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Tutorial 3: Solutions

Lecture 3: Liquidity Risk Management

Note:

This topic has more questions than can be covered in a 1 hour tutorial session. The questions to be covered by your tutor are indicated by an asterisk (*); the rest should be viewed as extra practice problems.

Question 1. How does the degree of liquidity risk differ for different types of financial institutions?  

Due to the nature of their asset and liability contracts, depository institutions are the FIs most exposed to liquidity risk. Mutual funds, hedge funds, pension funds, and PC insurance companies are the least exposed. In the middle are life insurance companies.

Question 2*. What are the two reasons liquidity risk arises? How does liquidity risk arising from the liability side of the balance sheet differ from liquidity risk arising from the asset side of the balance sheet? What is meant by fire-sale prices?

Liquidity risk arises for two reasons. Liability side liquidity risk arises from transactions whereby a creditor, depositor, or other claim holder demands cash in exchange for the claim. The withdrawal of funds from a bank is an example of such a transaction. Asset side risk arises from transactions that result in a transfer of cash to some other asset, such as the exercise of a loan commitment or a line of credit. Another type of asset side liquidity risk arises from the FI’s investment portfolio. During a sell-off, liquidity dries up and investment securities can be sold only at fire-sale prices. A fire-sale price refers to the price of an asset that is less than the normal market price because of the need or desire to sell the asset immediately under conditions of financial distress.

Question 3. What are core deposits? What role do core deposits play in predicting the probability distribution of net deposit drains?

Core deposits are those deposits that will stay with the bank over an extended period of time. These deposits are relatively stable sources of funds and consist mainly of demand, savings, and retail time deposits. Because of their stability, a higher level of core deposits will increase the predictability of forecasting net deposit drains from the bank.  

Question 4*. What are two ways a bank can offset the liquidity effects of a net deposit drain of funds? How do the two methods differ? What are the operational benefits and costs of each method?

If the bank has a net deposit drain, it can use purchased liquidity management and/or stored liquidity management methods. Stored liquidity management involves adjustments in its assets by drawing down on its cash reserves, selling securities, or calling back (or not renewing) its loans. Purchased liquidity management involves adjustments in its liabilities by borrowing more funds, issuing long-term debt, or equity. If a bank offsets the drain using the purchased liability management method, the size of the firm remains the same. However, if it offsets the drain using the stored liquidity management method, the size of the bank is reduced.

The operational benefit of addressing a net deposit drain is to restore the financial stability and health of the bank. However, this process does not come without costs. On the asset side, liquidating assets may occur only at fire-sale prices that will result in realized losses of value. Further, not renewing loans may result in the loss of profitable relationships that could have negative effects on profitability in the future. On the liability side, entering the borrowed funds market normally requires paying market interest rates that are above those rates that it had been paying on low interest deposits. Further, since most of these funds are not covered by deposit insurance, their availability may be limited should the depository institution incur insolvency difficulties.

Question 5. What are two ways a bank can offset the effects of asset-side liquidity risk such as the drawing down of a loan commitment?

A bank can use either purchased liquidity management or stored liquidity management.

Question 6*. A bank with the following balance sheet (in millions) expects a net deposit drain of $15 million.

Assets Liabilities and Equity

Cash $10 Deposits $68

Loans 50 Equity    7

Securities     15

Total assets $75 Total liabilities and equity $75

Show the bank's balance sheet if the following conditions occur:

a. The bank purchases liabilities to offset this expected drain.

If the bank purchases liabilities, then the new balance sheet is:

Cash $10 Deposits $53

Loans 50 Purchased liabilities 15

Securities  15 Equity          7

Total assets              $75 Total liabilities and equity    $75

b. The stored liquidity management method is used to meet the expected drain.

If the bank liquidates assets to meet the deposit withdrawals, a possible balance sheet may be:

Loans $50 Deposits $53

Securities  10 Equity    7

Total assets $60 Total liabilities and equity    $60

Banks will most likely use some combination of these two methods.

Question 7*. AllStarBank has the following balance sheet (in millions):

Assets Liabilities and Equity Cash $30 Deposits $110 Loans 90 Borrowed funds 40

         Securities   50 Equity   20         Total assets $170 Total liabilities and equity $170 AllStarBank’s largest customer decides to exercise a $15 million loan commitment. How will the new balance sheet appear if AllStar uses the following liquidity risk strategies?

a. Stored liquidity management.

Assets Liabilities and Equity Cash $15 Deposits $110 Loans 105 Borrowed funds 40

Securities   50 Equity   20 Total assets $170 Total liabilities and equity $170 

b. Purchased liquidity management.

Assets Liabilities and Equity Cash $30 Deposits $110 Loans 105 Borrowed funds  55

Securities         50 Equity   20 Total assets $185 Total liabilities and equity $185  

Question 8*. A bank has assets of $10 million consisting of $1 million in cash and $9 million in loans. The bank has core deposits of $6 million, debt of $2 million, and equity of $2 million. Increases in interest rates are expected to cause a net drain of $2 million in core deposits over the year.

a. The average cost of deposits is 6 percent and the average interest rate on loans is 8 percent.  The bank decides to reduce its loan portfolio to offset this expected decline in deposits. What will be the effect on net interest income and the size of the bank after the implementation of this strategy?

Assuming that the decrease in loans is offset by an equal decrease in deposits, the change in net interest income = (0.06 – 0.08) x $2 million = -$40,000. The average size of the bank will be $8 million after the drain.

b. If the interest cost of issuing new short-term debt is expected to be 7.5 percent, what would be the effect on net interest income of offsetting the expected deposit drain with an increase in interest-bearing liabilities?  

Change in net interest income = (0.06 – 0.075) x $2 million = -$30,000.

c.  What will be the size of the bank after the drain if the bank uses the strategy of issuing  new short-term debt above?

The size of the firm will be $10 million after the drain.

Question 9. Define each of the following four measures of liquidity risk. Explain how each measure would be implemented and utilized by a bank.

a. Financing gap and financing requirement.

The financing gap can be defined as average loans minus average deposits, or alternatively, as negative liquid assets plus borrowed funds. A positive financing gap implies that the bank must borrow funds or rely on liquid assets to fund the non-liquid assets. Thus, the financing requirement can be expressed as the financing gap plus liquid assets. This relationship implies that some level of loans and core deposits as well as some amount of liquid assets determine the need for the bank to borrow or purchase funds.

b. Sources and uses of liquidity.  

This statement identifies the total sources of liquidity as the amount of cash-type assets that can be sold with little price risk and at low cost, the amount of funds the bank can borrow in the money/purchased funds market, and any excess cash reserves over the necessary reserve requirements. The statement also identifies the amount of each category the bank has utilized. The difference is the amount of liquidity available for the bank. This amount can be tracked on a day-to-day basis.

c. Peer group ratio comparisons.

Banks can easily compare their liquidity with peer group institutions by looking at several easy to calculate ratios: borrowed funds to deposits, loans to deposits, core deposits to total assets, and commitments to lend to total assets. High levels of the loan to deposit and borrowed funds to total asset ratios will identify reliance on borrowed funds markets rather than core deposits to fund loans, while heavy amounts of loan commitments to assets may reflect a heavy amount of potential liquidity needs in the future.

d. Liquidity index.

The liquidity index measures the amount of potential losses suffered by a bank from a fire-sale of assets compared to a fair market value established under the conditions of normal sale. The lower is the index, the less liquidity the bank has on its balance sheet. The index should always be a value between 0 and 1.

Question 10*. Plainbank has $10 million in cash and equivalents, $30 million in loans, and $15 in core deposits.  

a. Calculate the financing gap.

Financing gap = Average loans – Average deposits = $30 million - $15 million = $15 million

b. What is the financing requirement?

Financing requirement = Financing gap + Liquid assets = $15 million + $10 million = $25 m

c. How can the financing gap be used in the day-to-day liquidity management of the bank?

A rising financing gap on a daily basis over a period of time may indicate future liquidity problems due to increased deposit withdrawals and/or increased exercise of loan commitments. Sophisticated lenders in the money markets may be concerned about these trends and they may react by imposing higher risk premiums for borrowed funds or stricter credit limits on the amount of funds lent.

Question 11*. A bank has the following assets in its portfolio: $10 million in cash reserves with the Fed, $25 million in T-bills, and $65 million in mortgage loans. If the bank has to liquidate the assets today, it will receive only $98 per $100 of face value of the T-bills and $90 per $100 of face value of the mortgage loans. Liquidation at the end of one month (closer to maturity) will produce $100 per $100 of face value of the T-bills and $97 per $100 of face value of the mortgage. Calculate the one-month liquidity index for this bank using the preceding information.

I = ($10m/$100m)(1.00/1.00) + ($25m/$100m)(0.98/1.00) + ($65m/$100m)(0.90/0.97)  = 0.948

Question 12. A bank has the following assets in its portfolio: $20 million in cash reserves with the Fed, $20 million in T-bills, and $50 million in mortgage loans. If the assets need to be liquidated at short notice, the bank will receive only 99 percent of the fair market value of the T-bills and 90 percent of the fair market value of the mortgage loans. Liquidation at the end of one month (closer to maturity) will produce $100 per $100 of face value of the T-bills and the mortgage loans. Calculate the liquidity index using the above information.

I = ($20m/$90m)(1.00/1.00) + ($20m/$90m)(0.99/1.00) + ($50m/$90m)(0.90/1.00) = 0.942

Question 13. How can an FI’s liquidity plan help reduce the effects of liquidity shortages? What are the components of a liquidity plan?

A liquidity plan requires forward planning so that an optimal mix of funding can be implemented to reduce costs and unforeseen withdrawals. In general, a plan could incorporate the following:

(a) Assigning a team that will take charge in the event of a liquidity crisis. Set the delineation of managerial details and responsibilities. Responsibilities are assigned to key management personnel should a liquidity crisis occur.

(b) Identifying the account holders that will most likely withdraw funds in the event of a crisis.

(c) Estimating the size of the run-offs and the sources of borrowing to stem the run-offs.

(d) Establishing maximum limits for borrowing by subsidiaries and affiliates, including inter-affiliate loans, and the maximum risk premium to be paid during crisis borrowing.

(e) Specifying the sequencing of asset disposal in the event of a crisis.

Planning will ensure an orderly procedure to stem the rush of withdrawals and avert a total breakdown during a crisis. This is very important for firms that rely on deposits or short-term funds as a source of borrowing because of the difficulty in rolling over debt in periods of crisis.

Question 14*. What is a bank run? What are some possible withdrawal shocks that could initiate a bank run? What feature of the demand deposit contract provides deposit withdrawal momentum that can result in a bank run?

A bank run is a sudden and unexpected increase in deposit withdrawals from a DI. Bank runs can be triggered by several economic events including (a) concerns about solvency relative to other banks, (b) failure of related banks, and (c) sudden changes in investor preferences regarding the holding of nonbank financial assets. The first-come, first-serve (full pay or no pay) nature of a demand deposit contract encourages priority positions in any line for payment of deposit accounts. Thus, even though money may not be needed, customers have an incentive to withdraw their funds.

Quesiton 15. The following is the balance sheet of a bank (in millions):

Assets Liabilities and Equity

Cash   $  2 Demand deposits $50

Loans     50

Premises and equipment      3 Equity     5

Total     $55 Total $55 The asset-liability management committee has estimated that the loans, whose average interest rate is 6 percent and whose average life is three years, will have to be discounted at 10 percent if they are to be sold in less than two days. If they can be sold in four days, they will have to be discounted at 8 percent. If they can be sold later than a week, the DI will receive the full market value. Loans are not amortized; that is, principal is paid at maturity.

a. What will be the price received by the bank for the loans if they have to be sold in two days. In four days?

Price of loan = PVA_n=3,k=10($3m) + PV_{n=3, k=10}($50m) = $45.03m if sold in two days.

Price of loan = PVA_n=3,k=8($3m) + PV_{n=3, k=8}($50m) = $47.42m if sold in four days.

b. In a crisis, if depositors all demand payment on the first day, what amount will they receive? What will they receive if they demand to be paid within four days? Assume no deposit insurance.

If depositors demand to withdraw all their money on the first day, the bank will have to dispose of its loans at fire-sale prices of $45.03 million. With its $2 million in cash, it will be able to pay depositors on a first-come basis until $47.03 million has been withdrawn. The rest will have to wait until liquidation to share the remaining proceeds.

Similarly, if the run takes place over a four-day period, the bank may have more time to dispose of its assets. This could generate $47.42 million. With its $2 million in cash it would be able to satisfy on a first-come basis withdrawals up to $49.42 million.

Question 16. What are the levels of defense against liquidity risk for a life insurance company? How does liquidity risk for a property-casualty insurer differ from that for a life insurance company?

In the normal course of business the amount of premium income and returns on the asset portfolio provide an adequate cushion against liquidity risk for life insurance companies. As additional policies are surrendered, the insurance company may need to sell some of the relatively liquid assets such as government bonds. In the case of extreme liquidity pressures, the company may need to begin to liquidate the less-liquid assets in the portfolio, possibly at distressed prices.

Property-casualty insurance covers short-term contingencies, and thus the assets of PC insurers generally are more short-term than for life insurance companies, and the policy premium adjustments come at shorter intervals. As a result, although the degree and timing of contingency payout is more uncertain for PC companies, the flexibility to deal with liquidity pressures is better.

Question 17. How is the liquidity problem faced by investment funds different from that faced by banks and insurance companies?

In the case of a liquidity crisis in banks and insurance firms, there are incentives for depositors and policyholders to withdraw their money or cash in their policies as early as possible. Latecomers will be penalized because the financial institution may have insufficient liquid assets to cover their cash needs. They will have to wait until the institution sells its assets at fire-sale prices, resulting in a lower payout. In the case of investment funds, the net asset value for all shareholders is lowered or raised as the market value of assets change, so that everybody will receive the same price if they decide to withdraw their funds. Hence, the incentive to engage in a run is minimized.