such as listed equities, there are regulatory obligations to disclose large holdings publicly. Most of this data, when it is available at all, is available at end-of-day frequency. As we will see, some liquidity risk measures call for data at intraday frequency, which is available in far fewer markets. Moreover, when intraday data can be obtained, it is often compromised by quality and synchronicity problems. For example, for the reasons set out above, it is quite difficult to identify bid-ask pairs intraday in order-driven markets. 10 Chordia, Roll and Subrahmanyam (2001) estimate effective spreads for U.S. stocks and find that they are significantly narrower on average than quoted spreads. Liquidity risk measures for normal markets 3 Liquidity risk measures for normal markets The academic literature on microstructure would suggest certain measures of liquidity and liquidity risk. For example, Kyle’s λ is a natural measure of adverse price impact. However, these are not generally implemented, either because of data limitations, or because they are not appropriate outside of a model context in which the equilibrium price can be held constant while only liquidity-related quantities fluctuate. In yet another stark contrast to market or credit risk management, we cannot directly observe most aspects of liquidity, particularly when it is dependent on the share of the market participant’s position in the total market as well as on market conditions. It is very difficult to backtest any position-dependent measure of liquidity. Rather, most standard approaches to measuring liquidity revolve around two types of data, the bid-ask spread, a measure of trading costs, and trading volume, turnover, or some other measure of the intensity of trading activity. The standard approaches are oriented primarily toward the first definition of risk of Section 1, liquidity as a property of an asset or market. We will present a general version of these types of liquidity risk measures, but we will try to give some feel for the many variants. 11 As we will see, these measures have a number of conceptual or pragmatic difficulties. Intuitively, one would expect it to be easier to carry through transactions in quiet rather than volatile markets. An important criterion we will apply in evaluating liquidity risk measures is therefore that a measure of liquidity risk should be positively correlated with the price volatility of the asset price. Other evaluation criteria for liquidity risk measures are the extent to which high quality data are likely to be available, and the degree to which the liquidity statistic actually captures the behavior it is meant to measure. Other measures of liquidity risk are also in use, but have more restricted range of application than those discussed here. For example, the on-the-run versus off-the-run spread, or the spread between the yields of the most recently-issued and less recently issued Treasury notes or bonds with the same initial maturity, is used as an indicator of the liquidity of non-benchmark Treasury securities.12 11 One of these variants, Roll’s measure discussed below, relies on the asset midprice as a proxy for liquidity data when the latter is unobtainable or of poor quality. 12 As we will see in subsequent work, it can also be used as an indicator of liquidity conditions in financial markets as a whole. 45 46 Liquidity risk: current research and practice 3.1 Measures of transactions cost risk Description of the statistics The first group of standard liquidity measures focuses on the risk of variation in transactions costs. It attempts to measure the likelihood that it will cost more than expected to liquidate the position. The starting point for this set of measures is a distributional hypothesis regarding the future bid-ask spread measured in relative or percentage terms. As in the measurement of market risk, it is typical to apply either historical simulation, or a parametric estimate under the assumption of normality. The mean of daily changes in the relative bid-ask spread is assumed to be zero and its variance is assumed equal to its sample variance σs .13 The expected transactions cost is the half-spread or mid-to-bid spread s ¯ E [Pt +1 ] , 2 where s=2 ask price - bid price ask price - bid price = , ask price + bid price midprice and s is an estimate of the expected or typical bid-ask spread and P is the asset midprice. ¯ Under the zero-mean normality hypothesis, we set s = s , the most recent observation on the ¯ relative spread. For at least some currency pairs, it may be preferable to set s conformably to a ¯ well defined “typical level.” Figure 1 illustrates for Euro-dollar and the Mexican peso. While there is considerable variation in the bid-ask spreads for these currency pairs, measures in currency units, there is clearly a strong tendency toward a level of USD 0.0004 and MXP 0.01. These typical levels can be identified only for currency pairs with small trend movements. For currency pairs such as dollar-Turkish lira this cannot be done, since the lira has a very pronounced depreciation trend. The 99 percent confidence interval on the transactions cost is ¯1 ¯ ±P (s + 2.33σs ), 2 13 See Bangia, Diebold, Schuermann and Stroughair (1999) for details. Note that the assumption that spreads are normally distributed introduces a non-zero probability of a negative spread, but this does not affect the practical applications. Liquidity risk measures for normal markets ¯ ¯ where P is an estimate of the next-day asset midprice. Again, we will typically set P = P , the most recent observation on price. We will refer to 1 (s ¯ 2 + 2.33σs ) as the 99 percent spread risk factor. The transactions cost risk at a 99 percent confidence level is then measured by the current value of the spread risk factor, or by the 99th percentile of the actual proportional daily changes in the half-spread over a given historical period, say, the past two years. We can see from Table 1 that bid-ask spread behavior is non-normal, and that particularly kurtosis is high. As suggested by Bangia et al. (1999), the parametric approach can take account of this by multiplying 2.33σs by an amount greater than one. Table 1 also displays rough estimates of liquidity risk for 34 developed and emerging market currencies. As can be seen, for many currencies, liquidity risk is a comparatively minor contributor to risk, accounting for as little as 2 to 5 percent of the market risk for the most widely-traded currency pairs. For these currencies, and other assets with general tight bid-ask spreads, liquidity risk is simply not terribly important, except possibly in market stress situations. For a number of less widely traded developed-country and key emerging market currencies, such as the Norwegian krone, Mexican peso, and Korean won, transactions liquidity risk is material, accounting for 5 to 20 percent of market risk. A handful of emerging markets currencies have quite high transactions liquidity risk, in excess of 20 percent of market risk. These are of two types. Some, like the Turkish lira, simply have quite volatile bid-ask spreads. Others, such as the Indian rupee, have tightly managed exchange rates and thus comparatively low exchange rate volatility, lowering the market risk of the currency. The liquidity risk then appears higher in comparison. In many markets, bid and ask data can be difficult or impossible to obtain, or inaccurate. Roll (1984) shows that, under some rather restrictive assumptions, an estimate of the bid-ask spread can √ be computed from the time series of midprice changes as 2 −Cov( Pt , Pt −1 ). The assumptions required are that the distribution of price changes be stationary and that the market be efficient. Critical assessment of transactions cost liquidity risk measures By our key criterion for a practically useful liquidity risk measure, that it be positively correlated with volatility in the asset midprice, the measures of transactions cost risk described above appear 47 48 Liquidity risk: current research and practice are valid. Table 3 displays the results of regressions of the 99-percent spread risk factor 1 (s ¯ 2 + 2.33σs ) on the volatility of the midprice for the same set of 34 currency pairs against the dollar. In most cases, the coefficient is significant and positive, indicating that transactions-cost based measures of liquidity risk are correlated with market risk. The measure, however, has a number of drawbacks: • It does not comprehensively capture the transactions cost risk, since it ignores brokers’ commissions. Data on commission rates are not typically publicly available, as they are dependent on the size of the transaction and the nature of the relationship of the counterparty and the broker. The measure thus captures only the risk of encountering a high bid-ask spread when coming to market.14 • The measure does not (and is not at all intended to) capture the impact on the market price of trading. The liquidity risk arising from the bid-ask spread is often called “exogenous” because the trader cannot influence the spread by trading more or less, but can only decide whether and how much to trade at a given spread.15 But this is true only to a certain extent. It often occurs that bid-ask spreads widen because of greater uncertainty about the equilibrium price, because short-term volatility has risen, or because dealers have less confidence that a lumpy order can be redistributed to other market participants without loss. However, it is just as often the case that spreads are wider for larger trades, since they impose larger changes in inventory and higher risk on dealers. They may also be narrower, representing a “quantity discount” on a large trade. • The measure is applicable only to assets with high-quality bid-ask data, which, as noted in Section 2, are rather limited. The discreteness of data is also a serious problem impairing the value of transactions liquidity measurement. Conventional bid-ask spreads are measured in the smallest units of price fluctuation in the market involved, called either ticks, basis points, or, in foreign exchange markets, pips. A pip can be a large fraction of the typical bid-ask spread measured in currency units. This can distort estimates for assets with relatively low-volatility bid-ask spreads and high tick size relative to the midprice, especially parametric estimates. For example, in the dollar-yen and dollar-Euro markets, a typical tight spread is 3 pips. Thus, at a Euro-dollar midprice of USD 1, a quote might be 99.99 to 100.02 and the relative spread is 14 See Jones (2002) for estimates of the shares of the bid-ask spread and commissions in the cost of equity trading on the NYSE. 15 The terminology is due to Bangia et al. (1999). Liquidity risk measures for normal markets 3/100 of 1 percent. If the spread now increases by one pip, the relative spread will go to 4/100 of 1 percent, an increase of one-third. As another example, the typical tight spread is 3 pips for both Euro-dollar and sterling-dollar. However, a typical midprice for Euro-dollar is USD 1.00, while for sterling-dollar it is USD 1.50, so the relative spread, when quotes are tight, is only 2/100 of 1 percent for then latter, or one-third lower than for Euro-dollar. Figure 1 illustrates for Euro-dollar and the Mexican peso. The discreteness issue also arises for U.S. bond and stock markets, especially prior to decimalization. Prior to June 1997, NYSE stocks traded in 1/16’s. Even after decimalization, $0.01 can be a significant fraction of the bid-ask spread. In the final analysis, this measure is valid under its own narrow terms, but is not very useful. It measures part of the transactions cost risk, but this risk is not usually important. In our foreign exchange example, we found a few instances of the peculiar case of assets with a low price volatility and high bid-ask spread risk factor. But this situation is unlikely to be encountered apart from managed currencies. For more typical assets, the risk is small relative to the market risk. More importantly, the liquidity risk according to this measure appears to become high only in times of market stress. In normal markets, this narrow measure of liquidity risk measures a risk that may be immaterial. In stressed markets, transactions cost risk can be quite a bit higher. To illustrate, Figure 3 displays the behavior of the dollar-Brazilian real foreign exchange rate and bid-ask spread. The volatility of both the midprice and the bid-ask spread increased significantly from the period leading up to the 2003 presidential election (Panel A). The general level of the bid-ask spread has risen substantially as well (Panel B). 3.2 Measures of the risk of adverse price impact Description of the statistics The second group of standard measures is aimed at quantifying the risk arising from the additional time over which a large position must be liquidated in order to avoid depressing the price. Rather than measuring the adverse price impact of trading, it measures the additional market risk imposed by an orderly liquidation, that is, avoiding trading at a pace fast enough to move prices. The starting point for these statistics is an estimate of the number of trading days T required for the orderly liquidation of a position. If the position is liquidated in equal parts at the end of each 49 50 Liquidity risk: current research and practice day, the trader faces a 1-day holding period on the entire position, a 2-day holding period on a fraction T −1 T of the position, a 3-day holding period on a fraction T −2 T of the position, etc. The next step is to arrive at an estimate of the 1-day position VaR. If the entire position were being held for T days, the T -day VaR would be estimated by adding uncorrelated increments to the quadratic variations in portfolio value, leading to the familiar square-root-of-time rule: 1-day position VaR × 12 + 12 + · · · + 12 = 1-day asset VaR × √ T However, this would be an overstatement of the VaR; the VaR has to be between the 1-day √ position VaR and 1-day position VaR × T . We will be holding a sequence of position sizes − − − 1, T T 1 , T T 2 , . . . , T T 2 , rather than 1, 1, . . . , 1, all with the same variance. The VaR is therefore 1-day position VaR × 1+ = 1-day asset VaR × T −1 2 T T t =1 1− T −2 2 T t −1 2 , T + + ··· + 12 T (1) which simplifies to 1-day position VaR × (1 + T )(1 + 2T ) . 6T (2) For example, supposing it is determined that a position can be liquidated in T = 5 trading days. √ The adjustment to the overnight VaR of the position is then 1 5 t = 1.48324, that is, to increase t 5 the VaR by 48 percent. For T ≈ 10, the liquidity risk adjustment is to double the overnight VaR of the position. These adjustments are thus quite large by comparison with the transaction cost liquidity risk measures of the previous section. The assumption that the position is liquidated in equal parts during the liquidation period is not necessary. The body of work referenced above in Section 1 on optimal trade execution models the trade-off between minimizing transactions costs or adverse price impact and the risk of holding a position longer. Liquidity risk measures for normal markets A related measure of illiquidity, based entirely on the asset price itself is the proportion of days on which the settlement or closing price does not change.16 This measure can be used to identify securities in which transactions are infrequent and in which the likelihood of adverse price impact is therefore greater. Critical assessment of adverse price impact risk measures As a rule of thumb, the expression (2) is sensible: it merely estimates the additional market risk imposed by avoiding a disorderly liquidation. Its accuracy as a VaR adjustment, however, depends entirely on the accuracy of the estimate of T , and this is where the difficulty begins. There are a number of approaches: sometimes, it is either arrived at judgmentally by traders, but in actual practice it is generally estimated as T= position size , daily trading volume (3) with daily trading volume is averaged over some period of time, generally about a month. Alternatively, the position may be normalized by the outstanding amount of the security. This VaR adjustment measure assumes a link between ability to liquidate position and trading volume. However, the linkage confuses the relationship across securities between volume and ease of liquidation and the relationship over time for a given security between volume and ease of liquidation. The adverse price impact from buying or selling 500,000 shares of a security for which 10,000,000 shares are traded on a particular day will be smaller than for a security with a typical volume of 100,000 shares per day. But the fact that daily trading for a particular stock has gone from 5,000,000 to 10,000,000 shares does not necessarily indicate higher liquidity. Trading volume tends to rise during periods of market volatility. Table 5 displays the results of regressions of daily trading volume on the volatility of the closing price for 71 randomly selected components of the Standard and Poor’s 500, MidCap 400, and SmallCap 600 indexes. In most cases, the coefficient is both significant and positive. 16 The measure was introduced by Lesmond, Ogden and Trzcinka (1999) and applied to emerging markets by Bekaert, Harvey and Lundblad (2003). It is validated by showing that the zero-return count is correlated, at least in U.S. equity markets, with other measures such as the bid-ask spread. 51 52 Liquidity risk: current research and practice Normalizing the position size by a higher volume will lead to a lower estimate of T and thus a lower estimate of the adjustment to the position’s market VaR. Hence, by our key criterion of relevance, correlation of high liquidity to low asset price volatility, a trader’s intuition is likely to a better estimator of T than those based on (3). To see how misleading the measure can become, imagine the trading volume rises extremely sharply. The estimate of T would then shrink down to a very small number, effectively, one day or instantaneous liquidation. But it would be unusual if traders could readily liquidate positions on a day of unprecedentedly high volume. Further undermining the case for volume-based liquidity measures, there is little evidence that trading volume is associated with other liquidity measures. For example, Chordia et al. (2001) find very low and even negative correlations between volumes and bid-ask spreads for U.S. stocks. Volume-based liquidity measures take a crude approach to the impact of a market participant’s own trading on the behavior of other market participants. Moving even a very large position, relative to trading volume or the outstanding stock, can sometimes be achieved without adverse price impact if the trader can preserve anonymity in spite of the size of the trade. The market reaction will also be quite different depending on what kind of information the market feels is revealed by the trade. In practice, this issue is dealt with by assuming that the trader can trade up to some fixed fraction of average volume. For example, Almgren and Chriss (2000/2001) cite 10 percent of daily volume as a common rule-of-thumb limit, although limits of one-third or more can be observed. A final difficulty with volume-based liquidity measures is that trading volume or outstanding stock data are not generally available for all traded assets, as discussed in Section 2. In view of the preceding discussion, this may be a blessing in disguise. There are other drawbacks to this measure, regardless of how T is estimated: • Estimates of T are inherently misleading unless they can be updated quite frequently. The nominal amount of an asset that can be transacted within a given time frame is not related to recent trading volume in a fixed and mechanical way, but depends on market conditions. While these market conditions can be assessed by a trader, possibly with reference to daily volume or outstanding stock, they are unlikely to be persistent. While a trader can revise his views on market conditions all day long, it is not usually practicable to revise the parameters of risk measures, position by position, on a daily basis. Liquidity risk measures for normal markets • Trading volume fluctuates, sometimes widely, so there is no unambiguous measure of the denominator in (3). • This measure is difficult to backtest or validate, because, while trade volumes can be observed, one cannot observe if they come from dispersed or concentrated positions, and thus one cannot identify the relationship between liquidation and price impact over a span of days. For this reason, it is also difficult to find an optimal measure of daily trading volume to use in the denominator of (3). In principle, the preferred measure of adverse price impact is Kyle’s λ, discussed in Section (1) above, which measures the response of the asset price to size of an order. Kyle’s λ is difficult to estimate, since it is quite specific to a particular model. It has therefore served primarily as a metaphor. More importantly, it is a measure of intraday price impact, and is therefore closer to a tool for optimal trade execution than to a tool for risk management.17 The time-to-liquidate measure focuses on the ability to liquidate a position without adverse price impact in normal markets, since it employs a typical daily trading volume to estimate T . This relationship will not hold up in periods of market stress. There is considerable evidence that trading volume increases in times of high volatility (see Table 5 and Figure 4). Traders likely are less able to liquidate a large position without depressing the price at such times. Clearly, there is a relationship between the volume typically traded in a market and the amount of the security that can be traded without moving the price. But this relationship is likely to be quite fragile. It may be possible to trade a very large amount, relative to typical turnover, on a day when markets are calm and unaware of the trader’s transactions. The same trade may may induce a large change in price on a day when markets are volatile and the market guesses what the trader is up to. Hence, a market participant with a security position that is large relative to typically traded volumes can roughly capture the increased risk of holding part of the position for a longer period than desired, at least in normal markets. In more volatile or stressed markets, trading volume is likely to give a misleading signal that liquidity has increased, when in fact the potential for adverse price impact is greater. 17 Berkowitz (2000) provides a less theoretical framework for estimating adverse impact that is similar in spirit and provides estimates for a set of mutual funds. However, it is not amenable to general implementation, since for most securities, net investment flows cannot be readily observed. In a less theoretically specific framework, the relationship of the flow parameter to liquidity is less clear than in Kyle (1985)’s model. 53 54 Liquidity risk: current research and practice An alternative data source on which to base liquidity assessment is Amihud (2002)’s illiquidity ratio, the ratio of the absolute midprice return to trading volume: illiquidity ratiot = | ln Pt − ln Pt −1 | , trading volumet where Pt is the closing midprice. The illiquidity ratio is intended to capture the rate of price change per unit traded and can thus be thought of as a version of Kyle’s λ using daily rather than intraday data. The illiquidity ratio is less correlated with volatility than is trading volume (see Table 6) and can therefore be a valid measure of liquidity risk.18 3.3 From position liquidity to portfolio liquidity risk The standard measures just described are aimed at measuring the liquidity risk of a position. Even if these measures are reliable, there remain several aggregation issues in estimating portfolio liquidity risk. First, market risk must be aggregated with liquidity risk to arrive at the total, for one position, of the risk induced by fluctuations in asset prices, which we will call price risk. This can be done statistically for the transaction-cost risk estimates, which are based on a measurable quantity, the bid-ask spread, that moves randomly over time. The total price risk is given by (total price risk)2 = (market risk)2 + ρ · (transaction-cost risk)2 , where ρ is the correlation between log returns in the midprice and changes in the relative spread. The correlation for this measure can be estimated or assigned the conservative value of unity. This type of aggregation is not applicable to time-to-liquidate estimates for which the liquidity risk is embedded in the total price risk. The liquidity component for the latter measure, however, can 18 The reciprocal of the illiquidity ratio is, naturally enough, called the liquidity ratio. When the liquidity ratio is computed using an average of volume and returns over some interval, it is referred to as the Amivest liquidity ratio: Amivest liquidity ratiot = t trading volumet . t | ln Pt − ln Pt −1 | Conclusion: liquidity in normal and stressed markets be proxied by 1-day position VaR × (1 + T )(1 + 2T ) −1 . 6T Next, the the liquidity or total price risk of positions within an asset class, i.e. foreign exchange, equities, etc., and across asset classes must be aggregated. At this level of aggregation, there is much less guidance either from intuition or the measured correlation of the liquidity measures. In practice, portfolio liquidity risk is generally not estimated, except perhaps as a rule-of-thumb adjustment to market risk. Marrison, Stroughair and Schuermann (2000) provide guidance on how such an adjustment can be made, given an estimate of the time-to-liquidate or enforced holding period of the portfolio. 4 Conclusion: liquidity in normal and stressed markets In discussing current practice in measuring liquidity risk, we have emphasized that, at best, the standard measures can be accurate only in normal markets, and not in times of stress. They appear to have some value in normal markets in identifying assets that may be somewhat more difficult or costly to liquidate at the expected or equilibrium price. In normal markets, most assets have a fairly predictable degree of liquidity and work-off time for a standard size of transaction, and bid-ask spreads are steady. Under these conditions, the standard liquidity measures retain some validity. In crises, the standard measures will likely be useless. In stressed markets, the liquidity of almost all assets is impaired, bid-ask spreads widen, and it can be difficult to work off even a small order without adverse price changes. We can distinguish in this context between local liquidity, the liquidity of a particular market, and global liquidity. In normal markets, the market for a particular asset may become illiquid for some localized reasons. There are often shocks to individual markets that do not threaten any broader disruption. In crises, however, illiquidity can become global and endemic. Much of the concern about liquidity risk is in fact displaced concern about financial policy and risk management in the event of extreme moves in market prices or financial crises. This concern 55 56 Liquidity risk: current research and practice should therefore be addressed as part of an overall approach to risk management through extreme events. The standard liquidity risk measures we discussed in Section 3 may be reasonably accurate during normal times. However, during normal times, what they measure is not terribly important. At times of unusually large market moves, or at times when markets are particularly apprehensive, the standard measures are likely to be seriously inaccurate. But just at these times, liquidity risk is likely to become quite material. Liquidity risk should be treated as a part of managing the risk of extreme events. During periods of market stress, time of the essence. Market participants can use early warning signals to review stress tests, identify vulnerabilities, and make earlier liquidation and hedging decisions. In future work, we will discuss approaches to the measurement of the risk of extreme events, with particular attention to the role of warning signals. Option prices play a particularly important role in this context, because they are forward looking, are refreshed minute by minute in competitive markets, and are sensitive to subtle changes in expectations. Conclusion: liquidity in normal and stressed markets References Almgren, R. and Chriss, N. (2000/2001). Optimal execution of portfolio transactions, Journal of Risk 3(2): 5–39. Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects, Journal of Financial Markets 5(1): 31–56. Amihud, Y. and Mendelson, H. (1986). Asset pricing and the bid-ask spread, Journal of Financial Economics 17(2): 223–249. Bangia, A., Diebold, F. X., Schuermann, T. and Stroughair, J. D. (1999). Modeling liquidity risk with implications for traditional market risk measurement and management, Working Paper 99-06, Wharton Financial Institutions Center. <http://fic.wharton.upenn.edu/fic/papers/99/p9906.html>. Bank for International Settlements (1999a). Market liquidity: research findings and selected policy implications, Technical Report 12, Monetary and Economic Department, Basel. <http://www.bis.org/publ/cgfs12.pdf>. Bank for International Settlements (1999b). Part 1. Overview, Technical Report 11, Monetary and Economic Department, Basel. <http://www.bis.org/publ/cgfs12.pdf>. Bank for International Settlements (2001). The new Basel capital accord, Basel. <http://www.bis.org/publ/bcbsca03.pdf>. Bekaert, G., Harvey, C. R. and Lundblad, C. (2003). Liquidity and expected returns: lessons from emerging markets. <http://faculty.fuqua.duke.edu/~charvey/Research/Working_Papers/ W67_Liquidity_and_expected.pdf>. Berkowitz, J. (2000). Breaking the silence, Risk 13(10): 105–108. Biais, B., Glosten, L. and Spatt, C. (2002). The microstructure of stock markets. <http://www.idei.asso.fr/Commun/Articles/Biais/survey2002.pdf>. Blume, M. (2002). The structure of the U.S. equity markets, Brookings-Wharton Papers on Financial Services pp. 35–59. Board of Governors of the Federal Reserve System (1998). Trading and Capital-Markets Activities Manual. <http://www.bog.frb.fed.us/boarddocs/supmanual/trading/trading.pdf>. Board of Governors of the Federal Reserve System (2003). Bank Holding Company Supervision Manual. <http://www.federalreserve.gov/boarddocs/supmanual/bhc/bhc0603.pdf>. 57 58 Liquidity risk: current research and practice Chordia, T., Roll, R. and Subrahmanyam, A. (2001). Market liquidity and trading activity, Journal of Finance 56(2): 501–530. Counterparty Risk Management Policy Group (1999). Improving counterparty risk management practices, mimeo. Available at <http://www.isda.org/educat/pdf/CRMPG-Report6-99.pdf>, but appendices missing. Cross, S. Y. (1998). All about. . . the foreign exchange market in the United States, Federal Reserve Bank of New York, New York. <http://www.ny.frb.org/pihome/addpub/usfxm>. Demsetz, H. (1968). The Cost Of Transacting, Quarterly Journal of Economics 82(1): 33–53. Deutsche Bundesbank (1999). Grundsatz II über die Liquidität der Institute, Bankrechtliche Regelungen 2b, Frankfurt. <http://www.bundesbank.de/bank/download/pdf/grundsatzii.pdf>. Duffie, D. and Ziegler, A. (2003). Liquidation risk, Financial Analysts Journal 59(3): 42–51. Glosten, L. R. and Milgrom, P. R. (1985). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders, Journal of Financial Economics 14(1): 71–100. Group of Ten (1996). The resolution of sovereign liquidity crises. <http://www.bis.org/publ/gten03.pdf>. Harris, M. and Raviv, A. (1993). Differences of opinion make a horse race, Review of Financial Studies 6(3): 473–506. Jones, C. M. (2002). A century of stock market liquidity and trading costs. <http://www.columbia.edu/%7Ecj88/papers/century.pdf>. Kyle, A. S. (1985). Continuous auctions and insider trading, Econometrica 53(6): 1315–1335. Lesmond, D. A., Ogden, J. P. and Trzcinka, C. A. (1999). A new estimate of transaction costs, Review of Financial Studies 12(5): 1113–1141. Lo, A. W., Petrov, C. and Wierzbicki, M. (2003). It’s 11pm—do you know where your liquidity is? The mean-variance-liquidity frontier. <http://web.mit.edu/alo/www/Papers/liquid5.pdf>. Madhavan, A. (2000). Market microstructure: a survey, Journal of Financial Markets 3(3): 205–258. Madhavan, A. (2002). Market microstructure: a practitioner’s guide, Financial Analysts Journal 58(5): 28–42. Managed Funds Association (2003). 2003 Sound Practices for Hedge Fund Managers. <http://www.mfainfo.org/images/pdf/2003SoundPractices_forHedgeFundManagers.pdf>. Conclusion: liquidity in normal and stressed markets Marrison, C., Stroughair, J. D. and Schuermann, T. (2000). Changing regulatory capital to include liquidity and management intervention, Journal of Risk Finance 1(4): 47–54. Roll, R. (1984). A simple implicit measure of the effective bid-ask spread in an efficient model, Journal of Finance 39(4): 1127–1139. 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The economic function of futures markets, Cambridge University Press, Cambridge, UK. 59 60 Liquidity risk: current research and practice Appendix Table 1 Descriptive statistics on foreign exchange bid-ask spreads Exchange rate ARP AUD BRL CAD CHF CLP CZK DKK EGP EUR GBP HUF IDR ILS INR JPY KRW LKR MXN NGN NOK NZD PHP PKR PLN RUB SEK SGD SIT THB TRL TWD VEB ZAR (a) Spread 0.405 0.039 0.121 0.023 0.076 0.052 0.131 0.046 0.459 0.042 0.018 0.193 0.268 0.204 0.177 0.040 0.071 0.071 0.094 0.673 0.089 0.100 0.323 0.229 0.184 0.051 0.083 0.042 0.314 0.095 0.740 0.174 0.172 0.296 (b) Spread vol 0.160 0.022 0.060 0.013 0.024 0.018 0.080 0.015 0.196 0.015 0.010 0.058 0.247 0.052 0.052 0.013 0.108 0.035 0.032 0.465 0.037 0.066 0.121 0.150 0.056 0.021 0.034 0.011 0.131 0.038 0.396 0.129 0.024 0.146 (c) Currency vol 22.4 10.1 20.6 6.0 10.0 9.1 10.1 9.3 8.9 9.4 7.1 10.8 13.2 6.6 1.3 9.4 6.9 1.9 8.5 9.7 9.1 10.6 5.2 3.3 9.0 1.6 9.8 4 .4 9.7 4.3 22.9 2.9 20.0 16.5 (d) Kurtosis 16.49 2.90 4.45 2.25 1.94 11.12 70.28 0.71 0.81 0.55 4.98 12.01 12.56 8.96 1.15 1.99 12.69 6.24 2.23 4.43 3.29 4.16 30.07 −0.54 −0.09 1.84 1.55 6.69 26.21 8.88 14.06 −1.81 2.10 −0.11 (e) Skewness 3.42 1.70 1.59 1.58 0.98 2.59 6.19 0.51 −0.39 0.46 1.85 1.71 2.84 0.91 −1.73 0.61 3.10 1.98 0.13 2.04 1.23 1.75 2.73 0.59 0.24 1.45 0.95 1.54 4.54 2.12 3.21 −0.20 0.84 0.69 All data are full-sample statistics based on London close spot bid and ask exchange rates against U.S. dollar, 23Mar2001 to 28Jun2003. Column (a): mean relative spread, in percent; Column (b): mean daily volatility of the relative spread, in percent, computed using EWMA with a decay factor of 0.94; Column (c): mean annual exchange rate volatility, in percent, computed using EWMA with a decay factor of 0.94; Column (d): Coefficient of excess kurtosis of spread. Column (e): Coefficient of skewness of spread. Conclusion: liquidity in normal and stressed markets Table 2 Transactions liquidity and market risk in the foreign exchange market Exchange rate ARP AUD BRL CAD CHF CLP CZK DKK EGP EUR GBP HUF IDR ILS INR JPY KRW LKR MXN NGN NOK NZD PHP PKR PLN RUB SEK SGD SIT THB TRL TWD VEB ZAR (a) 99% spread risk 0.390 0.045 0.131 0.027 0.066 0.047 0.159 0.040 0.457 0.039 0.021 0.165 0.422 0.162 0.149 0.035 0.162 0.076 0.085 0.878 0.088 0.127 0.303 0.290 0.157 0.050 0.081 0.034 0.310 0.092 0.831 0.237 0.114 0.319 (b) 99% log return 3.15 1.48 2.97 0.88 1.46 1.32 1.48 1.35 1.29 1.37 1.04 1.57 1.92 0.97 0.20 1.37 1.00 0.28 1.23 1.41 1.33 1.54 0.76 0.49 1.31 0.24 1.42 0.64 1.41 0.63 3.29 0.42 2.85 2.39 (c) Ratio (a)/(b) 14.8 3.1 4.7 3.2 4.7 3.7 11.0 3.1 54.0 2 .9 2.1 10.9 22.9 20.0 83.5 2.6 18.4 49.3 7.5 76.4 6.9 8.4 43.0 82.4 12.9 24.7 5.9 5.7 22.1 16.1 23.9 71.3 20.9 13.4 All data are full-sample statistics based on London close spot bid and ask exchange rates against U.S. dollar, 23Mar2001 to 28Jun2003. Column (a): mean daily spread risk factor at a 99 percent confidence 1 level 2 (s + 2.33σs ), where s is the contemporaneous relative spread and σs the spread volatility, in percent; Column (b): mean forecast extreme daily log exchange rate return at a 99 percent confidence level 1 − e2.33σ , where σ is the historical currency volatility at a daily rate; Column (c): Ratio of column (a) to column (b), in percent. 61 62 Liquidity risk: current research and practice Table 3 Foreign exchange bid-ask spreads and volatility Exchange rate ARP AUD BRL CAD CHF CLP CZK DKK EGP EUR GBP HUF IDR ILS INR JPY KRW LKR MXN NGN NOK NZD PHP PKR PLN RUB SEK SGD SIT THB TRL TWD VEB ZAR (a) Coefficient 43.45 17.54 20.31 4.55 −2.85 4.47 1.70 −1.44 −2.49 1.36 6.80 12.81 25.84 −10.20 3.61 1.81 −2.94 32.93 1.90 4.84 4.50 7.30 16.33 18.97 2.35 4.72 0.39 −3.04 4.06 −0.24 56.52 −1.29 13.95 19.85 (b) (c) ¯ p -value R 2 0.00 0.76 0.00 0.33 0.00 0.40 0.00 0.03 0.00 0.01 0.00 0.03 0.09 0.00 0.15 0.00 0.01 0.01 0.18 0.00 0.00 0.07 0.00 0.21 0.00 0.52 0.00 0.14 0.00 0.02 0.07 0.00 0.00 0.01 0.00 0.64 0.06 0.00 0.00 0.04 0.00 0.03 0.00 0.08 0.00 0.30 0.00 0.37 0.02 0.01 0.00 0.03 0.69 −0.00 0.00 0.01 0.00 0.02 0.81 −0.00 0.00 0.84 0.20 0.00 0.00 0.24 0.00 0.39 All data based on spot bid and ask London close exchange rates against U.S. dollar, 23Mar2001 to 28Jun2003. Results of regression of daily 1 spread risk factor at a 99 percent confidence level 2 (s + 2.33σs ), where s is the contemporaneous relative spread and σs the spread volatility, on daily exchange rate volatility. Column (a): regression coefficient of spread risk factor; Column (b): p -value for significance test on the regression coefficient; Column (c): adjusted R 2 of the regression. Conclusion: liquidity in normal and stressed markets Table 4 Full sample statistics on equity trading volume Company AK Steel Hldg Alcoa Allstate American Express Amsouth BanCorporation AT&T Becton Dickinson Boeing Borders Group Caterpillar Cigna Citigroup Citizens Communications City National Coca-Cola Colonial Properties Trust Computer Sciences Corning Deere & Company Delta Air Lines Dole Food Downey Financial DST Systems Dupont EI De Nemours Eastman Kodak Eaton Vance Engelhard Exxon Mobil Fairchild General Electric General Motors Great Atlantic & Pacific Harris HCA Hewlett-Packard Home Depot Honeywell Intl Hormel Foods Intl Business Machines Intl Paper John H Harland Johnson And Johnson JP Morgan Chase & Co Kinder Morgan Kroger Laclede Group Lehman Brothers Hldg Lucent Technologies MBNA McDonalds Merck & Company Mean 360.1 2369.2 2136.7 2796.4 595.9 9791.8 841.7 3192.1 384.2 1513.2 763.1 9666.5 587.4 158.4 3663.9 56.7 973.7 3857.3 1015.0 1030.0 215.6 68.5 235.7 2656.1 1538.9 93.8 364.2 5167.8 54.7 9930.7 2732.2 117.4 357.0 2201.1 4813.1 5811.8 2711.0 191.0 7429.4 1946.3 85.7 3636.8 5704.0 427.5 2569.4 19.0 1386.7 13575.7 2371.3 3959.2 5006.9 Min 3.4 262.2 256.8 306.5 38.0 1222.3 111.2 521.6 12.2 234.8 97.3 754.5 28.3 4.2 426.4 3.4 133.2 109.1 89.1 67.0 15.2 1.2 3.9 421.7 266.7 0 .8 19.5 692.5 0.9 917.3 401.3 7.4 35.3 240.9 567.8 682.5 310.7 16.6 1392.4 170.7 1.1 542.5 476.2 7.8 261.8 1.2 38.1 1204.4 373.4 544.4 1032.6 Max 6731 11325 15049 29188 12906 58120 7879 27790 11196 7948 26638 101034 19426 1536 15836 1077 19176 138551 5766 15056 6464 1644 3066 15001 15904 2375 9485 32133 1325 68902 19648 2255 5621 24315 43834 51387 70989 1085 50716 9489 2173 37760 37429 15431 37879 455 7326 136847 55817 28040 26791 S.D. Skewness Kurtosis 75.0 0.21∗∗ 2.19∗∗ 39.9 0.15∗ 1.13∗∗ 42.3 0.35∗∗ 1.65∗∗ 37.1 0.16∗ 0.95∗∗ 56.1 0.25∗∗ 1.74∗∗ 37.8 0.32∗∗ 1.89∗∗ 48.3 0.29∗∗ 1.60∗∗ 39.8 0.62∗∗ 3.30∗∗ 62.1 0.20∗∗ 1.06∗∗ 40.1 0.36∗∗ 1.20∗∗ 45.4 0.62∗∗ 3.72∗∗ 36.2 0.38∗∗ 2.52∗∗ 59.0 0.24∗∗ 1.52∗∗ 62.8 0.13∗ 0.98∗∗ 36.3 0.13∗ 1.76∗∗ 74.2 −0.12∗ 2.72∗∗ 49.8 0.47∗∗ 1.73∗∗ 48.9 0.28∗∗ 1.11∗∗ 45.1 0.34∗∗ 1.12∗∗ 47.1 0.30∗∗ 1.04∗∗ 66.4 0.28∗∗ 1.75∗∗ 80.8 0.14∗ 0.93∗∗ 64.4 0.20∗∗ 0.91∗∗ 37.8 0.32∗∗ 2.73∗∗ 46.3 0.61∗∗ 2.63∗∗ 71.5 0.18∗∗ 2.50∗∗ 55.6 0.15∗ 1.19∗∗ 31.3 0.06 2.17∗∗ 92.9 0.10 1.16∗∗ 32.7 0.07 2.10∗∗ 39.1 0.16∗ 1.36∗∗ 66.0 0.06 1.27∗∗ 56.2 0.25∗∗ 0.89∗∗ 52.5 0.44∗∗ 2.06∗∗ 39.3 0.35∗∗ 1.67∗∗ 39.1 0.43∗∗ 2.65∗∗ 44.3 0.40∗∗ 2.19∗∗ 66.1 −0.04 0.73∗∗ 36.2 0.35∗∗ 1.72∗∗ 40.3 0.27∗∗ 0.71∗∗ 81.6 0.14∗ 1.42∗∗ 35.4 0.07 1.68∗∗ 38.0 0.35∗∗ 2.45∗∗ 73.3 0.36∗∗ 2.12∗∗ 47.2 0.38∗∗ 2.22∗∗ 71.6 −0.10 1.03∗∗ 45.8 0.20∗∗ 1.24∗∗ 40.0 0.74∗∗ 3.80∗∗ 45.6 0.56∗∗ 5.09∗∗ 40.6 0.25∗∗ 1.28∗∗ 35.5 0.32∗∗ 2.08∗∗ continued on next page 63 64 Liquidity risk: current research and practice continued from previous page Company Mylan Laboratories New Jersey Resources New Plan Excel Realty Trust OGE Energy Hldg Omnicom Group Oneok New Pentair Philip Morris Companies Plantronics PNC Financial Services Group Proctor & Gamble SBC Communications Sierra Pacific Resources Snap-On Superior Industries Intl Temple Inland United Technologies Wal-Mart Stores Walt Disney Whirlpool Mean 664.6 24.8 159.4 172.5 872.6 97.9 144.5 5652.0 145.0 811.2 2690.8 4359.7 305.2 193.2 92.1 281.3 1773.3 6084.3 5235.0 430.9 Min 75.6 1.8 15.9 7.8 73.5 8.4 5.7 759.5 0 .2 85.3 256.1 615.6 9.5 19.1 6.2 27.6 130.4 1351.0 538.5 9.8 Max 7464 718 4773 2726 27183 3515 2618 32024 4465 12586 51366 21470 17820 2252 2001 3334 18263 19024 51767 4708 S.D. Skewness 58.3 0.50∗∗ 71.2 0.14∗ 57.3 0.34∗∗ 78.3 −0.03 49.9 0.24∗∗ 54.2 0.15∗ 72.9 0.09 30.4 0.22∗∗ 83.2 −0.03 46.2 0.31∗∗ 38.1 0.87∗∗ 35.1 0.11 77.1 0.10 53.0 0.33∗∗ 64.3 0.04 52.4 0.15∗ 41.0 0.24∗∗ 35.6 0.11 37.8 0.39∗∗ 51.6 0.25∗∗ Kurtosis 1.67∗∗ 1.93∗∗ 1.83∗∗ 2.37∗∗ 1.14∗∗ 1.18∗∗ 1.23∗∗ 5.16∗∗ 4.25∗∗ 2.90∗∗ 6.48∗∗ 1.87∗∗ 1.68∗∗ 1.22∗∗ 1.10∗∗ 0.76∗∗ 2.14∗∗ 1.31∗∗ 1.93∗∗ 0.91∗∗ Mean, Max, and Min: average, smallest and largest daily trading volume during sample period, in thousands of shares. S.D., Skewness, and Kurtosis: standard deviation, skewness and excess kurtosis coefficient of logarithmic changes in daily trading volume. * Significant at 0.975 confidence level. ** Significant at 0.99 confidence level. Conclusion: liquidity in normal and stressed markets Table 5 Equity trading volume and volatility Company AK Steel Hldg Alcoa Allstate American Express Amsouth BanCorporation AT&T Becton Dickinson Boeing Borders Group Caterpillar Cigna Citigroup Citizens Communications City National Coca-Cola Colonial Properties Trust Computer Sciences Corning Deere & Company Delta Air Lines Dole Food Downey Financial DST Systems Dupont EI De Nemours Eastman Kodak Eaton Vance Engelhard Exxon Mobil Fairchild General Electric General Motors Great Atlantic & Pacific Harris HCA Hewlett-Packard Home Depot Honeywell Intl Hormel Foods Intl Business Machines Intl Paper John H Harland Johnson And Johnson JP Morgan Chase & Co Kinder Morgan Kroger Laclede Group Lehman Brothers Hldg Lucent Technologies MBNA McDonalds Merck & Company ¯ Coefficient p -value R2 6.92 0.00 0.03 8.60 0.00 0.05 3.54 0.00 0.01 −3.76 0.00 0.01 3.40 0.00 0.01 9.02 0.00 0.05 5.24 0.00 0.02 −0.56 0.57 −0.00 9.13 0.00 0.05 0.13 0.89 −0.00 3.58 0.00 0.01 10.59 0.00 0.07 3.79 0.00 0.01 3.46 0.00 0.01 2.78 0.01 0.00 −3.05 0.00 0.01 2.64 0.01 0.00 19.02 0.00 0.20 0.39 0.69 −0.00 8.57 0.00 0.05 −1.55 0.12 0.00 2.91 0.00 0.01 9.03 0.00 0.05 −1.47 0.14 0.00 3.53 0.00 0.01 3.97 0.00 0.01 −0.76 0.45 −0.00 3.30 0.00 0.01 3.68 0.00 0.01 15.82 0.00 0.14 6.12 0.00 0.02 5.63 0.00 0.02 2.29 0.02 0.00 −2.99 0.00 0.01 6.83 0.00 0.03 7.75 0.00 0.04 5.57 0.00 0.02 1.63 0.10 0.00 −2.53 0.01 0.00 3.64 0.00 0.01 0.19 0.85 −0.00 −2.23 0.03 0.00 9.97 0.00 0.06 2.36 0.02 0.00 8.00 0.00 0.04 6.45 0.00 0.03 1.94 0.05 0.00 16.55 0.00 0.16 3.25 0.00 0.01 1.31 0.19 0.00 0.03 0.98 −0.00 continued on next page 65 66 Liquidity risk: current research and practice continued from previous page Company Mylan Laboratories New Jersey Resources New Plan Excel Realty Trust OGE Energy Hldg Omnicom Group Oneok New Pentair Philip Morris Companies Plantronics PNC Financial Services Group Proctor & Gamble SBC Communications Sierra Pacific Resources Snap-On Superior Industries Intl Temple Inland United Technologies Wal-Mart Stores Walt Disney Whirlpool Coefficient 1.05 7.10 3.00 5.35 10.08 5.70 6.51 3.69 16.96 2.09 6.19 11.33 11.18 4.39 4.78 2.36 1.80 2.73 4.08 1.43 p -value 0.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.02 0.07 0.01 0.00 0.15 ¯ R2 0.00 0.03 0.01 0.02 0.06 0.02 0.03 0.01 0.16 0.00 0.02 0.08 0.08 0.01 0.01 0.00 0.00 0.00 0.01 0.00 Results of regression of trading volume on daily share price volatility. Column (a): regression coefficient of spread risk factor; Column (b): p -value for significance test on the regression coefficient; Column (c): adjusted R 2 of the regression. Conclusion: liquidity in normal and stressed markets Table 6 Equity illiquidity ratio and volatility Company AK Steel Hldg Alcoa Allstate American Express Amsouth BanCorporation AT&T Becton Dickinson Boeing Borders Group Caterpillar Cigna Citigroup Citizens Communications City National Coca-Cola Colonial Properties Trust Computer Sciences Corning Deere & Company Delta Air Lines Dole Food Downey Financial DST Systems Dupont EI De Nemours Eastman Kodak Eaton Vance Engelhard Exxon Mobil Fairchild General Electric General Motors Great Atlantic & Pacific Harris HCA Hewlett-Packard Home Depot Honeywell Intl Hormel Foods Intl Business Machines Intl Paper John H Harland Johnson And Johnson JP Morgan Chase & Co Kinder Morgan Kroger Laclede Group Lehman Brothers Hldg Lucent Technologies MBNA McDonalds Merck & Company ¯ Coefficient p -value R2 −1.50 0.13 0.00 −0.01 0.99 −0.00 5.00 0.00 0.02 −0.20 0.84 −0.00 −1.53 0.13 0.00 −1.40 0.16 0.00 2.92 0.00 0.01 2.06 0.04 0.00 −0.28 0.78 −0.00 1.80 0.07 0.00 −1.76 0.08 0.00 −3.04 0.00 0.01 1.09 0.27 0.00 3.45 0.00 0.01 5.69 0.00 0.02 8.88 0.00 0.05 −1.11 0.27 0.00 −12.99 0.00 0.10 2.49 0.01 0.00 0.38 0.70 −0.00 5.01 0.00 0.02 −0.39 0.70 −0.00 −4.91 0.00 0.02 4.33 0.00 0.01 −0.28 0.78 −0.00 −0.37 0.71 −0.00 3.17 0.00 0.01 1.36 0.18 0.00 3.04 0.00 0.01 −9.45 0.00 0.06 1.69 0.09 0.00 1.96 0.05 0.00 0.40 0.69 −0.00 7.53 0.00 0.04 −0.73 0.47 −0.00 3.70 0.00 0.01 −5.67 0.00 0.02 3.46 0.00 0.01 6.42 0.00 0.03 −0.23 0.82 −0.00 2.41 0.02 0.00 2.65 0.01 0.00 0.70 0.49 −0.00 −3.39 0.00 0.01 −3.00 0.00 0.01 −1.72 0.09 0.00 2.30 0.02 0.00 −0.60 0.55 −0.00 4.92 0.00 0.02 5.53 0.00 0.02 2.98 0.00 0.01 continued on next page 67 68 Liquidity risk: current research and practice continued from previous page Company Mylan Laboratories New Jersey Resources New Plan Excel Realty Trust OGE Energy Hldg Omnicom Group Oneok New Pentair Philip Morris Companies Plantronics PNC Financial Services Group Proctor & Gamble SBC Communications Sierra Pacific Resources Snap-On Superior Industries Intl Temple Inland United Technologies Wal-Mart Stores Walt Disney Whirlpool Coefficient 2.38 −1.68 −2.99 −0.36 −3.82 −3.38 −7.97 2.90 −12.48 0.74 2.30 −3.54 −8.00 2.39 −1.75 0.29 4.39 7.44 1.03 1.39 ¯ p -value R2 0.02 0.00 0.09 0.00 0.00 0.01 0.72 −0.00 0.00 0.01 0.00 0.01 0.00 0.04 0.00 0.01 0.00 0.10 0.46 −0.00 0.02 0.00 0.00 0.01 0.00 0.04 0.02 0.00 0.08 0.00 0.78 −0.00 0.00 0.01 0.00 0.04 0.30 0.00 0.16 0.00 Results of regression of illiquidity ratio on daily share price volatility. Column (a): regression coefficient of spread risk factor; Column (b): p -value for significance test on the regression coefficient; Column (c): adjusted R 2 of the regression. Liquidity risk: current research and practice Figure 1 Data discreteness in the foreign exchange bid-ask spread A. Euro 0.0010 0.0008 0.0006 0.0004 0.0002 Jul00 Jan01 Jul01 Jan02 Jul02 Jan03 Jul03 Jul02 Jan03 Jul03 B. Mexican peso 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 Jul00 Jan01 Jul01 Jan02 Bid-ask spread in currency units. The tick size or pip is 10−4 dollars for Euro-dollar and10−3 pesos for dollar-Mexican peso. 69 70 Liquidity risk: current research and practice Figure 2 Spread and price volatility in the foreign exchange market A. Euro " return volatility H%L 1.000 3.00 2.50 0.750 2.00 0.500 1.50 Feb00 Spread risk factor HbpL # Aug00 Feb01 1.00 Aug01 Feb02 Aug02 Feb03 B. Mexican peso 1.00 " return volatility H%L 5.5 Spread risk factor HbpL # 4.5 0.75 3.5 0.50 2.5 1.5 0.25 Feb00 Aug00 Feb01 Aug01 Feb02 Aug02 Feb03 Volatility of exchange rate midprice in percent; volatility of relative bid-ask spread in basis points. Liquidity risk: current research and practice Figure 3 Spread behavior in the Brazilian real market A. Spread risk factor 4.00 20 3.00 15 " return volatility H%L 2.00 1.00 Feb00 Aug00 Feb01 Aug01 10 Spread risk factor HbpL # Feb02 Aug02 5 Feb03 B. Relative spread 4.00 Spread HbpL # 3.00 " return volatility H% L 2.00 1.00 60 50 40 30 20 10 Feb00 Aug00 Feb01 Aug01 Feb02 Aug02 Feb03 Volatility of exchange rate midprice in percent; volatility of relative bid-ask spread in basis points. Bid-ask spread in currency units. 71 72 Liquidity risk: current research and practice Figure 4 Trading volume and price volatility A. General Motors 100 Daily volume H∏105 L # 90 80 70 60 50 40 " Volatility Hann. % L 200 175 150 125 100 75 30 50 20 25 10 Jul97 Jan98 Jul98 Jan99 Jul99 Jan00 Jul00 Jan01 Jul01 Jan02 Jul02 Jan03 B. Lucent Technologies Daily volume H∏106 L # 150 125 100 75 50 150 125 100 " Volatility Hann. % L 25 75 50 25 Jul97 Jan98 Jul98 Jan99 Jul99 Jan00 Jul00 Jan01 Jul01 Jan02 Jul02 Jan03 ...
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This note was uploaded on 02/20/2012 for the course ECON 203 taught by Professor Wood during the Spring '12 term at London Business School.

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