a. If the risk premium for a given customer is 2.5 percent, what is the simple promised interest return on the loan?

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1 Selected Questions and Exercises Chapter Differentiate between a secured and an unsecured loan. Who bears most of the risk in a fixed-rate loan? Why would bankers prefer to charge floating rates, especially for longer-maturity loans? 3. How does a spot loan differ from a loan commitment? What are the advantages and disadvantages of borrowing through a loan commitment? 8. What are compensating balances? What is the relationship between the amount of compensating balance requirement and the return on the loan to the FI? 9. County Bank offers one-year loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost of this loan to the borrower? How does the cost change if the compensating balance is 15 percent? If the compensating balance is 20 percent? The true cost is the loan rate (1 compensating balance rate) = 9% ( ) = 10 percent. For compensating balance rates of 15 percent and 20 percent, the true cost of the loan would be percent and percent respectively. Note that as the compensating balance rate increases by a constant amount, the true cost of the loan increases at an increasing rate. 10. Metrobank offers one-year loans with a 9 percent stated or base rate, charges a 0.25 percent loan origination fee, imposes a 10 percent compensating balance requirement, and must pay a 6 percent reserve requirement to the Federal Reserve. The loans typically are repaid at maturity. a. If the risk premium for a given customer is 2.5 percent, what is the simple promised interest return on the loan? The simple promised interest return on the loan is BR + m = = or 11.5 percent. b. What is the contractually promised gross return on the loan per dollar lent? σf + ( BR + m) ( ) k = = = = percent 1 [ b(1 RR)] 1 [0.1(1 0.06)] c. Which of the fee items has the greatest impact on the gross return? The compensating balance has the strongest effect on the gross return on the loan. Without the compensating balance, the gross return would equal percent, a reduction of 1.22 percent. Without the origination fee, the gross return would be percent, a reduction of only 0.28 percent. Eliminating the reserve requirement would cause the gross return to increase to percent, an increase of 0.09 percent.

2 12. Why could a lender s expected return be lower when the risk premium is increased on a loan? In addition to the risk premium, how can a lender increase the expected return on a wholesale loan? A retail loan? An increase in risk premiums indicates a riskier pool of clients who are more likely to default by taking on riskier projects. This reduces the repayment probability and lowers the expected return to the lender. In both cases the lender often is able to charge fees that increase the return on the loan. However, in both cases also, the fees may become sufficiently high as to increase the risk of nonpayment of default on the loan. 14. Identify and define the borrower-specific and market-specific factors that enter into the credit decision. What is the impact of each type of factor on the risk premium? The borrower-specific factors are: Reputation: Based on the lending history of the borrower; better reputation implies a lower risk premium. Leverage: A measure of the existing debt of the borrower; the larger the debt, the higher the risk premium. Volatility of earnings: The more stable the earnings, the lower the risk premium. Collateral: If collateral is offered, the risk premium is lower. Market-specific factors include: Business cycle: Lenders are less likely to lend if a recession is forecasted. Level of interest rates: A higher level of interest rates may lead to higher default rates, so lenders are more reluctant to lend under such conditions. 15. Why is the degree of collateral as specified in the loan agreement of importance to the lender? If the book value of the collateral is greater than or equal to the amount of the loan, is the credit risk of the lender fully covered? Why, or why not? 22. If the rate of one-year T-Bills currently is 6 percent, what is the repayment probability for each of the following two securities? Assume that if the loan is defaulted, no payments are expected. What is the market-determined risk premium for the corresponding probability of default for each security? a. One-year AA rated bond yielding 9.5 percent? Probability of repayment = p = (1 + I)/(1 + k) For an AA-rated bond = (1 +.06)/ ( ) = 0.968, or 96.8 percent The market determined risk premium is = or 3.5 percent b. One-year BB rated bond yielding 13.5 percent? Probability of repayment = p = (1 + I)/(1 + k)

3 For BB-rated bond = (1 +.06)/( ) = percent The market determined risk premium is = or 7.5 percent 23. A bank has made a loan charging a base lending rate of 10 percent. It expects a probability of default of 5 percent. If the loan is defaulted, it expects to recover 50 percent of its money through the sale of its collateral. What is the expected return on this loan? E(r) = p(1 + k) + (1 - p)(1 + k)(α ) where α is the percentage generated when the loan is defaulted. E(r) =.95(1 +.10) +.05(1 +.10)(.50) = = = 7.25% 24. Assume a one-year T-Bill is currently yielding 5.5 percent, and a AAA-rated discount bond with similar maturity is yielding 8.5 percent. a. If the expected recovery from collateral in the event of default is 50 percent of principal and interest, what is the probability of repayment of the AAArated bond? What is the probability of default? p(1 + k) + γ (1 - p)(1 + k) = 1+I. Solve for the probability of repayment (p): 1+ i γ k p = = = or percent 1 γ Therefore the probability of default is = or 5.53 percent. b. What is the probability of repayment of the AAA-rated bond if the expected recovery from collateral in the case of default is percent of principal and interest? What is the probability of default? 1+ i γ k p = = = or percent 1 γ Therefore the probability of default is = or percent. c. What is the relationship between the probability of default and the proportion of principal and interest that may be recovered in the case of default on the loan? The proportion of the loan s principal and interest that is collectible on default is a perfect substitute for the probability of repayment should such defaults occur. 31. What is RAROC? How does this model use the concept of duration to measure the risk exposure of a loan? How is the expected change in the credit premium measured? What precisely is ΔLN in the RAROC equation?

4 RAROC is a measure of expected loan income in the form of interest and fees relative to some measure of asset risk. The RAROC model uses the duration model formulation to measure the change in the value of the loan for given changes or shocks in credit quality. The change in credit quality (ΔR) is measured by finding the change in the spread in yields between Treasury bonds and bonds of the same risk class of the loan. The actual value chosen is the highest change in yield spread for the same maturity or duration value assets. In this case, ΔLN represents the change in loan value or the change in capital for the largest reasonable adverse changes in yield spreads. The actual equation for ΔLN looks very similar to the duration equation. RAROC = Net Income Risk ( or ΔLN ) where ΔLN = D LN x LN ΔR x 1 + R where R is the change in yield spread 32. A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years and a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. Assume the bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 percent, based on two years of historical data. The current market interest rate for loans in this sector is 12 percent. a. Using the RAROC model, determine whether the bank should make the loan? RAROC = Fees and interest earned on loan/ Loan or capital risk Loan risk, or ΔLN = -D LN *LN*(ΔR/(1 + R) = = -7.5 * $5m * (.042/1.12) = - $1,406,250 Expected interest = 0.12 x $5,000,000 = $600,000 Servicing fees = x $5,000,000 = $25,000 Less cost of funds = 0.10 x $5,000,000 = -$500,000 Net interest and fee income = $125,000 RAROC = $125,000/1,406,250 = 8.89 percent. Since RAROC is lower than the cost of funds to the bank, the bank should not make the loan. b. What should be the duration in order for this loan to be approved? For RAROC to be 10 percent, loan risk should be: $125,000/ΔLN = 0.10 ΔLN = 125,000 / 0.10 = $1,250,000 -D LN * LN * (ΔR/(1 + R)) = 1,250,000 D LN = 1,250,000/(5,000,000 * (0.042/1.12)) = 6.67 years. Thus, this loan can be made if the duration is reduced to 6.67 years from 7.5 years. The duration can be reduced.

5 c. Assuming that duration cannot be changed, how much additional interest and fee income would be necessary to make the loan acceptable? Necessary RAROC = Income/Risk Income = RAROC * Risk = $1,406,250 *0.10 = $140,625 Therefore, additional income = $140,625 - $125,000 = $15,625. Chapter How do loan portfolio risks differ from individual loan risks? 2. What does loan concentration risk mean? 6. Explain how modern portfolio theory can be applied to lower the credit risk of an FI s portfolio. Modern portfolio theory has demonstrated that a well-diversified portfolio can provide opportunities for individuals to invest in a set of efficient frontier portfolios, defined as those portfolios that provide the maximum returns for a given level of risk or the lowest risk for a given level of returns. By choosing portfolios on the efficient frontier, a banker may be able to reduce credit risk to the fullest extent. As shown in Figure 11.1, a manager s selection of a particular portfolio on the efficient frontier is determined by his or her risk-return trade-off. Chapter 13 This chapter students should be able to identify Schedule L and non-schedule L Off- Balance-Sheet. 1. Classify the following items as either (1) on-balance-sheet assets, (2) onbalance-sheet liabilities, (3) off-balance-sheet assets, (4) off-balance-sheet liabilities, or (5) capital account. Classification a. Loan commitments 3 b. Loan loss reserves 5 c. Letter of credit 2 d. Banker s acceptance 2 e. Rediscounted banker s acceptance 2 f. Loan sales without recourse None of the above. g. Loan sales with recourse 3 h. Forward contracts to purchase 3 I. Forward contracts to sell 4 j. Swaps 4 (for liability swaps) k. Loan participations 1 l. Securities borrowed 3 m. Securities lent 4 n. Loss adjustment expense account (PC insurers) 2 o. Net policy reserves 2

6 2. How does one distinguish between an off-balance-sheet asset and an offbalance-sheet liability? Off-balance-sheet activities or items are contingent claim contracts. An item is classified as an off-balance-sheet asset when the occurrence of the contingent event results in the creation of an on-balance-sheet asset. An example is a loan commitment. If the borrower decides to exercise the right to draw down on the loan, the bank will incur a new asset on its portfolio. Similarly, an item is an off-balance-sheet liability when the contingent event creates an on-balance-sheet liability. An example is a standby letter of credit (LC). In the event that the original payer of the LC defaults, then the bank is liable to pay the amount to the payee, incurring a liability on the right-hand side of its balance sheet. 3. Contingent Bank has the following balance sheet in market value terms (in millions of dollars): Assets Liabilities Cash $20 Deposits $220 Mortgages $220 Equity $20 Total Assets $240 Total Liabilities & Equity $240 In addition, the bank has contingent assets with $100 million market value and contingent liabilities with $80 million market value. What is the true stockholder net worth? What does the term contingent mean? Net worth = ( ) + (100-80) = $40 million. The term contingent means an event that may or may not happen. In financial economics, the term is used in conjunction with the result given that some event does occur. 12. How is an FI exposed to interest rate risk when it makes loan commitments? In what way can an FI control for this risk? How does basis risk affect the implementation of the control for interest rate risk? 22. Distinguish between loan sales with and without recourse. Why would banks want to sell loans with recourse? Explain how loan sales can leave banks exposed to contingent interest rate risks. Chapter What are core deposits? What role do core deposits play in predicting the probability distribution of net deposit drains? 6. What are two ways a DI 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 DI has a net deposit drain, it needs to either increase its liabilities (by borrowing funds or issuing equity) or reduce its assets. An institution can reduce its assets by drawing down on its cash reserves, selling securities, or calling back (or not

7 renewing) its loans. It can increase liabilities by issuing more Federal funds, longterm debt, or new issues of equity. If a DI offsets the drain by increasing liabilities, the size of the firm remains the same. However, if it offsets the drain by reducing its assets, the size of the firm is reduced. If it has a net negative deposit drain, then it needs to follow the opposite strategy. The operational benefit of addressing a net deposit drain is to restore the financial stability and health of the DI. 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, or asset-mix instability. Further, not renewing loans may result in the loss of profitable relationships that could have negative affects 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. 8. A DI 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 & Equity $75 Show the DI's balance sheet if the following conditions occur. a. The DI purchases liabilities to offset this expected drain. If the DI purchases liabilities, then the new balance sheet is: Cash $10 Deposits $53 Loans $50 Purchased liabilities $15 Securities $15 Equity $ 7 b. The stored liquidity management method is used to meet the liquidity shortfall. If the DI uses reserve asset adjustment, a possible balance sheet may be: Loans $50 Deposits $53 Securities $10 Equity $ 7 DIs will most likely use some combination of these two methods. 9. 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 & Equity $170 AllStarBank s largest customer decides to exercise a $15 million loan

8 commitment. How will the new balance sheet appear if AllStar uses the following liquidity risk strategies? a. Asset management. Assets Liabilities and Equity Cash $30 Deposits $110 Loans $105 Borrowed funds $40 Securities $35 Equity $20 Total Assets $170 Total Liabilities & Equity $170 b. Liability management. Assets Liabilities and Equity Cash $30 Deposits $110 Loans $105 Borrowed funds $55 Securities $50 Equity $20 Total Assets $185 Total Liabilities & Equity $185 Chapter 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? 2. How is an FI s liability and liquidity risk management problem related to the maturity of its assets relative to its liabilities? 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 Bank B Assets Cash $10 Cash $20 Treasury securities $40 Consumer loans $30 Commercial loans $90 Commercial loans $90 Total Assets $140 Total Assets $ Rank these financial assets according to their liquidity: cash, corporate bonds, NYSE-traded stocks, and T-bills. Chapter How does federal deposit insurance help mitigate the problem of bank runs. What other elements of the safety net are available to banks in the U.S.? 5. What is moral hazard? How did the fixed-rate deposit insurance program of the FDIC contribute to the moral hazard problem of the savings and loan industry?

9 What other changes in the savings association environment during the 1980s encouraged the developing instability of the industry? 6. How does a risk-based insurance program solve the moral hazard problem of excessive risk taking by FIs? 10. What is capital forbearance? How does a policy of forbearance potentially increase the costs of financial distress to the insurance fund as well as the stockholders? Capital forbearance refers to regulators permitting an FI with depleted capital to continue operations. The primary advantage occurs in the short run through the savings of liquidation costs. In the longer run, the likely cost is that the poorly managed FI will become larger, more risky, but no more solvent. Eventually even larger liquidation costs must be incurred. 13. Why did the fixed-rate deposit insurance system fail to induce insured and uninsured depositors to impose discipline on risky banks in the United States in the 1980s? 15. What failure resolution methods were available to regulators before the passage of FDICIA in 1991? What was the essentiality provision? Prior to FDICIA, the failure resolution methods included the payoff method, the purchase and assumption method, and the open assistance method. The FDIC was forced to use liquidation unless an alternative method cost less than liquidation to implement. Further, the FDIC could choose to keep open a bank if the continued operation was considered essential to providing financial services to the local community. Chapter Identify and briefly discuss the importance of the five functions of an FI s capital? a. How does economic value accounting recognize the adverse effects of credit and interest rate risk? The loss in value caused by credit risk and interest rate risk is borne first by the equity holders, and then by the liability holders. In market value accounting, the adjustments to equity value are made simultaneously as the losses due to these risk elements occur. Thus economic insolvency may be revealed before accounting value insolvency occurs. b. How does book value accounting recognize the adverse effects of credit and interest rate risk? Because book value accounting recognizes the value of assets and liabilities at the time they were placed on the books or incurred by the firm, losses are not recognized until the assets are sold or regulatory requirements force the firm to make balance sheet accounting adjustments. In the case of credit risk, these

10 adjustments usually occur after all attempts to collect or restructure the loans have occurred. In the case of interest rate risk, the change in interest rates will not affect the recognized accounting value of the assets or the liabilities. 8. How is the leverage ratio for an FI defined? 10. Identify and discuss the weaknesses of the leverage ratio as a measure of capital adequacy. 13. What is the total risk-based capital ratio? 14. Identify the five zones of capital adequacy and explain the mandatory regulatory actions corresponding to each zone. Zone 1: Well capitalized. The total risk-based capital ratio (RBC) ratio exceeds 10 percent. No regulatory action is required. Zone 2: Adequately capitalized. The RBC ratio exceeds 8 percent, but is less than 10 percent. Institutions may not use brokered deposits except with the permission of the FDIC. Zone 3: Undercapitalized. The RBC ratio exceeds 6 percent, but is less than 8 percent. Requires a capital restoration plan, restricts asset growth, requires approval for acquisitions, branching, and new activities, disallows the use of brokered deposits, and suspends dividends and management fees. Zone 4: Significantly undercapitalized. The RBC ratio exceeds 2 percent, but is less than 6 percent. Same as zone 3 plus recapitalization is mandatory, places restrictions on deposit interest rates, interaffiliate transactions, and the pay level of officers. Zone 5: Critically undercapitalized. The RBC ratio is less than 2 percent. Places the bank in receivorship within 90 days, suspends payment on subordinated debt, and restricts other activities at the discretion of the regulator. The mandatory provisions for each of the zones described above include the penalties for any of the zones prior to the specific zone. 15. What are the definitional differences between Tier I and Tier II capital? 17. Explain the process of calculating credit risk-adjusted on-balance-sheet assets. Balance sheet assets are assigned to four categories of credit risk exposure. The dollar amount of assets in each category is multiplied by an appropriate weight of 0 percent, 20 percent, 50 percent, and 100 percent respectively for the categories representing no risk to full credit risk respectively. The weighted dollar amounts of each category are added together to get the total risk-adjusted on-balance-sheet assets. a. What assets are included in the four (five) categories of credit risk exposure under Basel I (Basel II)?

11 Category 1 includes cash, United States Treasury bills, notes and bonds, mortgage-backed securities, and Federal Reserve Bank balances. Category 2 includes U.S. agency-backed securities, municipal issued general obligation bonds, FHLMC and FNMA mortgage-backed securities, and interbank deposits. Category 3 includes other municipal revenue bonds and regular residential mortgage loans. All other commercial, consumer, and credit card loans, real assets and any other asset not included above are included in category 4. Basel II attempts to align capital requirements more closely with the banking risk of the FI. In addition to the above classifications, the Basel II categories include the following: Category 1: Loans to sovereigns with an S&P rating of AA- or better. Category 2: Loans to sovereigns with an S&P rating between A- and A+ inclusive, and loans to banks and corporates with an S&P rating of AA- or better. Category 3: Loans to sovereigns with an S&P rating between BBB- and BBB+ inclusive, and loans to banks and corporates with an S&P rating between AA- and A+ inclusive. Category 4: Loans to sovereigns with an S&P rating of B- to BB+. Loans to banks with an S&P rating of B- to BBB+. Loans to corporates with a credit rating of BB- to BBB+. Category 5: This is a new category introduced by Basel II. Loans to sovereigns, banks, and securities firms with an S&P credit rating below B-. Loans to corporates with a credit rating below BB-. b. What are the appropriate risk-weights for each category? Category 1 has a risk weight of 0 percent, category 2 has a risk weight of 20 percent, category 3 has a risk weight of 50 percent, and category 4 has a risk weight of 100 percent. In addition for Basel II, category 5 has a risk weight of 150 percent.

12 18. National Bank has the following balance sheet (in millions) and has no offbalance-sheet activities: Assets Liabilities and Equity Cash $20 Deposits $980 Treasury bills $40 Subordinated debentures $40 Residential mortgages $600 Common stock $40 Other loans $430 Retained earnings $30 Total Assets $1,090 Total Liabilities and Equity $1,090 a. What is the leverage ratio? The leverage ratio is ($40 + $30)/$1,090 = or percent. b. What is the Tier I capital ratio? Risk-adjusted assets = $20x0.0 + $40x0.0 + $600x0.5 + $430x1.0 = $730. Tier I capital ratio = ($40 + $30)/$730 = or 9.59 percent. c. What is the total risk-based capital ratio? The total risk-based capital ratio = ($40 + $40 + $30)/$730 = or percent. d. In what capital category would the bank be placed? The bank would be place in the well-capitalized category. Chapter What has been the effect of securitization on the asset portfolios of financial institutions? 6. An FI is planning to issue $100 million in commercial loans. The FI will finance the loans by issuing demand deposits. a. What is the minimum capital required by the Basle accord? The minimum capital required on commercial loans = $100 x 1.0 x 0.08 = $8 million. b. What is the minimum amount of demand deposits needed to fund this loan assuming there is a 10 percent average reserve requirement on demand deposits? Since there is an interaction between the demand deposits and cash reserves held, the answer requires solving the following, assuming the $8 is funded by equity and the reserve requirements are kept as cash: $100 + (0.10 x DD) = DD + 8 DD = 92/.9 = $102.22

13 c. Show a simple balance sheet with total assets, total liabilities, and equity if this is the only project funded by the bank. Assets Liabilities Cash $10.22 Demand deposits $ Loan Equity 8.00 Total d. How does this balance sheet differ from Table 28-1? Why? The example in Table 28-1 assumes that the capital ratio is only 4 percent, since the loans are residential mortgages. Thus, because the loans in this problem are commercial loans, the bank must keep a full 8 percent risk-based capital ratio and the balance sheet is $0.44 less than the Table 28-1 example. In effect, although the capital is higher, the reserve requirement tax is lower. 10. Consider the mortgage pass-through example presented in Table 28-3 and Figure The total monthly payment by the borrowers reflecting a 12 percent mortgage rate is $1,028, The payment passed through to the ultimate investors reflecting an 11.5 percent return is $990, Who receives the difference in these two payments? How are the shares determined? The difference in the two payments (438,321.17) goes to the mortgage-serviceprovider and to GNMA for the insurance premium. If the total fee is 50 basis points, and GNMA receives 6 basis points for the insurance premium, GNMA would receive 12 percent (6/50) of the difference ($4,598.54) in the two payments, and the mortgage service provider would receive 88 percent (44/50) of the difference ($33,722.63) in the two payments. 11. Consider a GNMA mortgage pool with principal of $20 million. The maturity is 30 years with a monthly mortgage payment of 10 percent per annum. Assume no prepayments. a. What is the monthly mortgage payment (100 percent amortizing) on the pool of mortgages? The monthly mortgage payment, R, is (the monthly interest rate is.10/ 12 =.00833): $20m = PVA n=360, k= *(R) R = $175, b. If the GNMA insurance fee is 6 basis points and the servicing fee is 44 basis points, what is the yield on the GNMA pass-through? The GNMA's annual interest rate is = 9.5 percent. The monthly interest rate is 0.095/12 = or percent. c. What is the monthly payment on the GNMA in part (b)?

14 The monthly GNMA payment, R, is: $20m = PVA n=360, k= % *R R = $168, d. Calculate the first monthly servicing fee paid to the originating FIs. The first monthly servicing fee, R, is (the monthly fee rate is.44%/12 =.0367%): R = ( )$20m = $7,340 e. Calculate the first monthly insurance fee paid to GNMA. The first monthly insurance payment, R, is (monthly insurance rate is.06%/12 =.005%): R = (.00005)$20m = $1,000