### Liquidity and Leverage

In this chapter, the differences between liquidity risk sources will be explained, ranging from balance sheet/funding liquidity risk to transactions liquidity risk, and a further explanation will be given on how each of these risks can arise. The process of asset-liability management at a fractional reserve bank will be summarized.

The chapter will give a description of specific liquidity challenges that money market mutual funds and hedge funds faces, especially in situations of stress. A comparison will also be given on applied transactions in the collateral market, with an explanation of risks arising through the collateral market transactions.

Furthermore, the relation between leverage and the company’s return profile will be described, and the leverage ratio computed. The chapter will also explain how a purchase of long equity positions on margin, short sales entry, and derivatives trading will affect a company’s leverage and its balance sheet.

The methods applied in the evaluation and management of funding liquidity risk and transaction liquidity risk will be discussed. A transaction’s expected cost and risk factor will be computed and a further calculation of the liquidity adjustment to VaR for a position to be liquidated over several trading days will be given.

Finally, the chapter provides an explanation of how different types of liquidity risk interact and how systemic risk can be increased by liquidity risk events. The following distinct but related phenomena are described by the term liquidity risk:

1. Transaction liquidity risk: The risk of adversely moving an asset price when purchasing or selling it;
2. Balance sheet risk or funding liquidity risk: Is the risk of credit withdrawal or changing terms on which credit is granted by creditors, in a way that enables positions to be unwound or are no longer profitable; and
3. Systemic risk: This is the risk of a financial system being generally impaired.

# Funding Liquidity Risk

## Maturity Transformation

To finance investments needing a longer time to be profitable, market participants will borrow at short-term rates. This leads to the rising of funding liquidity risk. A maturity mismatch is the balance sheet situation in which a longer-term asset is funded using a shorter-term liability.

For banks and other financial intermediaries, the management of maturity mismatches is their core function. A maturity transformation and liquidity transformation are done by financial intermediaries. Shorter-term funding is obtained and longer-term funding is provided for project financing. Matched funding is the funding of longer-term assets with longer-term debt.

Maturity mismatch is generally profitable, hence intermediaries engage in them. The cost of capital is incurred by every market participant, with the most costly capital being equity since it takes the most risk, but also should provide the highest expected return.

The net interest margin is the spread between the interest intermediaries pay and the interest they earn. There is a powerful incentive to possibly borrow short term due to the fact that short-term rates are generally lower than long-term rates.

An intermediary is exposed to rollover risk due to the funding of long-term assets with short-term debt. Cash flow can become negative in the event of a rollover risk. This is the risk of failure to refinance short-term debt or only refinance it at very disadvantageous terms.

A rapid change in funding conditions can be experienced, with an investor or company suddenly finding itself in a negative cash flow situation which may be difficult to get out of in the event that short-term funding suddenly becomes impossible.

## Liquidity Transformation

Since short-term rates generally carry lower interests as compared to longer-term debt, net interest margins are earned by intermediaries from the transformation process. An intermediary’s short-term funding is the lender’s short-term asset. It may provide the investor with liquidity and payment services, including a flow of interest payments.

However, short-term interest rates on currencies in the imminent danger of devaluation is the major exception to the above observation. The means-of-payment function of money is served by some very short-term debt, especially the checkable forms.

Due to the usefulness of these debt types as a means of payment and debt settling, their yields are even lower than can be explained by their short maturities. The net interest margin is contributed by providing liquidity and payment services.

Since money goes back to the origins of banking, the process by which assets are created using balance sheets by financial intermediaries can be applied. Today, the definition of money supply includes certain non-bank liabilities including bank notes and bank deposits.

Money is held by market participants to conduct transactions and speculation. The balances held for transacting include a portion attributed to the uncertainty regarding the cash flow’s volume and timing. In speculative motive, the uncertainties are about future asset prices and risk preferences.

Assets with minimal credit risk but with future maturities are still uncertain since their values depend on interest rates. Fluctuation in interest rates affect the prices of even short-term T-bills.

During the subprime crisis, Keynes’ term for the money demand, liquidity preference, became particularly pertinent. The zero or low yields earned by cash and liquid assets counterbalances the liquidity desire in normal times.

A larger proportion of the market participants’ assets was held in liquid form due to uncertainties and high-risk aversion. Therefore, there was a drastic decline in the velocity of money, in economics terminology.

# Bank Liquidity

Taking deposits from customers and providing loans to non-financial institutions are the core function of all commercial banks. This enables the banks to carry out a liquidity, credit, and maturity transformation.

## Liquidity Transformation by Banks

By operating on both sides of the balance sheet, banks can effectively execute their duties. However, a high proportion of the banks’ revenues nowadays comes from loan origination, investment banking, and other fees.

Market making also provides important revenues through the bid-ask spreads earned on transactions executed for clients, and proprietary trading, where risky positions are taken from assets with the bank’s own capital.

By borrowing from the public in the form of liabilities to be fully repaid upon demand in cash, on a first-come-first-served basis, banks become depository institutions. The sequential service constraint refers to this aspect of the depository contract, and it differs sharply with bankruptcy, where claims are paid pro rata.

Tapping the broader capital markets and raising funds by issuing bonds, commercial paper, and other forms of debt is another area of expertise. These wholesale funding sources are generally longer than deposits, which can be redeemed on short notice.

However, deposits are considered sticky as depositors tend to remain with a bank unless a change in lifestyle compels them to do otherwise. Reliance on a small number of lenders is reduced by a large deposit base since depositors are a set of counterparties that is naturally diversified.

Compared to a solid deposit base, there is reduced reliability on shorter-term forms of wholesale funding and are potentially more concentrated sources of longer-term liquidity. The loan proceeds invested by borrowing companies are usually in the form of physical and other capital.

To match the maturity of its assets, banks borrow at a longer term, despite their net interest margin being reduced by this activity. Borrowers can directly turn to the bond markets in the event that the delegated monitoring function of the banks does not produce added value.

On the assets side of the banks’ balance sheet, the investments have longer-term maturities than the liabilities, and less liquidity, while deposits closely substitute cash.

By engaging in asset-liability management (ALM), the available cash and short-term assets get aligned with the expected requirements.

## Fragility of Commercial Banking

The classic depository institution is a bank that lends deposits. An alternative to this is a 100% reserve bank which lends only its capital/funds raised in the capital market and keeps cash reserve/liquid securities equal to its deposit base. In banking history, many banks have been fraction reserve banks. Money was stored in form of silver and gold coins in safes, and the receipt from the warehouses was used as money as long as the bank was trusted.

This made it easier to transport and exchange. Commercial loans by the warehouse could be made with owners’ equity or with capital market borrowing. Later, bank loans were given by issuing banknotes. In fractional reserve, if withdrawals were needed in excess by depositors and the bank was unable to liquidate all of it, it was forced into a suspension of convertibility. Fraction-reserve banking cannot be protected by asset-liability management from the loss of confidence to pay out debtors.

As long as liquidity and maturity transformation is done by the bank, it is required to pay on demand. No degree of liquidity can protect a bank completely from ruin. Fragility can be reduced through higher capital, while higher reserves reduce worry about liquidity.

Apart from deposits, banks are dependent on short-term financing exposing them to rollover risks. Commercial banks’ main source of funding is deposits and they rely on capital markets for the rest of the funding. Commercial paper is an important component and accounts for roughly 1.5% of banks liabilities. The commercial paper market in the pre outcomes of the Lehman’s bankruptcy is an example of how fast funding conditions change.

The panels below show the shares in the total issuance of short and long-term commercial papers. With the coming of the subprime crisis, financial firms increased the average term of the smaller total. After the Lehman’s episode, banks found it difficult to roll over long-term commercial papers. The Federal Reserve intervenes in the Lehman bankruptcy to support liquidity through the commercial paper funding facility.

## Structured credit and off-balance sheet funding

As structures credit products are maturity matched, they do not face funding liquidity problems. However, the securitization liabilities financed by investors can introduce liquidity risks. Difficulties faced by securitization are related to the questionable credit quality of the underlying assets. The short-term financing of securitizations had an important role to play in the opaque increase of financial system leverage before the subprime crisis.

Off-balance sheet vehicles are special purpose vehicles defined by their assets and liabilities. They give an asset-backed commercial paper which is secured rather than unsecured debt. They are mainly two types: asset-backed commercial paper that buys various types of assets, and structured investment vehicles that do not enjoy the full support of sponsors.

The two are economically similar in that both vehicles profit from the spread between the funding cost and the asset yield. They have a common economic function of liquidity and maturity transformation. The vehicles also do liquidity transformation which is on a much shorter term and a more liquid asset than the underlying assets.

Financial innovations after the crisis were accompanied by changes in regulatory capital rules that allowed firms to hold less capital against given levels of economic risks.

## Funding Liquidity of Other Intermediaries

Securities firms hold inventories of security for sale and finance them by short-term borrowing. The collapse of bear sterns was an extreme case of a securities firm lender suddenly withdrawing credit.

## Money Market Mutual Funds

Depository institutions and money market mutual funds (MMMFs) are extreme positions since they repay depositors on demand.

MMMFs provide instant liquidity for their investors through the ability to draw on their accounts via electronic bank transfer and checks. It is designed to invest in money market securities of high credit quality in a short time. MMMFs permit the instantaneous withdrawal of equity.

The structure works only if liquidity, credit, and market risks are managed well. Some losses cannot be disregarded under the amortized cost method, so liquidity risk jeopardizes the ability of an MMMF to maintain a \$1.00 net asset value.

## Hedge funds

Hedge funds face liquidity risk all through their structured capital. They permit investors to withdraw their funds at agreed times, which was quite a problem during the subprime crisis. Hedge funds also face short-term funding risk on their assets.

## Systematic Funding Liquidity Risk

In major corporate financial transactions, systematic funding liquidity risk is a latent risk factor. The funding liquidity is both systematic and idiosyncratic. Participants in the transactions also experience losses. Investors having exposure to such transaction are exposed to the idiosyncratic risk of deals and the systematic risk posed by credit.

Systemic funding liquidity risk is pervasive. Theoretical prices are based on replication portfolios of pure vanilla equity, and its prices are slightly higher than convertible bond prices. They have a systemic extreme low risk.

## The Structure of Market for Collateral

The market for collaterals is formed when securities are used to secure cash loans or other securities. Collaterals play an important role in credit transactions by producing a sentiment of security for the lenders. The most direct effect of securitization is to remove the intermediation of credit from the balance sheet of the financial intermediaries.

Borrowing or lending on collateral against securities can be done by most firms. Borrowing can be both short and long-term since overnight borrowing can be extended. The market for collateral has existed for a long time in three basic forms:

1. Margin loans: is lending for purposefully financing a security transaction where the loan is collateralized by the security. Collateralization for the loan is gotten by having the broker retain custody of the securities.
2. Repurchase agreements: These are matched pairs of the forward repurchase and spot sale. The difference between them implies an interest rate, so it is an old form of finance. The mechanics of repo lending are similar to margin loans.
3. Securities lending: Here, one party lends a security to another in exchange for a fee. The security lender receives dividends and cash continuously.

## The Economic Function of Markets for Collateral

The purpose of collateral markets is to create the ability to establish short and long positions in securities. It enhances the ability of the participating firms to borrow money and helps in understanding the risks of securities lending. It has historically functioned as the primary source of short-term financing for financial firms. The programs provide a channel through which firms are using cash collateral to invest in higher-risk bonds.

## Prime Brokerage and Hedge Funds

Most of the growth in the collateral market is intermediated through prime brokers. Hedge funds maintain portfolios of short and long positions. Prime brokerage businesses are valued by large intermediaries, and the interest rate paid on these cash balance is usually higher than the funds can obtain from alternative investments.

## Risks in Markets for Collateral

These risks are similar to those of leverage positions. The collateral markets permit owners of high quality to finance position in high-quality collateral at low-interest rates. The structure and size of the collateral markets also contribute to systemic risk.

Calling and remerging loans collateralized by securities gives rise to a phenomenon that is similar to classic bank runs, but involving nonbank intermediaries as well as banks, and focused on wholesale funding rather than deposits.

# Leverage and Forms of Credit in Contemporary Finance

## Defining and measuring leverage

The leverage ratio is defined as:

$$L=\frac { A }{ E } =\frac { E+D }{ E } =1+\frac { D }{ E }$$

or

$$1+the\quad debt-to-equity\quad ratio\quad \left( { D }/{ E } \right).$$

The leverage for a single collateralized loan is the reciprocal of one minus the loan-to-value ratio.

The importance of leverage is that it provides an opportunity to increase returns to equity by investors (leverage effect). This effect is the increase in equity returns from increasing leverage and is equal to the difference between the returns on the assets and the cost of funding.

If we consider the assets returns, $${ r }^{ a }$$ , the equity returns, $${ r }^{ e }$$ , and the cost of debt, $${ r }^{ d }$$:

$${ r }^{ e }=L\quad { r }^{ a }-\left( L-1 \right) { r }^{ d }$$

The effect of increasing leverage is:

$$\frac { \delta { r }^{ E } }{ \delta L } ={ r }^{ a }-{ r }^{ d }$$

Leverage trades in foreign countries involve borrowing a low-interest rate currency and using the proceeds to buy a higher interest rate currency. The net carry is $${ r }_{ a }{ -r }_{ d }$$, using the higher and lower interest rates, respectively.

The equity denominator is dependent on the type of entity we are looking at and the purpose of the analysis. Hybrid capital securities are also issued by firms. It can be included or excluded from the denominator of a leverage ratio depending on the purpose of analysis.

The appropriate equity denominator for a hedge fund is the net asset value of the fund which is the current value of the investor’s capital.

The alternative definition usually used in fundamental credit analysis relates the debts to the cash flows of the firm. The cash flow measure used is EBITDA (earnings before interest, taxes, depreciation, and amortization), which captures the net revenues of the firm and excludes interests which are determined by the firm’s business opportunities and also excludes the costs that are particularly heavily influenced by accounting techniques.

In reality, asset returns are not fixed but risky. The effect of leverage depends as much on the cost of funding as on the asset return. Investors sometimes choose a degree of leverage based on the return that they need to achieve.

Many leveraged fixed income instruments involve spreads and, if a fixed income security has a coupon rate higher than the borrowing rate on a loan collateralized by the security, the rate of return to a leveraged purchase is limited only by the haircut.

The tension between the required returns and the leverage played an important role in creating the conditions of the subprime crisis. Higher leverage was required to achieve a given required rate of return on capital as the spread contracts and mechanisms to achieve this were found.

The use of leverage also applies that households were able to borrow to finance asset purchases. Many households have borrowed at least part of the purchase price by means of a mortgage loan. Leverage ratios can amplify the sensitivity to changes in cash flows.

These relationships illustrate why leverage is often used as a measure of risk and sometimes considered as an independent source of risk, and also show why firms employ leverage.

It is important to state the unambiguousness definition of leverage. Most severe losses suffered by financial intermediaries involve leverage in some ways and it important to have an understanding of the extent of borrowing required, implicitly or explicitly, so as to boost returns. Some forms of credit used by firms to take on leverage have grown enormously because of:

1. Lower transaction costs than traditional banks or capital market debts;
2. Granting of credit is an inherent part of trading in the assets being financed; and
3. Collateralization of the loan and adjustments to the amount lent occur naturally as part of brokering and trading.

These forms of borrowing are collateralized in some way, which also has effects on the economic leverage.

## Margin loans and leverage

Margin leverage has a straightforward impact on leverage; the haircut determines the amount of the loan made. At a haircut of $$h$$ percent, $$1 – h$$ is lent against a given market value of collateral, and $$h$$ is the borrowers’ equity in the position.

## Short Positions

Short positions lengthen the balance sheet because both the cash generated by their sale and the value of borrowed short securities appear on the balance sheet.

## Gross and Net Leverage

They reduce risk if there are long positions with which they are positively correlated or other short positions to which they are negatively correlated.

The definition of gross leverage is the sum of all the asset values divided by capital while 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 give full information to the risk manager whether the short positions are risk-augmenting or risk-reducing.

## Derivatives

Derivatives are means to gain an economic exposure to some asset without buying or selling it outright.

Although they are generally off-balance sheet items in standard accounting practice, they belong to the economic balance sheet because they may have a large impact on returns. Each side of the derivative contract is synthetically long or short in an asset or risk factor.

There are two types of derivatives, namely:

1. Futures, forwards, and swaps: are linear and symmetric in the underlying asset price and can be hedged statically; and
2. Options: have a nonlinear relationship to the underlying asset price and must be hedged dynamically.

Derivatives also generate counterparty credit risk such as margin arrangements.

## Structured Credit

Structured credit provides embedded leverage. There is a property of thin subordinate securitization tranches called “cuspiness,” because it materializes when the attachment point of the bond is at the cusp of the default losses in the pool.

## Asset Volatility and Leverage

Investments in this field are similar to leverage because of higher return volatility. An asset with more volatile returns provides a higher leverage return to the investor.

Leverage ratios don’t capture the effect of volatility on convexity that amplifies economics leverage and can make it more attractive.

# Transactions Liquidity Risk

Transaction liquidity refers to the ability to buy or sell an asset without moving its price.

## Causes of Transactions Liquidity Risk

Transaction liquidity risk is ultimately due to the cost of searching for a counterparty, to the market institutions that help in the search, and to the cost of persuading another party to take the trade. These market microstructure fundamentals can be classified as:

2. Inventory management by dealers;
4. Difference of opinion.

## Characteristics of Market Liquidity

There is a standard set of characteristics of market liquidity:

1. Tightness: the cost of a round-trip transaction, or the bid-ask spread plus the commission;
2. Depth: describing how large an order takes to move the market adversely;
3. Resilience: the length of time for which a lumpy order moves the market away from the equilibrium price;
5. Adverse price impact: the impact on equilibrium prices.

# Liquidity Risk Measurement

## Asset-Liability Management

Part of the traditional asset-liability management function in major banks is to reduce the funding liquidity risk. This process includes measures such as:

1. Keeping a certain ratio of available cash and readily marketable securities. This is done so as to meet unusual demands by depositors and other short-term lenders; and
2. Forecasting and tracking available cash and sources of funding on the one hand and cash needs on the other hand.

## Funding Liquidity Management for Hedge Funds

Hedge funds are vulnerable to the withdrawal of liquidity. They have a number of sources of liquidity that can be monitored as part of their overall risk management:

1. Cash provides unfettered liquidity that can be held in form of money market accounts or treasury bills;
2. Unpledged assets which are unencumbered and not used as collateral; and
3. Unused borrowing capacity on pledged assets which can be used to finance additional positions.

However, a systemic risk event, in which hedge funds are regarded as potential sources of liquidity, will be a challenge even for most effective liquidity risk management.

## Measuring Transactions Liquidity Risk

There are different types of transactions liquidity risk measures:

1. Transaction or turnover volume data;
3. Data on the size outstanding of securities issues.

Although these quantitative measures are used, they are not as widely used as funding liquidity measures. This is because they are not incorporated in the regulatory framework to the same extent as standard models of market and credit risk measurement.

## Transaction Cost Liquidity Risk

This type of risk focuses more on the risk of variation in transaction costs. The starting point is the distributional hypothesis regarding the future bid-ask spread.

$$E\left[ { P }_{ t+1 } \right] \frac { \bar { S } }{ 2 }$$

Where:

$$S=2\frac { Ask\quad price-Bid\quad price }{ Ask\quad price+Bid\quad price } =\frac { Ask\quad price-Bid\quad price }{ Mid\quad Price }$$

$$S$$ is an estimate of the expected or typical bid-ask spread, and $$P$$ is the asset’s mid-price.

Under zero-mean normality, the hypothesis is that $$\bar { S } =S$$.

$$\pm \bar { P } \frac { 1 }{ 2 } \left( \bar { s } +2.33{ \sigma }_{ s } \right)$$

Where $$P$$ is an estimate of the next day asset mid-price, and since $$\bar { P } =P$$, the 99 percent risk factor is referred to as:

$$\frac { 1 }{ 2 } \left( \bar { s } +2.33{ \sigma }_{ s } \right)$$

## Measuring the Risk of Adverse Price Impact

Measuring the risk of an adverse price impact is done using the liquidity-adjusted VaR. The starting point is an estimated number of trading days, $$T$$, required for the orderly liquidation of a position.

$${ VaR }_{ t }=\left( \alpha ,\frac { 1 }{ 252 } \right) \left( X \right) \times \sqrt { { 1 }^{ 2 }+{ 1 }^{ 2 }+\cdots .+{ 1 }^{ 2 } } ={ VaR }_{ \tau }\left( \alpha ,\tau \right) =\left( X \right) \times \sqrt { T }$$

In extreme cases, there may be many constraints on liquidation decisions, such as trade-offs among adverse price impact, solvency, and funding liquidity. The liquidation decision may also interact with the incentive structure of credit markets.

# Liquidity and System Risk

Systemic risks can be thought of as resulting from external costs in the production of financial services. Those who are participants in this approach incur risks that are partially shifted to the market as a whole.

Liquidity is ephemeral for many securities and tends to become impaired at precisely moments when market participants most need it.

## Funding and Solvency

Liquidity is the capability to immediately meet demands for cash. Solvency is referred to as possessing assets in excess of liquidity. Solvency and liquidity pertain to the capability to repay debts. In extreme cases, liquidity can become insolvency, since debtors become unable to realize the funds required to meet debt obligations by selling assets or borrowing.

Both insolvency and illiquidity played a role in the collapse of financial institutions during financial crises. The sequence to the collapse can be described as:

1. Report of losses at the intermediary;
2. All firms become more reluctant to lend to the intermediary;
3. The intermediary is forced to raise cash by liquidating assets;
4. Lenders are aware that the intermediary problems are being compounded by realizing mark-to-market losses; and
5. The process accelerates.

The draining of cash is what destroys a firm, and pure liquidity events cannot occur for one firm in isolation.

## Funding and Market Liquidity

Key mechanisms in linking market liquidity and funding is leverage. A market participant is forced to sell long positions which can no longer obtain funding. Mark-to-market risk combines credit risk and market aspects. Funding liquidity can be constrained by market liquidity.

## Systemic Risk and the Plumbing

Risk events can become systemic risk events when having problems in the payments, settlement system, and clearing process. The tri-party repo system is a recently developed infrastructure that gained rapid importance in the past decade. Mostly tri-party repo transactions are short-term ways to finance security portfolios.

However, there is liquidity risk in the mechanics of tri-party repo. Many funding liquidity risks are intrinsic in this process. A clearing bank declining credit to its customer provokes a rollover risk event for the customer.

## Interconnectedness

Credit transactions have a set of participants in the market as lenders/borrowers in some credit transactions even in less developed economies. The most enmeshed entities in this network are financial intermediaries.

Off-balance sheet vehicle, MMMFs, and traditional intermediaries are aspects of this interconnectedness.

# Practice Questions

1) The two types of quantitative liquidity risk measures primarily focus on the available data that is pertinent to liquidity risk. Which of the following is NOT a type of available data which are pertinent to liquidity risk?