• If we assume that daily changes in the bid-ask spread are normally distributed, The 99% confidence interval on the transactions cost in dollars is:<

  where

  \(\pm \overline{P} \times \frac{1}{2} \left(\overline{s} + 2.33\sigma_s\right)\)

  \(\overline{P}\) = an estimate of the next day asset midprice, usually set to 𝑃, the most recent price

  \(\overline{s}\) = expected or typical bid-ask spread calculated as: (ask price — bid price) / midprice

  observation

  \(\overline{s}\) = expected or typical bid-ask spread calculated as: (ask price — bid price) / midprice

  \(\sigma_s\) = sample standard deviation of the spread

  The \(\overline{s} + 2.33\sigma_s\) component is known as the 99% spread risk factor.

• A tool for measuring the risk of adverse price impact is liquidity-adjusted (VaR). The starting point 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 day, the trader faces a one-day holding period on the entire position, a two-day holding period on a fraction \(\frac{T – 1}{T}\) of the position, a three-day holding period on a fraction \(\frac{T – 2}{T}\) of the position, and so forth if he wishes to liquidate the position with no adverse price impact. The 1-day position (VaR) adjusted by the square root of time is estimated for a given position as:

  \(\text{VaR}_t \times \sqrt{T}\)

  But this formula overstates (VaR) for positions that are liquidated over time because there is an implicit assumption that the whole position is held for (T) days. The following formula can be used to account for the liquidation over a period of days.

 

\(\text{VaR}_t \times \sqrt{\frac{(1 + T) \times (1 + 2T)}{6T}}\)

Characteristics Of Market Liquidity

• A standard set of characteristics of market liquidity, focusing primarily on asset liquidity, helps to understand the causes of illiquidity:
  • 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 is 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.

• Lack of liquidity manifests itself in these observable, if hard-to-measure ways:
  • Bid-ask spread – If the bid-ask spread were a constant, then going long at the offer and short at the bid would be a predictable cost of doing the trade. However, the bid-ask spread can fluctuate widely, introducing a risk.
  • Adverse price impact is the impact on the equilibrium price of the trader’s own activity.
  • Slippage is the deterioration in the market price induced by the amount of time it takes to get a trade done. If prices are trending, the market can go against the trader, even if the order is not large enough to influence the market.

    These characteristics, and particularly the latter two, are hard to measure, making empirical work on market liquidity difficult. Data useful for the study of market microstructure, especially at high-frequency, are generally sparse. Bid-ask spreads are available for at least some markets, while transaction volume data is more readily available for exchange-traded than for (OTC) securities.

Funding Liquidity Management For Hedge Funds

• Hedge funds have a number of sources of liquidity that can be monitored as part of overall risk management:
  1. Cash provides unfettered liquidity. It can be held in the form of money market accounts or Treasury bills. Excess cash balances with brokers and money market accounts are not entirely riskless and therefore are not perfectly liquid. Broker balances carry with them the counterparty risk of the broker; in the event the broker fails, the cash balances will be immobilized for a time and only a fraction may ultimately be paid out. Money market funds, as was demonstrated during the subprime crisis, may suspend redemptions or “break the buck” and pay out at less than 100 percent of par.
  2. Unpledged assets (or assets “in the box”) are unencumbered assets not currently used as collateral. They are generally also held with a broker, who in this case is acting only as a custodian and not as a credit provider. This source of liquidity is limited by the price volatility of the assets and the ability to use the assets as collateral. Unpledged assets can be sold, rather than pledged, to generate liquidity. However, in times of market stress, asset prices are far lower than their fair values.
  3. Unused borrowing capacity on pledged assets can be used to finance additional positions. Like unpledged assets, this form of liquidity is not unfettered. Rather, it is subject to revocation by counterparties, who may raise haircuts or decline to accept the securities as collateral when the time comes to roll over a collateralized securities loan. Since most of these collateralized loans are very short term, credit can disappear rapidly. This occurred for many lower-quality forms of collateral during the subprime crisis.
• However, a systemic risk event, in which hedge fund investments are regarded as potential sources of liquidity by investors, will be a challenge even for the most effective liquidity risk management. We referred to this phenomenon earlier in this chapter: Many hedge funds that had not experienced large losses received redemption requests for precisely that reason from investors who were themselves seeking liquidity.

Liquidity

• The term “liquidity” has been defined in myriad ways that ultimately boil down to two properties: transaction liquidity, a property of assets or markets, and funding liquidity, which is more closely related to credit-worthiness.
  • Transaction liquidity is the property of an asset being easy to exchange for other assets. Most financial institutions are heavily leveraged; that is, they borrow heavily to finance their assets, compared to the typical non financial firm.
  • Funding liquidity is the ability to finance assets continuously at an acceptable borrowing rate. For financial firms, many of those assets include short positions and derivatives.

Liquidity Risk

• As with “liquidity,” the term “liquidity risk” is used to describe distinct but related phenomena:
• 1. Transaction liquidity risk is the risk of moving the price of an asset adversely in the act of buying or selling it. Transaction liquidity risk is low if assets can be liquidated or a position can be covered quickly, cheaply, and without moving the price “too much.” An asset is said to be liquid if it is “near” or a good substitute for cash. An asset is said to have a liquidity premium if its price is lower and expected return higher because it isn’t perfectly liquid. A market is said to be liquid if market participants can put on or unwind positions quickly, without excessive transaction costs and without excessive price deterioration.
  2. Balance sheet risk or funding liquidity risk is the risk that creditors either withdraw credit or change the terms on which it is granted in such a way that the positions have to be unwound and/or are no longer profitable. Funding liquidity can be put at risk because the borrower’s credit quality is, or at least perceived to be, deteriorating, but also because financial conditions as a whole are deteriorating.
  3. Systemic risk refers to the risk of a general impairment of the financial system. In 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.

• These types of liquidity risks interact. For example, if a counterparty increases collateral requirements or otherwise raises the cost of financing a long position in a security, the trader may have to unwind it before the expected return is fully realized. By shrinking the horizon of the trade, the deterioration of funding liquidity also increases the transaction liquidity risk. The interaction also works the other way. If a leveraged market participant is perceived to have illiquid assets on its books, its funding will be in greater jeopardy.

Funding Liquidity Risk – Maturity Transformation

• Funding liquidity risk arises for market participants who borrow at short term to finance investments that require a longer time to become profitable. The balance-sheet situation of a market participant funding a longer-term asset with a shorter-term liability is called a maturity mismatch.
• Managing maturity mismatches is a core function of banks and other financial intermediaries. All financial and economic investment projects take time, in some cases a very long time, to come to fruition. To provide the needed capital, financial intermediaries effect a maturity transformation and possibly also a liquidity transformation; they obtain shorter-term funding and provide longer-term funding to finance projects. Funding longer-term assets with longer-term debt is called matched funding.
• Intermediaries engage in maturity mismatch because it is generally profitable. The most “expensive” capital is equity because it takes the most risk; it has no contractually stipulated remuneration and is the first liability to bear losses. At the other end of the spectrum, short-term debt instruments generally have lower required returns and contribute less to the cost of capital, as long as the borrower’s credit risk is perceived to be low.
• The spread between the interest intermediaries pay (their funding cost) and the interest they earn is called the net interest margin. Yield curves are typically upward sloping. Intermediaries therefore have a powerful incentive to introduce maturity mismatches into their balance sheets. In the aftermath of economic downturns and financial crises, the yield curve typically has a sharper upward slope, increasing net interest margin, which becomes an important part of banks’ rebuilding following the downturn.
• Because short-term rates are generally lower than long-term rates, there is a powerful incentive to borrow short-term if possible. Funding long-term assets with short-term debt exposes an intermediary to rollover risk, the risk that the short-term debt cannot be refinanced, or can be refinanced only on highly disadvantageous terms. In a rollover risk event, cash flow can become negative.
• Funding conditions can change rapidly. After a long period of short-term funding with positive cash flow, a firm can suddenly find itself in a negative cash flow situation from which there is no obvious escape if short-term funding is suddenly closed to it or its costs escalate. Because of this binary character, rollover risk is sometimes called “cliff risk.”

Funding Liquidity Risk – Liquidity Transformation

• Intermediaries earn net interest margin from maturity transformation because short-term debt generally carries lower interest than longer-term debt. Very short-term yields (or money-market rates) are almost invariably lower. However, the short-term funding of an intermediary is the short-term asset of the lender and may provide liquidity and payment services to the investor, as well as a flow of interest payments. Money-market instruments, such as short-term interbank loans to sound banks, commercial paper of creditworthy issuers, repos with adequate haircuts, and government bills, are not generally classified as money but have certain characteristics of money. They can be readily exchanged for cash and roll off into cash within a short time. Short-term yields are lower because short-term debt partially satisfies the need for liquidity as well as having far less interest-rate risk.
• The major exception to this general observation is short-term interest rates on currencies in imminent danger of devaluation. Because a discrete depreciation causes an instantaneous capital loss to market participants long on the currency, short-term yields of currencies under pressure can rise to extremely high levels, limited only by uncertainty about whether and when the depreciation will take place.
• Some forms of very short-term debt can be very easily transferred to a third party: demand deposits and money market mutual fund (MMMF) liabilities. These types of debt have even lower yields than can be explained by their short maturities because of their usefulness as means of payment and settling debts. Providing liquidity and payment services contributes to intermediaries’ net interest margin. The liquidity and maturity transformations have made banks more efficient intermediaries.
• Nowadays, the money supply is defined to include certain nonbank liabilities, such as those of MMMFs, as well as banknotes and bank deposits. Their values don’t depend on interest rates, and they can be used to buy both goods and assets. To the extent that an asset has the characteristics of immediacy and certainty, they resemble money and are said to be liquid.
• With the introduction and growth of money market funds, an important new type of short-term asset that could be used as money was created. In the United States, retail MMMF balances are included in the M2 measure of the money supply, accounting for roughly 10 percent of the total. Institutional MMMF balances are about twice as large as retail but are not included in U.S. monetary aggregates.
• Market participants hold money not only to conduct transactions but also for speculative reasons. The speculative motive is a function of current asset prices, especially interest rates, uncertainty about future asset prices, and risk preferences. In times of financial crises, there are asset-price spirals in which market participants want to hold cash because they expect asset prices to be lower in the future, thus driving prices lower in fact.
• Interest rates fluctuate and affect the price even of short-term T-bills; hence, T-bills are not money. However, their interest-rate risk is very low, and they also have little or no credit risk, making them relatively liquid and close in character to money.
• In normal times, the desire for liquidity is counterbalanced by the zero or low yields earned by cash and liquid assets. In crises, risk-aversion and uncertainty are high, so market participants wish to hold a much larger fraction of their assets in liquid form and are relatively indifferent to the yield. The velocity of money declines drastically. Market participants prefer cash to money-market instruments and become abruptly more sensitive to even the relatively low credit and counterparty risk of instruments other than government bills.
• The core function of a commercial bank is to take deposits and provide commercial and industrial loans to nonfinancial firms. In doing so, it carries out liquidity, maturity, and credit transformation. It transforms long-term illiquid assets (loans to businesses) into short-term liquid ones, including deposits and other liabilities that can be used as money.
• Banks carry out their functions through operations on both sides of the balance sheet. Net interest margin is a crucial source of revenues. The balance sheet of a “classic bank,” that is, one chiefly reliant on deposits for funding, might look like this:
  
• Banks and similar intermediaries are depository institutions, that is, institutions that borrow from the public in the form of liabilities that must be repaid in full on demand, instantly, in cash, on a first-come, first-served basis. This is called the sequential service constraint, and contrasts sharply with bankruptcy, in which claims are paid pro rata.

Bank Liquidity – Liquidity Transformation By Banks

• Banks can also tap the broader capital markets and raise funds by issuing bonds, commercial paper, and other forms of debt. These sources of wholesale funding are generally of longer term than deposits, which can be redeemed at short notice. However, deposits are considered “sticky.” Depositors tend to remain with a bank unless impelled to switch by a life change, such as moving house; bankers joke that depositors are more apt to divorce than remove deposits. Depositors are also a naturally diversified set of counterparties, so a large deposit base reduces reliance on a small number of lenders.
• Shorter-term forms of wholesale funding, such as commercial paper, are less reliable and potentially more concentrated sources of longer-term liquidity than a solid deposit base. These funding decisions are nowadays heavily influenced by regulatory capital requirements, which can favor or disfavor some assets and thus influence their funding costs as liabilities.
• The borrowing firms invest the loan proceeds in physical and other capital. A span of time and many stages are needed before these projects produce goods and services that can be sold to repay the loans that finance them. Until then, the invested capital can be sold only at a loss, so the firms cannot, in general, repay the loans in full prior to maturity.
• The bank could borrow at a longer term to match the maturity of its assets, but this would reduce its net interest margin.
• The investments on the asset side of the bank’s balance sheet not only have longer terms to maturity than their liabilities, they are also less liquid; deposits, in contrast, are very close substitutes for cash. The liquidity transformation function of banks has been described as “turning illiquid assets into liquid ones.” However, this transformation depends on confidence in the bank’s solvency.
• Banks engage in asset-liability management (ALM), which is used for aligning available cash and short-term assets with expected requirements. A well-managed bank leaves an ample buffer of cash and highly liquid assets for unexpected redemptions of deposits and other funding.

Fragility Of Commercial Banking

• No asset-liability management system can protect a fractional-reserve bank against a bank run. This fragility can be mitigated through higher capital, which reduces depositors’ concern about solvency (the typical trigger of a run) and higher reserves, which reduce concern about liquidity. Historically, banks have also protected themselves through individual mechanisms, such as temporary suspension of convertibility, and collective mechanisms, such as clearing-houses.
• Apart from deposits, banks are generally dependent on short-term financing, exposing them to rollover risk events that, while less extreme than runs, can be costly or increase fragility. Commercial banks’ main source of funding is deposits, but they also rely on capital markets for much of the rest of their funding. Commercial paper is an important component of that.
• The commercial paper market in the immediate aftermath of the Lehman bankruptcy provides an example of how quickly funding conditions can change. Financial firms’ issuance of commercial paper had grown rapidly before 2007, as their leverage and balance-sheet expansion increased. The amount borrowed via commercial paper became more volatile but continued to grow, as banks sought to finance previously off-balance-sheet assets and credit lines they granted earlier were drawn upon. Eventually, commercial paper borrowing could no longer be placed.

Structured Credit And Off-Balance Sheet Funding

• Structured credit products do not face funding liquidity problems, as they are maturity matched. Asset-backed securities (ABS), mortgage-based securities (MBS), and commercial mortgage-based securities (CMBS) primarily carry out a credit and liquidity transformation rather than a maturity transformation. They can be viewed as providing matched funding for the assets in the collateral pool. The securities issued typically include at least some longer-term bonds.
• The way the securitization liabilities themselves are financed by investors can, however, introduce liquidity risk. The difficulties experienced by securitization have been related not only to the questionable credit quality of underlying assets such as real estate loans. Prior to mid-2008, the liabilities were held substantially by investors relying on short-term financing, increasing the fragility of the financial system.
• The short-term financing of securitizations played a crucial role in the subprime crisis and in the opaque increase in financial system leverage prior to the subprime crisis. Two types of short-term financing included:
  • Securities lending (i.e., applying structured credit products as collateral to short-term loans)
  • Off-balance sheet vehicles
• Like securitizations, off-balance-sheet vehicles are “robot companies” or special-purpose vehicles (SPVs), defined by their assets and liabilities. They issue asset-backed commercial paper (ABCP), which, in contrast to most commercial paper, is secured rather than unsecured debt. The two major types are:
• 1. Asset-backed commercial paper conduits purchase various types of assets, including securities as well as whole loans and leases, and finance the assets by issuing ABCP. They typically enjoy explicit credit and liquidity support from the sponsors in the form of credit guarantees and liquidity support should the conduit be unable to roll over the debt. Because of the guarantees, ABCP conduits generally have little equity.
  2. Structured investment vehicles (SIVs) are similar to ABCP conduits in some respects but differ in the crucial matter of credit and liquidity support. SIVs typically did not enjoy full explicit support by sponsors. They invested primarily in highly rated securitized credit products, and to a lesser extent in whole loans. Their funding mix was also generally somewhat different from that of ABCP conduits. In addition to ABCP, many SIVs issued medium-term notes (MTNs), which are at least somewhat less vulnerable to rollover risk. They also typically had larger equity cushions.

Special Purpose Vehicles

• In spite of their differences, the two types of vehicles were economically similar in many ways. Both types profited from the spread between the asset yields and the funding cost. Another similarity is their economic function of maturity and liquidity transformation. The assets in the vehicles have longer, and possibly much longer, maturities than the commercial paper with which they are funded. This is typical for a bank; indeed, this maturity intermediation is the essence of what a bank does. However, instead of carrying out this function on its own balance sheet, the sponsoring bank has been able to reduce its balance sheet and its regulatory capital while still deriving the economic benefits.
• The vehicles also carried out liquidity transformation, creating ABCP, which is not only a much shorter-term asset but, until the subprime crisis, was more liquid than the underlying assets in the conduit or SIV. The final step in the liquidity transformation was the purchase of ABCP and money-substitute creation by MMMFs.
• The use of these vehicles did not lead to bona fide risk transfer. Despite the fact that the vehicles were off-balance-sheet from an accounting and regulatory perspective, they contributed greatly to the leverage and fragility of the sponsors, largely banks.

Funding Liquidity Of Other Intermediaries

SECURITIES FIRMS

• Securities firms hold inventories of securities for sale, and finance them by borrowing at short term. The collapse of Bear Stearns in March 2008 was an extreme case of a securities firm’s lenders abruptly withdrawing credit. Bear Stearns, like other large broker-dealers, had relied to a large extent on short-term borrowing. Bear was particularly dependent on free cash deposits of the firm’s large base of brokerage and clearing customers, including many hedge funds. These cash deposits were often collateralized, but generally not by better-quality collateral. Hedge funds withdrew deposits – and their business – rapidly towards the end of Bear’s existence, in what was essentially a run. Bear also issued 𝑀𝑇𝑁𝑠 and commercial paper to fund its activities.

Funding Liquidity Of Other Intermediaries

MONEY MARKET MUTUAL FUNDS

• MMMFs provide instant liquidity for their investors by giving them the ability to draw on their accounts via checks and electronic bank transfers. MMMFs are designed to invest in money market securities of high credit quality with just a few weeks or months to maturity. In this design, the market and credit risks of the assets are low, but still material. They are similar to banks in that their investments are less liquid than their liabilities. The liabilities of an MMMF, however, are quite different from those of banks. The account holders’ claims are not first-priority unsecured debt, like those of bank depositors, but rather equity. A further structural feature is therefore required for these liabilities to become money substitutes.
• MMMFs use the amortized cost method, under the Securities and Exchange Commission’s (SEC) Rule 2a-7. According to this, MMMF assets do not have to be marked-to-market each day, as required for other types of mutual funds. This is because extremely short-term securities are not likely to revalue based on changes in interest rates and credit spreads. MMMFs set a notional value of each share equal to $1.00.
• The residual claim represented by the shares is paid the net yield of the money market assets, less fees and other costs. MMMF shares thereby become claims on a fixed nominal value of units, rather than proportional shares of an asset pool. This structure only works if market, credit, and liquidity risks are managed well. However, credit write-downs are possible, and net asset values (NAVs) can fall below $1.00. This is known as breaking the buck.
• Liquidity risk can also jeopardize the ability of an MMMF to maintain a $1.00 net asset value. In this respect, it is much like a classic commercial bank and similarly vulnerable to runs. If a high proportion of shareholders attempt to redeem their shares simultaneously under adverse market conditions, the fund may have to liquidate money market paper at a loss, forcing writedowns and potentially breaking the buck. An episode of this kind involving credit writedowns by an MMMF, the Reserve Fund, was an important event in the subprime crisis.

HEDGE FUNDS

• Hedge funds face liquidity risk throughout their capital structures, as their capital can be redeemed. Hedge funds permit investors to withdraw their funds at agreed intervals. Quarterly withdrawals are the rule, though some funds have annual and a very small number have monthly withdrawals. These withdrawal terms, colloquially called the “liquidity” of the fund, are generally subject to additional restrictions called “gates,” which permit a suspension or limitation of withdrawal rights if investors collectively request redemptions in excess of some limit.
• The potential extent of liquidity demands by investors is shown in the decline in assets under management by hedge funds during the subprime crisis; the decline in assets was a result of both investment losses and redemptions of capital. These redemptions hit not only those hedge funds experiencing losses but also hedge funds that were profitable or had low losses. Like other intermediaries, hedge funds also face short-term funding risk on their assets. Hedge funds typically have no access to wholesale funding and rely entirely on collateral markets, short positions, derivatives, and other mechanisms to take on leverage.

LBOs AND LEVERAGED LOANS

• LBOs (Leveraged Buyouts) are generally financed by large loans, called leveraged loans. As LBOs and private equity funds grew, leveraged loans became the dominant type, by volume, of syndicated loans, originated by banks but distributed to other investors and traded in secondary markets. Many leveraged loans became part of CLO (Collateralized Loan Obligation) pools, and tranches of CLOs were important in CDO (Collateralized Debt Obligation) pools. The shadow banking system and the “CDO machine” were important providers of funding to private equity and LBOs. Other corporate events, such as mergers and acquisitions, are also dependent on financing.
• The funding liquidity risk in corporate transactions is both idiosyncratic and systematic. Funding for a particular LBO or merger might fall through, even if the deal would otherwise have been consummated. However, funding conditions generally can change adversely. This occurred in mid-2007 as the subprime crisis took hold. Many LBO and merger deals fell apart as financing came to a halt. Banks also incurred losses on inventories of syndicated loans, called “hung loans,” that had not yet been distributed to other investors or into completed securitizations. As risk aversion and demand for liquidity increased, the appetite for these loans dried up, and their prices fell sharply.

MERGER ARBITRAGE HEDGE FUNDS

• Mergers typically result in an increase in the target acquisition price, though not usually all the way to the announced acquisition price, and in a decrease in the acquirer’s price, since the acquirer often takes on additional debt to finance the acquisition. Merger arbitrage exploits the remaining gap between the current and announced prices. The risk arises from uncertainty as to whether the transactions will be closed. In the early stages of the subprime crisis, merger arbitrage strategies generated large losses as merger plans were abandoned for lack of financing.
• Investors taking on exposure to such transactions are therefore exposed not only to the idiosyncratic risk of the deal but to the systematic risk posed by credit and funding conditions generally. This risk factor is hard to relate to any particular time series of asset returns. Rather, it is a “soft factor,” on which information must be gathered from disparate sources ranging from credit and liquidity spreads to quantitative and anecdotal data on credit availability.

CONVERTIBLE ARBITRAGE HEDGE FUNDS

• Convertible bond prices are generally only slightly lower than their theoretical prices based on the replicating portfolio of plain-vanilla equity options and bonds that should mimic the convert bonds’ values. Traders, many of them at hedge funds and dependent on credit extended by broker-dealers, take advantage of this gap to earn excess returns. The strategy is only attractive with leverage, as it has relatively low unlevered returns, but is generally also relatively low-risk given the arbitrage relationship between the convert bonds and the replicating portfolio.
• Convert returns do, however, have a systematic extreme-loss risk. When the financing becomes unavailable because of credit conditions in the economy, converts cheapen dramatically. This effect is compounded by redemptions from convertible-bond funds, compounding the funding liquidity problem with a market liquidity problem. These episodes of convertible bond illiquidity also illustrate the effect of concentrated positions. Convertible bonds have a limited “clientele” among investors. When the existing clientele develops an aversion to the product during a period of market stress, it is difficult to move the product smoothly into new hands without large price declines.
• This figure displays a measure of arbitrage opportunities in the convertible bond market: the cheapness of bonds to their theoretical replicating portfolios. At the height of the pre-crisis boom, the gap had not only disappeared but became negative. In a sense, investors were overpaying for the package in their search for yield. As the subprime crisis evolved, the positive discount to theoretical was first reestablished, and eventually widened to an unprecedented extent. Viewed from a different angle, under conditions of severe liquidity stress, even a large gap between convert bonds and their replicating portfolio did not bring arbitrage capital into the market.
  

OTHER PRODUCTS

• The clientele for securitized credit products had relied to a large extent on short-term finance via repo, SIVs (Structured Investment Vehicles), and other mechanisms. When financing for the SIVs disappeared, a new investor base for the bonds could not be established quickly, and spreads on securitized credit products widened dramatically.
• Like convert arbitrage, statistical arbitrage requires some degree of leverage for profitability. In August 2007, as the subprime crisis got underway, one of its first effects was on statistical arbitrage strategies. Curtailing the liquidity of these strategies caused losses and return volatility that were extremely far outside the range of historical experience. In fact, this episode was one of the first overt signs of how severe the crisis could potentially become.

Markets For Collateral

• Collateral markets are an important institutional element supporting the growth of nonbank intermediation. Participants in these markets include:
  • Firms such as life insurance companies may own portfolios of high-quality securities that can be used as collateral to borrow cash at the low interest rates applicable to well-collateralized loans. The motivation is to borrow cash at a low rate, which it can then reinvest, earning a spread.
  • Firms such as hedge funds have inventories of securities that they finance by pledging the securities as collateral. The motivation is to obtain financing of the portfolio at a lower rate than unsecured borrowing, if the latter is available at all.
  • Firms may have excess cash that they are willing to lend out at a low interest rate, as long as they are appropriately secured by collateral.

Economic Function Of Markets For Collateral

• There are two main purposes served by collateral markets.
• 1. First, they create the ability to establish leveraged long and short positions in securities. Without these markets, there would be no way to short a cash security; short positions could only be created synthetically.
  2. Second, collateral markets enhance the ability of firms to borrow money. In collateral markets, cash is just another—and not necessarily the primary—asset to be borrowed and lent, alongside securities of all types, hence the term “cash collateral.”

• Different forms of collateral markets serve different trading motivations, but these forms are economically so similar that no hard-and-fast distinctions can be drawn:
  1. Margin lending, the simplest form of a market for collateral, is primarily used by investors wishing to take leveraged long positions in securities, most often equities.
  2. Reverse repo transactions are often used to finance long positions in securities, typically bonds. Repo transactions, in contrast, are usually intended to borrow cash by owners of bonds. However, in some instances, a repo or reverse repo transaction is focused on the need of one counterparty to establish a long position in a particular security. An important example is the U.S. Treasury specials market, in which a scarcity arises of a particular bond. The mechanism by which the market is cleared is a drop in the implied interest rate for loans against a bond “on special,” which can become zero or even negative. Recently issued U.S. Treasury notes typically go on special when dealers sell them to customers prior to the issue date on a when-issued basis, and have underestimated the demand. Following the next U.S. government bond auction, when the bond is issued, the dealer must borrow it to deliver to the customer at a penalty rate, expressed in the cheap rate at which the dealer must lend cash collateral to borrow the security.
  3. Securities lending has typically been focused on the securities rather than the cash collateral, typically to establish short positions. In recent years, the focus of their use has shifted to borrowing cash collateral.
• Collateral markets bring owners of securities, such as institutional investors and insurance companies, into the financing markets. They lend their securities to earn extra return. Whether through repo or securities lending, they earn an extra return by making their securities available for other market participants to use as collateral.
• A crucial element in permitting bonds to serve as collateral is their credit quality.
• Credit-rating agencies are important participants in collateral markets because of the need for highly rated bonds. Conversely, awarding high ratings to lower-quality bonds added a large volume of collateral to these markets that evaporated almost overnight during the subprime crisis.
• These markets grew tremendously in volume in the years preceding the subprime crisis, as the range and amount of collateral that could be lent expanded.

Structure Of Markets For Collateral

• Firms can borrow or lend collateral against cash or other securities. A haircut ensures that the full value of the collateral is not lent. A haircut of 10 percent, for example, means that if the borrower of cash wants to buy $100 of a security, he can borrow only $90 from the broker and must put $10 of his own funds in the margin account by the time the trade is settled. Similarly, the lender of cash will be prepared to lend $90 against $100 of collateral.
• Borrowing may be at short term, such as overnight, or for longer terms. Overnight borrowing may be extended automatically until terminated. As the market value of the collateral fluctuates, variation margin may be paid. Most collateralized borrowing arrangements provide for such remargining. The total margin at any point in time, if adequate, provides a liquidation cushion to the lender. If, for example, the loan has a maturity of (or cannot be remargined for the duration of) one week, a 10 percent haircut ensures that the value of the securities held as collateral can fall 10 percent and still leave the loan fully collateralized. The variation margin protects the lender of cash against fluctuations in the value of the collateral.

Three Forms Of Markets For Collateral – Margin Loans

• Margin lending is lending for the purpose of financing a security transaction in which the loan is collateralized by the security. It is generally provided by the broker intermediating the trade, who is also acting as a lender. Margin lending is generally short term, but rolled over automatically unless terminated by one of the counterparties.
• The broker maintains custody of the securities in a street name account i.e., registered in the name of the broker rather than the owner. This makes it easier to sell securities in case it is required to meet margin calls. Also, securities in street name accounts can be used for lending to other customers for short sales. The broker borrows money in the money market by using the customers’ collateral, and that money is used to provide margin loans to customers. That margin loan is collateralized by the repledged customer collateral.
• In the US, initial haircuts on equity purchases are set at 50 percent by the Federal Reserve Board’s Regulation T (“Reg T”), but derivatives can be used to increase the amount implicitly borrowed. Many transactions occur outside U.S. jurisdiction in order to obtain lower haircuts. Cross-margin agreements generally involve transferring excess margin in one account to another account with insufficient margin, resulting in lower overall margin for the investor.

Three Forms Of Markets For Collateral – Repos

• Repurchase agreements or repos are matched pairs of the spot sale and forward repurchase of a security. Both the spot and forward price are agreed now, and the difference between them implies an interest rate. The collateralization of the loan is achieved by selling the security temporarily to the lender. The collateralization is adjusted for the riskiness of the security through the haircut.
• In recent decades, the range of collateral underlying repos has widened. At one time, repo lending could be secured only by securities with no or de minimis credit risk. A few decades ago, repo began to encompass high-yield bonds and whole loans, and more recently, structured credit products. It has been a linchpin of the ability of large banks and brokerages to finance inventories of structured credit products, facilitated also by extending high investment-grade ratings to the senior tranches of structured credit products such as ABS and CDOs.
• The mechanics of repo lending are similar to margin loans. Like margin lending, repo creates a straightforward liability on the economic balance sheet. However, under certain circumstances, such as back-to-back security lending and borrowing for customers, transactions can be combined so as to permit the gross economic exposure to remain off-balance-sheet.

Three Forms Of Markets For Collateral – Securities Lending

• In a securities lending transaction, one party lends a security to another in exchange for a fee, generally called a rebate. The security lender, rather than the borrower, continues to receive dividend and interest cash flows from the security. A common type of securities lending is stock lending, in which shares of stock are borrowed. Like repos, the collateral is enhanced by structuring the transaction as a sale.
• There are a few typical patterns of securities lending:
  • In a stock lending transaction, the source of securities is a large institutional investor in equities or a hedge fund. It is generally “born” on the broker’s balance sheet. The securities are already in a margin account when a customer indicates a desire to go short.
  • A typical fixed-income securities lending transaction aims to earn a spread between less- and more-risky bonds. It involves U.S. Treasury or agency bonds that can be used as collateral for a short-term loan at a rate lower than other money-market rates, and a low haircut.
• Much securities lending is carried out via agency securities lending programs, whereby a third party, usually a large broker-dealer, or a custodial bank with many institutional clients (e.g., State Street), intermediates between the lender and borrower of securities.

Gross And Net Leverage

• Gross leverage is defined as the sum of all the asset values, including cash generated by shorts or assets acquired with that cash, divided by capital. It can be thought of as the total “length” of the balance sheet divided by the capital.
• Net leverage is computed as the ratio of the difference between the market values of the long and short positions to the capital.
• The balance sheet alone will not tell the risk manager whether the short positions are risk-augmenting or risk-reducing. Other information in addition to the long and short leverage, such as VaR and stress test reports, or a qualitative examination, are needed. For this reason, in reporting leverage, long positions and short positions should be reported separately. Leverage reporting is important, but far from a complete view of the risks of a portfolio.

Derivatives And Leverage

• One motivation for market participants to use derivatives is as a means of increasing leverage. Although derivatives are generally off-balance-sheet items in standard accounting practice, they belong on the economic balance sheet, since they may have a large impact on returns. Each side of a derivatives contract is synthetically long or short an asset or risk factor. But the market values of derivative securities are not equal to the value of the underlying asset, or the riskiness of the positions. Therefore, their market values or (NPVs) are generally not the best values to represent them. Rather, for purposes of measuring economic leverage, we wish to find, for each type of derivative, a cash-equivalent market value. As with most issues around the measurement and interpretation of leverage, as much judgment as science is involved.
• Futures, forwards, and swaps are linear and symmetric in the underlying asset price and can be hedged statically. Therefore, the amount of the underlying that the derivatives contract represents is set once and for all at the initiation of the contract, even though the net present value ((NPV)) may vary over time. The cash-equivalent market value of futures, forwards, and swaps can be represented on an economic balance sheet by the market value of the underlying security, rather than the (NPV).
• Options have a nonlinear relationship to the underlying asset price and must be hedged dynamically. Therefore, the amount of the underlying that the derivatives contract represents varies over time. It can be fixed approximately at any point in time by the option delta, or by a delta-gamma approximation. In general, volatility is important in the value of an option, so option contracts cannot generally have a zero (NPV) at initiation. Rather, it has a market value that can be decomposed into an intrinsic value, which may be zero, and a time value, which is rarely zero.
• The cash-equivalent market value of options can be represented on an economic balance sheet by their delta equivalents rather than their market values. As the underlying price varies, the amount of the economic balance sheet exposure, and the leverage, will vary. Measured this way, the cash-equivalent market value doesn’t take the time value and volatility of the option into account, except insofar as it influences the option delta.
• Like margin arrangements, derivatives also generate counterparty credit risk.

Transactions Liquidity Risk

• An asset is liquid if it resembles money, in that it can be exchanged without delay for other goods and assets, and in that its value is certain. Most assets other than money do not completely share these characteristics of immediacy and certainty. They cannot be exchanged directly for other goods and assets, because we don’t live in a barter economy; only money can do that. Nonmoney assets must be sold or liquidated before they can be exchanged for other goods or assets. This takes at least some time, and the proceeds from the sale are uncertain to at least some extent.
• Transactions liquidity includes the ability to buy or sell an asset without moving its price. An order to buy an asset increases demand and causes its price to increase. The effect is usually small, but can be large when the order causes a large transitory imbalance between the demand and supply of the asset at the initial price. A market participant can thereby be locked into a losing position by lack of market liquidity.

Sources Of Transactions Liquidity Risk – Fundamentals

• 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. While processing may be a significant part of transaction costs, it is unlikely to contribute materially to liquidity risk. An 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 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.
• 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, or responses to non-fundamental signals such as recent returns (“liquidity” or “noise” traders) from those who recognize that the prevailing price is wrong (“information” traders). A dealer cannot be sure for which of these reasons he is being shown a trade and therefore needs to be adequately compensated for this “lemons” risk through the bid-ask spread. A dealer does, however, have the advantage of superior information about the flow of trading activity, and learns early if there is a surge in buy or sell orders, or in requests for two-way prices.
• 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.

Sources Of Transactions Liquidity Risk – Forms Of Fundamentals

• The four fundamentals just described take different forms in different types of market organization:
• In a quote-driven system, certain intermediaries, who may be dealers, market makers, or specialists, are obliged 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 and with the “buy side” in order to redistribute inventories of securities and reduce them overall. Quote-driven systems are typically found in (OTC) markets.
• 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, for example, 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. Order-driven systems are typically found on organized exchanges.

Transactions Cost

• If we assume that daily changes in the bid-ask spread are normally distributed, The 99% confidence interval on the transactions cost in dollars is:<

  where

  \(\pm \overline{P} \times \frac{1}{2} \left(\overline{s} + 2.33\sigma_s\right)\)

  \(\overline{P}\) = an estimate of the next day asset midprice, usually set to 𝑃, the most recent price

  \(\overline{s}\) = expected or typical bid-ask spread calculated as: (ask price — bid price) / midprice

  observation

  \(\overline{s}\) = expected or typical bid-ask spread calculated as: (ask price — bid price) / midprice

  \(\sigma_s\) = sample standard deviation of the spread

  The \(\overline{s} + 2.33\sigma_s\) component is known as the 99% spread risk factor.

• A tool for measuring the risk of adverse price impact is liquidity-adjusted (VaR). The starting point 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 day, the trader faces a one-day holding period on the entire position, a two-day holding period on a fraction \(\frac{T – 1}{T}\) of the position, a three-day holding period on a fraction \(\frac{T – 2}{T}\) of the position, and so forth if he wishes to liquidate the position with no adverse price impact. The 1-day position (VaR) adjusted by the square root of time is estimated for a given position as:

  \(\text{VaR}_t \times \sqrt{T}\)

  But this formula overstates (VaR) for positions that are liquidated over time because there is an implicit assumption that the whole position is held for (T) days. The following formula can be used to account for the liquidation over a period of days.

 

\(\text{VaR}_t \times \sqrt{\frac{(1 + T) \times (1 + 2T)}{6T}}\)

Characteristics Of Market Liquidity

• A standard set of characteristics of market liquidity, focusing primarily on asset liquidity, helps to understand the causes of illiquidity:
  • 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 is 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.

• Lack of liquidity manifests itself in these observable, if hard-to-measure ways:
  • Bid-ask spread – If the bid-ask spread were a constant, then going long at the offer and short at the bid would be a predictable cost of doing the trade. However, the bid-ask spread can fluctuate widely, introducing a risk.
  • Adverse price impact is the impact on the equilibrium price of the trader’s own activity.
  • Slippage is the deterioration in the market price induced by the amount of time it takes to get a trade done. If prices are trending, the market can go against the trader, even if the order is not large enough to influence the market.

    These characteristics, and particularly the latter two, are hard to measure, making empirical work on market liquidity difficult. Data useful for the study of market microstructure, especially at high-frequency, are generally sparse. Bid-ask spreads are available for at least some markets, while transaction volume data is more readily available for exchange-traded than for (OTC) securities.

Funding Liquidity Management For Hedge Funds

• Hedge funds have a number of sources of liquidity that can be monitored as part of overall risk management:
  1. Cash provides unfettered liquidity. It can be held in the form of money market accounts or Treasury bills. Excess cash balances with brokers and money market accounts are not entirely riskless and therefore are not perfectly liquid. Broker balances carry with them the counterparty risk of the broker; in the event the broker fails, the cash balances will be immobilized for a time and only a fraction may ultimately be paid out. Money market funds, as was demonstrated during the subprime crisis, may suspend redemptions or “break the buck” and pay out at less than 100 percent of par.
  2. Unpledged assets (or assets “in the box”) are unencumbered assets not currently used as collateral. They are generally also held with a broker, who in this case is acting only as a custodian and not as a credit provider. This source of liquidity is limited by the price volatility of the assets and the ability to use the assets as collateral. Unpledged assets can be sold, rather than pledged, to generate liquidity. However, in times of market stress, asset prices are far lower than their fair values.
  3. Unused borrowing capacity on pledged assets can be used to finance additional positions. Like unpledged assets, this form of liquidity is not unfettered. Rather, it is subject to revocation by counterparties, who may raise haircuts or decline to accept the securities as collateral when the time comes to roll over a collateralized securities loan. Since most of these collateralized loans are very short term, credit can disappear rapidly. This occurred for many lower-quality forms of collateral during the subprime crisis.
• However, a systemic risk event, in which hedge fund investments are regarded as potential sources of liquidity by investors, will be a challenge even for the most effective liquidity risk management. We referred to this phenomenon earlier in this chapter: Many hedge funds that had not experienced large losses received redemption requests for precisely that reason from investors who were themselves seeking liquidity.