Book 4. Liquidity and Treasury Risk

FRM Part 2

LTR 2. Liquidity and Leverage

Presented by: Sudhanshu

Module 1. Sources of Liquidity Risk, Liquidity Transformation and Systematic Funding

Module 2. Collateral Market and Leverage

Module 3. Funding and Transactions, Liquidity Risk and Transactions Cost

Module 1. Sources of Liquidity Risk, Liquidity Transformation and Systematic Funding

Topic 1. Sources of Liquidity Risk

Topic 2. Liquidity Transformation by Banks

Topic 3. Structured Credit Products and Off-Balance Sheet Vehicles

Topic 4. Systematic Funding Liquidity Risk

Topic 1. Sources of Liquidity Risk

• Liquidity has two essential properties, which are related to two forms of risk:

  • An asset is liquid if it can be sold quickly and cheaply without a significant price decrease.

  • A market is liquid if positions can be unwound quickly and at a low transaction cost, without an "undue price deterioration".

• Transactions vs. Funding Liquidity

  • Transactions (or Market) Liquidity: This is the risk that buying or selling an asset will cause an adverse price movement.

  • Funding Liquidity: This is the risk that a firm's or individual's creditworthiness is deteriorating or is perceived to be deteriorating by the market. This can lead to creditors withdrawing credit or changing its terms, such as increasing required collateral.

• Key Concepts & Risks

  • Maturity Mismatch: This occurs when a firm funds longer-term assets with shorter-term liabilities. It's often profitable because short-term debt has a lower required rate of return.

  • Rollover Risk: The risk that short-term debt cannot be refinanced or can only be refinanced at escalating rates.

• Systemic Risk: This is the risk that the entire financial system is impaired due to severe financial stress, which can lead to a breakdown in credit allocation.

• Interaction of Liquidity Risks

  • Transactions and funding liquidity risks are interrelated and can worsen problems.

  • An increase in funding liquidity risk can lead to an increase in transactions liquidity risk. For example, if a counterparty is forced to unwind a position early due to increased collateral requirements, they may have to sell at a loss.

  • Transactions liquidity can also impair funding liquidity. For instance, if a hedge fund must sell assets to meet redemptions, selling highly liquid assets leaves a more illiquid portfolio, while selling illiquid assets can increase realized losses and put more pressure on funding.

  • Systemic Risk: A rapid deleveraging of assets can lead to a "debt-deflation crisis". Liquidity risk events can become systemic through disruptions in payment, clearing, and settlement systems. The illiquidity or insolvency of one firm can have a "domino effect" on others.

Practice Questions: Q1

Q1. Jackson Grimes, a trader for Glenn Funds, works on the repurchase agreement (repo) desk at his firm. Markets have been highly volatile but Glenn Funds has a large capital base and is sound. Grimes reports to the CEO that in the last month, the firm Glenn Funds borrows from has been consistently increasing collateral requirements to roll over repos. From the perspective of Glenn Funds, this represents:

A. systematic risk.

B. transactions liquidity risk.

C. balance sheet risk.

D. maturity transformation risk.

Practice Questions: Q1 Answer

Explanation: C is correct.

Funding liquidity risk or balance sheet risk results when a borrower's credit position is either deteriorating or is perceived by market participants to be deteriorating. It also occurs when the market as a whole deteriorates. Under these conditions, creditors may withdraw credit or change the terms of credit. In this case, the lender is increasing the haircut and is thus changing the terms of credit. Glenn Fund's creditworthiness does not actually have to decline for a lender to withdraw credit or change the terms of credit.

Practice Questions: Q2

Q2. Chris Clayton, an analyst for a private equity fund, noticed that merger arbitrage strategies at several hedge funds experienced large losses in late 2007 to early 2008. These losses were likely due to:

A. abandoned merger plans due to a lack of available financing.

B. target prices falling precipitously due to stock market corrections.

C. acquirers filing for bankruptcy as the subprime mortgage crisis unfolded.

D. idiosyncratic risks surrounding the merger arbitrage strategy.

Practice Questions: Q2 Answer

Explanation: A is correct.

Systematic funding risks were apparent in many market sectors during the subprime mortgage crisis. Hedge funds engaged in merger arbitrage experienced losses in the early stages of the subprime mortgage crisis. After a merger is announced, the target's stock price typically increases and the acquirer's price sometimes declines due to increased debt. The merger arbitrage strategy exploits the difference between the current and announced acquisition prices. Hedge funds experienced large losses as mergers were abandoned when financing dried up.

Topic 2. Liquidity Transformation by Banks

• Fractional-Reserve Banking:  Asset-Liability Management (ALM): A bank's assets (e.g., loans) are typically longer-term and less liquid than its liabilities (e.g., deposits). This process of using deposits to finance loans is called ALM.

• Fractional Reserves: Banks don't hold all deposits in liquid assets because they only expect a fraction of deposits to be redeemed at any given time. They lend out the rest. This is the basis of a fractional-reserve bank.

• Bank Runs and Rollover Risk: Suspension of Convertibility: If withdrawals exceed a bank's reserves, the bank may be forced into a "suspension of convertibility," meaning it can't immediately convert deposits to cash as expected.

• Bank Runs: An extreme case where depositors, concerned about a bank's liquidity, rush to withdraw their money before others.

• Rollover Risk: Similar to bank runs but less extreme, rollover risk on other short-term financing can increase a bank's fragility. Higher capital levels can help reduce this fragility.

• The Role of Regulators: The Lehman Brothers failure illustrated the fragility of bank funding, with commercial paper markets freezing up.

• In response, the Federal Reserve created facilities like the Commercial Paper Funding Facility (CPFF) and the Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity Facility (AMLF) to provide liquidity.

Topic 3. Structured Credit Products and Off-Balance Sheet Vehicles

• Structured Credit and Liquidity Risk

  • Structured credit products like asset-based securities (ABSs) and mortgage-backed securities (MBSs) match investor funding needs with pooled assets.

  • These products themselves are maturity-matched, meaning they are not subject to funding liquidity issues.

  • However, liquidity risk arises when investors in these products use

    short-term financing to fund their investments. This was a major driver of the 2007-2009 subprime crisis.

• Off-Balance Sheet Vehicles

  • Special-purpose vehicles (SPVs) act as off-balance sheet vehicles by issuing secured debt in the form of asset-backed commercial paper (ABCP) to finance asset purchases.

  • Structured investment vehicles (SIVs) are similar to ABCP conduits but do not receive the same level of liquidity and credit support.

Topic 4. Systematic Funding Liquidity Risk

• Both conduits and SIVs profited from the spread between their lower funding costs and higher asset yields. They engaged in maturity and liquidity transformation by creating shorter-term, more liquid ABCP to fund longer-term assets.

• Systematic funding risks affect both borrowers and lenders at the same time, particularly when loans become shorter term.

• These "soft risks" are difficult to link to a specific series of asset returns. Analysts must examine data on credit and liquidity spreads, as well as the availability of credit, to understand the probability of a liquidity freeze.

• Examples from the 2007-2009 Crisis

  • Leveraged Buyouts (LBOs): During the crisis, funding for LBOs dried up, causing deals to fall apart and banks to incur significant losses on "hung loans" that couldn't be distributed to investors.

  • Merger Arbitrage Hedge Funds: These funds, which exploit the price difference between a target company's stock and the acquisition price, experienced large losses when mergers were abandoned due to a lack of financing.

  • Convertible Arbitrage Hedge Funds: These funds rely on leverage from broker-dealers. When financing became unavailable during the crisis, convertible bond values dropped sharply. This funding liquidity problem was compounded by redemptions, a market liquidity problem.

• Money Market Mutual Funds (MMMFs)

  • MMMFs are like banks in that they are obligated to repay investors on demand, even though their liabilities are more liquid than their underlying investments.
  • Breaking the Buck: While MMMFs' assets are typically high-credit, short-term instruments valued at a notional $1.00 per share, credit write-downs can cause the net asset value (NAV) to fall below this value.
  • Runs on MMMFs: Similar to banks, MMMFs are subject to runs. If many investors try to redeem shares during adverse market conditions, the fund may be forced to sell assets at a loss, potentially resulting in write-downs and "breaking the buck".
  • Amortized Cost Method: Under SEC Rule 2a-7, MMMFs are not required to mark their assets to market daily, unlike other mutual funds.

Practice Questions: Q3

Q3. With respect to the valuation of money market mutual fund (MMMF) assets, funds:

A. are not required to mark-to-market the underlying assets daily.

B. must reflect changes in the values of underlying assets that are the result of changes in credit risks but may ignore value changes that are the result of changes in interest rates.

C. will set the notional values of each of the underlying assets equal to $ 1.00.

D. are not allowed to invest in any asset with a rating below AAA because asset values must not fluctuate outside of a 10% range around the historical value in order to keep the notional value equal to $1.00.

Practice Questions: Q3 Answer

Explanation: A is correct.

MMMFs use a form of accounting called the amortized cost method, under the Securities and Exchange Commission's (SEC) Rule 2a-7. This means that MMMF assets do not have to be marked-to-market each day, as required for other types of mutual funds. However, the values of the underlying assets in the fund, despite their relative safety, are subject to change. As such, redemptions may be limited if asset values fall.

Module 2. Collateral Market And Leverage

Topic 1. Economics of the Collateral Market

Topic 2. Leverage Ratio and Leverage Effect

Topic 3. Marginal Loans and Leverage

Topic 4. Short Positions and Leverage

Topic 5. Derivatives and Leverage

Topic 1. Economics of the Collateral Market

• Definition: Markets where assets (securities) are pledged to secure a loan.

• Two Primary Purposes:

  1. Enhance Borrowing: Allows firms with excess cash to lend at lower rates, and firms with high-quality assets (collateral) to borrow cash at low rates.

  2. Enable Short Positions: Makes it possible to borrow securities to execute short sales.

• Key Risk: Collateral values fluctuate, necessitating regular adjustments.

• Role in Securitization: Collateral markets grew hand-in-hand with securitization, which created securities that can be pledged as collateral for credit.

• Forms of Collateral Market Transactions

  • Margin Loans: Collateralized by the purchased security, typically provided by the broker.

    • Regulation T: Sets the initial margin requirement at 50% for securities purchases.

    • Street Name Accounts: Securities are registered in the broker's name, making it easier to seize and sell them to meet margin calls.

• Repurchase Agreements (Repos): Collateralized short-term loans. The interest is implied from the difference between the spot sale price and the forward repurchase price.

• Securities Lending: Loan of securities (often to short-sellers) in exchange for cash collateral and a fee (rebate). The lender continues to receive dividends/interest.

• Total Return Swaps (TRS): One party pays a fixed fee for the total return (income + capital gains) of a reference asset, gaining synthetic ownership without the balance sheet implications.

• Mechanisms of Collateralized Transactions

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Topic 2. Leverage Ratio and Leverage Effect

• Leverage Ratio (L): The ratio of a firm's assets (A) to its equity (E).

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

  • Lowest value is 1.0 (all-equity financed).

• Leverage Effect: The principle that Return on Equity (     ) is magnified by leverage, provided the Return on Assets (      ) exceeds the Cost of Debt (    ).

• Quantifying the Leverage Effect

• Return on Equity (       ) Formula:

  $$r_{E} = L r_{A} - (L - 1) r_{D}$$

  • Where:

    •         = Return on Assets

    •         = Cost of Debt

    • L = Leverage Ratio

    • (L - 1) = The multiplier for the cost of debt, which represents the proportion of the balance sheet financed with debt.

• ​The cost of debt is multiplied by the factor (L-1). For L=4, (L-1)=3, meaning debt costs are multiplied by 3 because 3/4 of the balance sheet is financed with debt.

• Impact of Changing Leverage

  • Change in ROE (       ) due to Change in Leverage (      ):

    $$\frac{\partial r_{E}}{\partial L} = r_{A} - r_{D}$$

  • Key Insight: ROE increases when leverage increases, but only if the firm's assets generate a return greater than the cost of the borrowed funds used to finance them.

  • Double-Edged Sword: Leverage amplifies both gains and losses.

Practice Questions: Q1

Q1. Charleston Funds intends to use leverage to increase the returns on a convertible arbitrage strategy. The return on assets (ROA) of the strategy is 8 %. The fund has $ 1,000 invested in the strategy and will finance the investment with 75 % borrowed funds. The cost of borrowing is 4 %. The return on equity (ROE) is closest to:
A. 4 %.
B. 32%.
C. 20%.
D. 12%.

Practice Questions: Q1 Answer

Explanation: C is correct.

Topic 3. Marginal Loans and Leverage

• Explicit Leverage: Directly using borrowed funds to finance assets (e.g., issuing bonds, purchasing stock on margin).

• Implicit Leverage: Embedded in transactions that offer large exposure with a small capital outlay (e.g., short sales, derivatives).

• Margin Loan Mechanics:

  $$\text{Economic Leverage} = \frac{1}{h}$$

  • The stock purchased is collateral for the loan.

  • The haircut (h) is the borrower's equity contribution.

  • Regulation T Minimum: $$h = 50\% \implies \text{Leverage} = 1/0.50 = \mathbf{2.0}$$

• ​Economic Balance Sheet: Levered Margin Trade

• Scenario: Initial Equity: $100. Firm uses 50% equity (h=50%) to purchase $100 of stock, resulting in a $50 margin loan.

• Full Economic Balance Sheet:

  • Original Equity: $100

  • After trade: $100 Stock + $50 remaining Cash = $150 Assets.

• Note: The leverage ratio increased to 1.5 (or 1/0.667). The broker retains custody of the stock.

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Topic 4. Short Positions and Leverage

• Process: An investor borrows shares of a security and immediately sells them for cash.

• Liability: The obligation to return the borrowed shares (Short Position).

• Asset: The cash proceeds from the sale are held by the broker, often with an initial margin requirement.

• Balance Sheet Impact: The transaction lengthens the balance sheet because both the cash proceeds and the obligation to return the securities appear.

• Economic Balance Sheet for a Short Sale

• Transaction: Short sale of $100 of stock, requiring 50% initial margin ($50). (Initial Equity: $100)

• Accounting (Focus on the $50 Equity used):

  • The $100 Short Position is a liability.

  • The $100 Cash proceeds from the sale are an asset.

  • The $50 Margin Deposit (from the initial equity) is an asset.

• Result: This structure creates a hidden form of leverage on the firm's equity:

  $$\text{Economic Leverage} = \frac{\text{Total Assets}}{\text{Equity}} = \frac{\$150}{\$50} = \mathbf{3.0}$$

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Practice Questions: Q2

Q2. Assume a broker provides a margin loan to a U.S. hedge fund that puts up the minimum equity amount required by the Federal Reserve. If the hedge fund wants to take a $ 250,000 equity position, determine the margin loan amount and the leverage ratio of this position.
A. Margin loan = $125,000; leverage ratio = 1.0.
B. Margin loan = $125,000; leverage ratio = 2.0.
C. Margin loan =$ 250,000; leverage ratio =0.0.

D. Margin loan=$250,000; leverage ratio =1.0.

Practice Questions: Q2 Answer

Explanation: B is correct.

The Federal Reserve requires an initial margin of 50 % (i.e., haircut is 50 % ). Therefore, the margin loan will be                                            . The leverage ratio is equal to total assets divided by equity. Therefore, the hedge fund's leverage ratio is 2.0(=$ 250,000 / $ 125,000).

Topic 5. Derivatives and Leverage

• Derivatives (options, futures, swaps) provide exposure to an underlying asset's price movement without requiring the full capital outlay of owning the asset.

• This characteristic embeds implicit leverage into the balance sheet, as a small premium or margin deposit controls a large notional value.

• Options and Leverage

  • Mechanism: Purchasing an option premium (small capital) provides the right to control the price movement of the underlying asset (large notional value).

  • Example: A $5 option premium on a $100 stock has an initial leverage factor of 100/5 =20x.

  • Balance Sheet Effect: Only the premium is recognized as an asset and paid in cash. The large exposure is off-balance sheet, but the risk exposure is real.

• Total Return Swaps (TRS) and Synthetic Leverage

  • Definition (Recap): A contract where one party receives the "total return" (capital change + income) of a reference asset in exchange for paying a fixed fee.

• Synthetic Ownership: The receiver gets all the economic benefits of owning the asset without holding the underlying asset on their balance sheet.

• Leverage: The receiver gains leveraged exposure to the asset's price change for only the cost of the periodic fee. The party providing the return (e.g., a hedge fund) is essentially short the asset and uses its balance sheet capacity to finance the transaction.

Module 3. Funding And Transactions, Liquidity Risk, And Transactions Cost

Topic 1. Sources of Transactions Liquidity Risk

Topic 2. Transactions Cost

Topic 3. Adjusting VaR for Position Liquidity

Topic 4. Measuring Market Liquidity

Topic 5. Funding Liquidity Risk Management

Topic 1. Sources of Transactions Liquidity Risk

• Definition of Liquidity: An asset is considered liquid if it's "close to cash," meaning it can be sold quickly and cheaply without a significant impact on its price.

• Transactions (Market) Liquidity Risk: This is the risk that buying or selling an asset will result in an unfavorable price change.

• Interrelation with Funding Liquidity: Transactions liquidity risk can be increased by an increase in funding liquidity risk. For instance, if collateral requirements are raised, a counterparty might be forced to unwind a position early, potentially leading to a loss.

• Impact of Leverage: The connection between funding and transactions liquidity is leverage. An investor with a long position may be forced to sell an asset if funding is no longer available. This can lead to a decrease in the number of potential asset holders and a reduction in the asset's value. This can, in turn, negatively affect the solvency of the initial investor. A rapid deleveraging of assets could lead to a "debt-deflation crisis".

• Hedge Fund Example: If a hedge fund needs to raise cash to meet redemptions, it must sell assets. Selling highly liquid assets has less of a price impact but leaves the fund with a more illiquid portfolio. Conversely, selling highly illiquid assets can increase losses, putting further pressure on the fund's funding liquidity.

• Systemic Risk: Liquidity risk events can become systemic risk events through disruptions in payment, clearing, and settlement systems. In a situation of severe financial stress, the illiquidity or insolvency of one counterparty can have a domino effect on others in the system.

Practice Questions: Q1

Q1. Brett Doninger recently placed an order to sell a stock when the market price was $42.12. The market was volatile and, by the time Doninger’s broker sold the stock, the price had fallen to $41.88. In the market, this phenomenon is known as:

A. adverse selection.

B. transactional imbalance.

C. slippage.

D. the spread risk factor.

Practice Questions: Q1 Answer

Explanation: C is correct.

Liquidity risks are introduced when bid-ask spreads fluctuate, when the trader’s own actions impact the equilibrium price of the asset (called adverse price impact), and when the price of an asset deteriorates in the time it takes a trade to get done. When the price deteriorates in the time it takes to get a trade done, it is called slippage.

Topic 2. Transactions Cost

• Definition: A market is considered liquid if positions can be unwound quickly and at a low transactions cost, without causing excessive price deterioration.

• Transactions Liquidity Risk: This is the risk that the act of buying or selling an asset will result in an adverse price move. This risk is directly related to the transaction cost, as higher costs lead to less favorable prices.

• Hedge Fund Example: When a hedge fund is forced to sell assets to raise cash for redemptions, selling highly liquid assets will lead to fewer adverse price impacts. This implies a lower transaction cost for these assets. Selling illiquid assets, however, will increase realized losses, which can be seen as a higher effective transaction cost.

• Collateral Markets: In collateral markets, firms with excess cash are more willing to lend at a low interest rate if the loan is secured by collateral. This highlights how collateral reduces the risk for the lender, which in turn lowers the borrowing cost (a form of transaction cost) for the firm.

Topic 3. Adjusting VaR for Position Liquidity 

• Liquidity-adjusted value at risk (LVaR) is a tool used to measure the risk of adverse price impact. The trader will often liquidate the position over a period of days in order to ensure an orderly liquidation of the position.

• Adjusting VaR for liquidity requires an estimate of the number of days it will take to liquidate a position. The number of trading days is typically denoted T. Assuming the position can be divided into equal parts across the number of trading days and liquidated at the end of each trading day, a trader would face 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, and so on. The 1-day position VaR adjusted by the square root of time is estimated for a given position as:

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• This formula overstates VaR for positions that are liquidated over time because it assumes that the whole position is held for T days. To adjust for the fact that the position could be liquidated over a period of days, the following formula can be used:

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Topic 4. Measuring Market Liquidity

• The provided document discusses three key concepts for understanding liquidity risk:

  • Tightness: This refers to the transaction costs, which are the costs incurred to reverse a position.

  • Depth: This relates to the size of a position that a market can absorb without a significant price impact.

  • Resiliency: This describes how quickly prices return to their long-run equilibrium after a random, uninformative shock.

• A market is considered liquid if it's possible to unwind positions quickly, cheaply (at low transaction costs), and without significant price deterioration. This directly relates to the concepts of tightness, depth, and resiliency.

Topic 5. Funding Liquidity Risk Management

• Sources of Funding Liquidity Risk: This risk, also known as balance sheet risk, occurs when a borrower's credit position is deteriorating or is perceived to be deteriorating by market participants. It can also happen when the market as a whole deteriorates.

• Maturity Mismatch: Balance sheet risks are higher when borrowers use short-term liabilities to fund longer-term assets, a practice known as maturity mismatch. While this can be profitable for firms, it exposes the borrower to rollover risk (or cliff risk), which is the risk that debt can't be refinanced or can only be refinanced at escalating rates.

• Liquidity Transformation: Banks are fractional-reserve banks, meaning they don't hold all deposits in liquid assets. Instead, they use deposits to make loans, a process called asset-liability management (ALM). This is an example of liquidity transformation, where banks convert short-term, liquid deposits into longer-term, less liquid assets (loans). This process exposes banks to liquidity risk, as a bank run can occur if withdrawals are greater than the bank's reserves.

• Higher Capital: Increasing a bank's capital can reduce its fragility.

• Off-Balance Sheet Vehicles: Structured investment vehicles (SIVs) and asset-backed commercial paper (ABCP) conduits provided both liquidity and maturity transformation. They created ABCP with shorter terms and greater liquidity than the assets they held. Despite being off-balance sheet, which allowed firms to hold less capital, these vehicles still contributed to the fragility and leverage issues of the financial system during the subprime crisis.

• Money Market Mutual Funds (MMMFs): Like banks, MMMFs are obligated to repay investors on demand. Their liabilities are more liquid than their investments. They are also subject to runs. If a large number of investors try to redeem shares during adverse market conditions, the fund may be forced to sell assets at a loss, potentially causing the Net Asset Value (NAV) to fall below $1.00, which is known as "breaking the buck".