Hi! at the bottom of the third page, how did they come up with the numbers to plug into the equation in 8. a.?

Chapter Eighteen Liability and Liquidity Management Chapter Outline Introduction Liquid Asset Management Monetary Policy Implementation Reasons Taxation Reasons The Composition of the Liquid Asset Portfolio Return-Risk Trade-Off for Liquid Assets The Liquid Asset Reserve Management Problem for U.S. Depository Institutions Undershooting/Overshooting of the Reserve Target Liability Management Funding Risk and Cost Choice of Liability Structure Demand Deposits Interest-Bearing Checking (NOW) Accounts Passbook Savings Money Market Deposit Accounts (MMDAs) Retail Time Deposits and CDs Wholesale CDs Federal Funds Repurchase Agreements (RPs) Other Borrowings Liquidity and Liability Structures for U.S Depository Institutions Liability and Liquidity Risk Management in Insurance Companies Liability and Liquidity Risk Management in Other FIs Summary 211 Solutions for End-of-Chapter Questions and Problems: Chapter Eighteen 1. What are the benefits and costs to an FI of holding large amounts of liquid assets? Why are Treasury securities considered good examples of liquid assets? A major benefit of an FI holding a large amount of liquid cash is that it can offset any unexpected and large withdrawals without reverting to asset sales or emergency funding. If assets have to be sold at short notice, FIs may not obtain a fair market value. It is more prudent to anticipate withdrawals and keep liquid assets to meet the demand. On the other hand, liquid assets provide lower yields, so the opportunity cost for holding a large amount of liquid assets is high. FIs taking conservative positions by holding large amounts of liquid assets will therefore have lower profits. Treasury securities are considered good examples of liquid assets because they can be converted into cash quickly with very little loss of value from current market levels. 2. How is an FI's liability and liquidity risk management problem related to the maturity of its assets relative to its liabilities? For most FIs, the maturity of assets is greater than the maturity of liabilities. As the difference in the average maturity between the assets and liabilities increases, liquidity risk increases. In the event liabilities began to leave the FI or to be not reinvested by investors at maturity, the FI may need to liquidate some of its assets at fire sale prices. These prices would tend to deviate farther from the market value as the maturity of the assets increased. Thus the FI may sustain larger losses. 3. Consider the assets (in millions) of two banks, A and B. Each bank is funded by $120 million in deposits and $20 million in equity. Which bank has the stronger liquidity position? Which bank probably has a higher profit? Bank A Asset Cash $10 Treasury securities $40 Commercial loans $90 Total Assets $140 Bank B Assets Cash Consumer loans Commercial loans Total Assets $20 $30 $90 $140 Bank A is more liquid because it has more liquid assets than Bank B, although it has less cash. Bank B probably earns a higher profit because the return on consumer loans should be greater than the return on Treasury securities. However, comparing the loan portfolios is difficult because it is impossible to evaluate the credit risk contained in each portfolio. 4. What concerns motivate regulators to require DIs to hold minimum amounts of liquid assets? Regulators prefer DIs to hold more liquid assets because this ensures that they are able to withstand unexpected and sudden withdrawals. In addition, regulators are able to conduct 212 monetary policy by influencing the money supply through liquid assets held by DIs. Finally, reserves held at the Fed by financial institutions also are a source of funds to regulators, since they do not pay interest on these deposits. 5. How do liquid asset reserve requirements enhance the implementation of monetary policy? How are reserve requirements a tax on DIs? In the case of banks and other lending institutions, reserve requirements on demand deposits allow regulators to increase or decrease the money supply in an economy. The reserve requirement against deposits limits the ability of banks to expand lending activity. Further, reserves represent a form of tax that regulators can impose on DIs. By raising the reserve requirements, regulators cause banks to transfer more balances into non-earning assets. This tax effect is even larger in cases where inflation is stronger. 6. Rank these financial assets according to their liquidity: cash, corporate bonds, NYSEtraded stocks, and T-bills. The liquidity ranking from most liquid to least liquid would be cash, T-bills, NYSE-traded stocks, and corporate bonds. 7. Define the reserve computation period, the reserve maintenance period, and the lagged reserve accounting system. The reserve computation period is a two-week period beginning on a Tuesday and ending on a Monday over which the required reserves are calculated. The actual reserve calculation is accomplished by multiplying the average deposit balance over this 14-day period times the required reserve ratio. The exact amount of this reserve calculation is not known with certainty until the end of the computation period. The reserve maintenance period is the 14-day period over which the average level of reserves must equal or exceed the required reserve target. The lagged reserve accounting system occurs when the reserve maintenance period begins after the reserve computation period is completed. As long as these two periods do not overlap, the FI should have little uncertainty regarding the amount of reserves necessary to be in compliance with regulatory guidelines. 8. City Bank has estimated that its average daily demand deposit balance over the recent 14day computation period was $225 million. The average daily balance with the Fed over the 14-day maintenance period was $11 million, and the average daily balance of vault cash over the two-week computation period was $7 million. a. Under the rules effective in 2004, what amount of average daily reserves is required to be held during the reserve maintenance period for these demand deposit balances? Reserve requirements = (0 x $6.0m) + ($42.1 - $6.0)(0.03) + ($225 - $42.1) (0.10) 213 = 0 + $1.083 + $18.29 = $19.373 million After subtracting the average daily balance of vault cash of $7 million, the bank needs to maintain a daily average of $12.373 million ($19.373 million - $7 million) during the maintenance period. b. What is the average daily balance of reserves held by the bank over the maintenance period? By what amount were the average reserves held higher or lower than the required reserves? The average daily balance over the maintenance period was $11 million. Therefore, average reserves held were short $1.373 million. c. If the bank had transferred $20 million of its deposits every Friday over the two-week computation period to one of its off-shore facilities, what would be the revised average daily reserve requirement? For the 14-day period, the sum of its daily average is = $225 x 14 = $3,150. If $20 million is transferred on Friday, the total reduction is $120 million over two weekends ($20 x 3 days x 2 weekends), and the total 14-day balance is $3,030. The average daily deposits will be $216.4286 million. Reserve requirements = (0 x $6.0m) + ($42.1 - $6.0)(0.03) + ($216.4286 - $42.1) (0.10) = 0 + $1.083 + $17.4329 = $18.5159 million. City Bank needs to maintain average reserves of $11.5159 million ($18.5159 million - $7 million) during the maintenance period. Since it had $11 million of reserves, extra reserves of $0.5159 per day will need to be set aside. 9. Assume that the 14-day reserve computation period for problem (8) above extended from May 18 through May 31. a. What is the corresponding reserve maintenance period under the rules effective in 2004? The reserve maintenance period would extend from June 17 through June 30. The period begins 30 days after the beginning of the reserve computation period. This makes it easier for bank managers to meet their reserve requirements. By beginning two weeks and two days after the end of the computation period, managers can more easily make up for any errors in their forecast of reserve requirements. b. Given your answers to parts (a) and (b) of problem (8), what would the average required reserves need to be for the maintenance period for the bank to be in reserve compliance? The average required reserves necessary to be in compliance is $12.373 million. 214 10. The average demand deposit balance of a local bank during the most recent reserve computation period is $225 million. The amount of average daily reserves at the Fed during the reserve maintenance period is $16 million, and the average daily vault cash corresponding to the maintenance period is $4.3 million. a. What is the average daily reserve balance required to be held by the bank during the maintenance period? Reserve requirements = (0 x $6.0m) + ($42.1 - $6.0)(0.03) + ($225 - $42.1) (0.10) = 0 + $1.083 + $18.29 = $19.373 million After subtracting the average daily balance of vault cash of $4.3 million, the bank needs to maintain a target daily average of $15.073 million ($19.373 million - $4.3 million) during the maintenance period. b. Is the bank in compliance with the reserve requirements? Yes. The bank has average reserves of $16 million. This amount exceeds the required amount by $0.927 million. c. What amount of reserves can be carried over to the next maintenance period, either as excess or shortfall? A maximum of 4 percent of the required reserves can be carried over to the next maintenance period. Thus, 0.04 x $19.373 million = $0.7749 million can be carried over to the next maintenance period. d. If the local bank has an opportunity cost of 6 percent, what is the effect on the income statement from this reserve period? A total of $0.1521 million (0.927 - 0.7749) has an opportunity cost of no earnings at the 6 percent rate. Thus the loss would be $0.1521(0.06)(14/365) = $350.04. 11. The following demand deposits and cash reserves at the Fed have been documented by a bank for computation of its reserve requirements (in millions) under two-day lagged contemporaneous reserve accounting. The average vault cash for the computation period has been estimated to be $2 million per day. (See the data on the following page.) a. What level of average daily reserves is required to be held by the bank during the maintenance period? Average daily demand deposits = 300 + 250 + 280 + 260 + 260 + 260 + 280 + 300 + 270 + 260 + 250 + 250 + 250 + 240 = 3710/14 = 265 Reserve requirement = (6.0 - 0)(0) + (42.1 - 6.0)(0.03) + (265 - 42.1)(0.10) = 0 + 1.083 + 22.29 = 23.373 215 b. Is the bank in compliance with the requirements? The maintenance period begins on Thursday (11th) of the second month. Average Reserves at Fed = 18 + 27 + 27 + 27 + 20 + 35 + 21 + 18 + 28 + 28 + 28 + 19 + 19 + 21 = 336/14 = 24. Average reserves maintained = 24 + 2 = 26 Excess over required reserves = 26 - 23.373 = 2.627 Monday 10th Demand Deposits $200 Reserves at Fed $20 Tuesday 11th $300 $22 Wednesday 12th $250 $21 Thursday 13th $280 $18 Friday 14th $260 $27 Monday 17th Demand Deposits $280 Reserves at Fed $20 Tuesday 18th $300 $35 Wednesday 19th $270 $21 Thursday 20th $260 $18 Friday 21th $250 $28 Monday 24th Demand Deposits $240 Reserves at Fed $19 Tuesday 25th $230 $19 Wednesday 26th $250 $21 Thursday 27th $260 $19 Friday 28th $270 $24 Monday New Month 1st Demand Deposits $200 Reserves at Fed $20 Tuesday 2nd $300 $22 Wednesday 3rd $250 $21 Thursday 4th $280 $18 Friday 5th $260 $27 8th Demand Deposits $280 Reserves at Fed $20 9th $300 $35 10th $270 $21 11th $260 $18 12th $250 $27 Monday 15th Demand Deposits $240 Reserves at Fed $20 Tuesday 16th $230 $35 Wednesday 17th $250 $21 Thursday 18th $260 $18 Friday 19th $270 $28 Monday 22th Demand Deposits $200 Reserves at Fed $19 Tuesday 23th $300 $19 Wednesday 24th $250 $21 Thursday 25th $280 $19 Friday 26th $260 $24 c. What amount of required reserves can be carried over to the following computation period? Excess that can be carried over = 0.04 x $23.373 million = $0.9349 million. 216 d. If the average cost of funds to the bank is 8 percent per year, what is the effect on the income statement for this bank for this reserve period? Loss = (2.627 - 0.9349 = 1.6921) x (0.08/365) * 14 = .005192 x 1,000,000= $5,192.20. 12. In July of 1998 the lagged reserve accounting (LRA) system replaced a contemporaneous reserve accounting (CRA) system as the method of reserve calculation for DIs. a. Contrast a contemporaneous reserve accounting (CRA) system with a lagged reserve accounting (LRA) system. Under LRA, the bank held reserves against the amount of deposits that had been in the bank two weeks prior. The bank knew its required reserves on every day of the reserve maintenance period. Since reserve requirements are stated in the form of average daily balances, the bank could adjust its reserves over the maintenance period to exactly equal the average reserve requirement. Moreover, under LRA the reserve maintenance and calculation periods were one week while under CRA they are two weeks. b. Under which accounting system, CRA or LRA, are DI reserves higher? Why? Ceteris paribus, one would expect reserves to be higher under the CRA than under the LRA, because under the LRA the bank knew its reserve requirement exactly on every day of the reserve maintenance period. There was no need for the bank to hold excess reserves as a cushion against an unforeseen increase in reserve requirements. Banks were able to keep their reserves to the minimum required level. Under CRA, the bank does not know its reserve requirement until the last two days of the reserve maintenance period. Since those are the days during which Fed fund rates are most volatile, banks attempt to avoid large reserve shortages late in the reserve maintenance period. They will therefore tend to hold excess reserves early in the maintenance period that may be reduced on the last two days of the settlement week. c. Under which accounting system, CRA or LRA, is DI uncertainty higher? Why? Since information was complete during the entire settlement week under LRA, but complete under CRA only during the last two days of the maintenance period, there is more uncertainty about reserve requirements under the CRA than under the LRA. 13. What is the \"weekend game\"? Contrast the DI's ability and incentive to play the weekend game under LRA as opposed to CRA. Since Friday balances are carried over the weekend and are counted for Saturday and Sunday, they carry more weight in the reserve computations. Thus, the DIs developed a strategy to send deposits off-shore on Friday, thereby reducing their Friday closing deposit balances. When these deposits were bought back on Monday, average daily deposit balances were reduced, thereby decreasing reserve requirements. Although the ratio of weekends to total days in the reserve computation period is the same under LRA as under 217 CRA (2/7 or 4/14), there was greater flexibility for DIs to play the weekend game under LRA. That is because the DI had complete information about reserve requirements on each day of the maintenance period. However, because of the uncertainty under CRA, there is greater incentive for DIs to play the weekend game under CRA than under LRA. 14. Under CRA, when is the uncertainty about the reserve requirement resolved? Discuss the feasibility of making large reserve adjustments during this period of complete information. Under CRA, the uncertainty regarding reserve requirements is resolved on the last two days of the reserve maintenance period (on the last Tuesday and Wednesday of the 14 day period). However, since these are also the days of greatest volatility in the Fed funds rate, it could be very costly for the reserve manager to make large reserve adjustments or corrections during this two-day period. Moreover, since the Fed funds market is comprised of active traders that deal daily with one another, a large reserve imbalance would lead to abnormal Fed funds transactions and would be quickly detected and exploited (to the detriment of the original DI) by other DI traders. 15. What is the relationship between funding cost and funding or withdrawal risk? Liabilities that have a low cost often have the highest risk of withdrawal. Thus a bank that chooses to attract low cost deposits may have high withdrawal risk. 16. An FI has estimated the following annual costs for its demand deposits: management cost per account = $140, average account size = $1,500, average number of checks processed per account per month = 75, cost of clearing a check = $0.10, fees charged to customer per check = $0.05, and average fee charged per customer per month = $8. a. What is the implicit interest cost of demand deposits for the FI? Cost of clearing checks = $0.10 x 75 x 12 Cost of managing each account Per check fee per account = $0.05 x 75 x 12 Fee received per account = $8 x 12 Total cost per account = $90.00 = $140.00 = -$45.00 = -$96.00 = $89.00 The average (imputed) interest cost of demand deposits = $89.00/1,500 = 5.93 percent. b. If the FI has to keep an average of 8 percent of demand deposits as required reserves with the Fed, what is the implicit interest cost of demand deposits for the FI? If the bank has to keep 8 percent as reserves, its use of funds is limited to 0.92 x $1,500 per account, or $1,380. The average (imputed) interest cost = $89/$1,380 = 6.45 percent. c. What should be the check-clearing fees to reduce the implicit interest costs to 3 percent? Ignore the reserve requirements. 218 For an average imputed interest cost of 3 percent, the total cost per account = 1,500 x 0.03 = $45. This means that the per-check fee should be increased to $89 from $45. Thus, the fee per check should be raised to $89/(75 x 12) = $0.10 (actually $0.0989) per check. 17. A NOW account requires a minimum balance of $750 for interest to be earned at an annual rate of 4 percent. An account holder has maintained an average balance of $500 for the first six months and $1,000 for the remaining six months. She writes an average of 60 checks per month and pays $0.02 per check, although it costs the bank $0.05 to clear a check. a. What average return does the account holder earn on the account? Gross interest return = Explicit interest return + Implicit interest return Interest earned by account holder $1,000 x (0.04/2) Implicit fee earned on checks $0.03 x 60 x 12 Average deposit maintained during the year (500) + (1,000) = $20.00 = $21.60 = $750.00 Average interest earned = $41.60/750 = 5.55 percent b. What is the average return if the bank lowers the minimum balance to $400? If the minimum balance requirement is lowered to $400, the account holder earns an extra $500 x (0.04/2) = $10 in interest. The average interest earned = $51.60/750 = 6.88 percent. c. What is the average return if the bank pays interest only on the amount in excess of $400? Assume that the minimum required balance is $400. If the bank only pays interest on balances in excess of $400, the explicit interest earned = $100 x 0.02 + $600 x 0.02 = $2 + $12 = $14. The implicit fee earned on checks = $21.60, and the average interest earned = $35.60/$750 = 4.75% d. How much should the bank increase its check-clearing fee to ensure that the average interest it pays on this account is 5 percent? Assume that the minimum required balance is $750. Interest earned (both explicit and implicit) = $750 x 0.05 = $37.50. Fees to be earned through check clearing = $37.50 - $20 = $17.50. Fee subsidy per check = 7.50/(60 x 12) = $0.0243. So, the bank should charge $0.05 - $0.0243 = $0.0257 per check. 18. Rank order the following liabilities, with respect first to funding risk and then to funding cost: Funding Risk Funding Cost a. Money market mutual funds. b. Demand deposits. 12 1 c. Certificates of deposit. 8 5 d. Federal funds. 6 7 219 e. f. g. h. i. j. k. l. Bankers acceptances. Eurodollar deposits. Money market demand deposits. NOW accounts. Wholesale CDs. Passbook savings. Repos. Commercial paper. 4 3 9 11 7 10 5 2 9 10 4 2 6 3 8 11 The rankings above are not meant to be definitively precise, but are made to illustrate that the funding cost and the funding risk are inversely related. For example, demand deposits usually are considered to be the least-cost source of funding, but they also are easily withdrawn from the bank. On the other hand, repos, wholesale CDs, and term fed funds are not liquid during their term, but can be extremely liquid at maturity if the bank has any kind of financial distress. The cost of each of these types of funds is directly linked to money market conditions. The contrast between funding risk and funding cost for several of the liabilities is discussed below: Demand deposits have low funding costs, but technically have high amounts of funding risk since they can be withdrawn at any time. However, in practical terms, demand deposits are often quite stable and may behave like long-term core deposits. Certificates of deposit have high funding costs (because of reserve requirements and risk premiums on negotiable CDs), but they have low funding risk since they can be withdrawn only upon payment of interest penalties. Federal funds have relatively low funding costs (although these costs are higher than those for demand deposits) because of their overnight maturity, but they can have high funding risk if the bank is distressed or not an active participant in the Fed funds market. However, for major money center banks, the funding risk on Fed funds is quite low. Eurodollar CD deposits have high funding costs because of the default risk premium, but they are low funding risk. Eurodollar interbank deposits, however, are akin to demand deposits and may have high funding risks, particularly if the bank is rumored to be in financial distress. 19. How is the withdrawal risk different for Federal funds and repurchase agreements? Withdrawal risk is lower for repurchase agreements (RPs) because they are collateralized usually by government securities. Since RPs are collateralized, they require a lower risk premium but they require time to process because of the need to post collateral. In every other respect, the transaction of an RP is similar to Federal funds. 20. How does the cash balance, or liquidity, of an FI determine the types of repurchase agreement into which it will enter? If the FI has surplus cash, it would buy securities with the understanding that the seller would repurchase them later. In this case the repurchase agreement is an asset for the firm that bought 220 the securities. If an FI is low on cash, it would sell securities for cash with the understanding that it would repurchase the securities later. Here the repo is a liability. 21. How does the cost of MMMFs differ from the cost of MMDAs? How is the spread useful in managing the withdrawal risk of MMDAs? MMMFs earn rates of return that are directly related to the money market conditions for the assets held by the funds. MMDAs can be priced to reflect these conditions, but they do not necessarily need to be priced in this manner. Since the two products compete for investor funds, banks can control the rate of withdrawal of funds from the MMDAs by raising or lowering the explicit interest rate paid to depositors. Allowing the MMDA-MMMF spread to become increasingly negative will increase the rate of withdrawal from the MMDA accounts. 22. Why do wholesale CDs have minimal withdrawal risk to the issuing bank? Wholesale CDs are negotiable instruments that can be sold (discounted) in the secondary market. Thus if the initial investor needs funds before the CDs mature, the CDs can be liquidated at money market rates by the investor without withdrawing the funds from the issuing bank. 23. What characteristics of fed funds may constrain a DI's ability to use fed funds to expand quickly its liquidity? Fed funds are uncollateralized loans. As such, DIs selling fed funds often will limit the amount of funds they will provide to any one borrowing institution. Further, fed funds do have risk of non-rollover at maturity. 24. What does a low Fed funds rate indicate about the level of bank reserves? Why does the Fed funds rate have higher than normal variability around the last two days in the reserve maintenance period? A low fed funds rate would indicate low levels of bank borrowing and an ample or at least adequate supply of reserves among banks. Whether the general level of the fed funds rate is low or high, the variability of the rate around the last two days in the reserve maintenance period will accelerate as banks attempt to meet the required reserve levels. 25. What trends have been observed between 1960 and 2004 in regard to liquidity and liability structures of commercial banks? What changes have occurred in the management of assets that may cause the measured trends to be overstated? From Table 18-4, it is clear that commercial banks have reduced their composition of liquid assets to illiquid assets from 52 percent to 32 percent (liquid assets = cash; government and agency securities; and other securities). However, this may be overstated because the illiquid assets, such as commercial and mortgage loans, are significantly different today from prior years because they can be securitized and sold in the secondary markets. As a result, they are not as illiquid as they were in the past, which may be one reason why banks held more liquid assets in prior years. Table 18-5 also shows that there has been a shift away from transaction accounts to 221 time accounts, CDs, and borrowed funds. Although this reduces withdrawal risk, these funds are more expensive for commercial banks. 26. What are two primary methods that insurance companies can use to reduce their exposure to liquidity risk? First, insurance companies can reduce their exposure by diversifying the distribution of risk in the contracts they write. In addition, insurance companies can meet liquidity needs by holding relatively marketable assets to cover claim payments. 222