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financial institutions management
ISE Financial Institutions Management A Risk Management Approach 10th International Edition Anthony Saunders Professor, Marcia Millon Cornett, Otgo Erhemjamts - Solutions
1. Why is credit risk analysis an important component of FI risk management? What recent activities by FIs have made the task of credit risk assessment more difficult for both FI managers and regulators?
3. What is the link between the implied volatility of a firm’s assets and its expected default frequency?
2. How should the risk premium on a loan be affected if there is a reduction in a borrower’s leverage and the underlying volatility of its earnings?
1. Which is the only credit risk model discussed in this section that is really forward looking?
2. Why would any FI manager buy loans that have a cumulative default probability of 33.75 percent? Explain your answer.
1. In Table 10–9, the cumulative default probability over three years for CCC-rated corporate bonds is 33.75 percent. Check this calculation using the individual year MMRs.
2. How should the posting of collateral by a borrower affect the risk premium on a loan?
1. What is the difference between the marginal default probability and the cumulative default probability?
3. What are two problems in using discriminant analysis to evaluate credit risk?
2. Suppose X3 = 0.5 in Example 10–3. Show how this would change the default risk classification of the borrower. (Z =3.95)
1. Suppose an estimated linear probability model looked as follows: Z = 0.03X1 + 0.01X2 + error, where X1 = Debt-to-equity ratio X2 = Total assets-to-working capital ratio Suppose, for a prospective borrower, X1 = 1.5 and X2 = 3.0.What is the projected probability of default for the borrower?(7.5%)
2. How should the risk premium on a loan be affected if there is a reduction in a borrower’s leverage?
1. Make a list of key borrower characteristics you would assess before making a mortgage loan.
2. How do loan covenants help protect an FI against default risk?
1. Is it more costly for an FI manager to assess the default risk exposure of a publicly traded company or a small, singleproprietor firm? Explain your answer.
2. What might happen to the expected return on a wholesale loan if an FI eliminates its fees and compensating balances in a low–interest rate environment?
1. Can an FI’s expected return on its loan portfolio increase if it cuts its loan rates?
2. What is the expected return on this loan if the probability of default is 5 percent? (10.42%)
1. Calculate the promised return (k) on a loan if the base rate is 13 percent, the risk premium is 2 percent, the compensating balance requirement is 5 percent, fees are ½ percent, and reserve requirements are 10 percent. (16.23%)
3. Referring to Table 10–6, explain why credit card loan rates are much higher than car loan rates.
2. Will more ARMs be originated in high- or low-interest rate environments? Explain your answer.
1. What are the four major types of loans made by U.S.commercial banks? What are the basic distinguishing characteristics of each type of loan?
2. What are some of the newer, nontraditional activities that create credit risk for today’s FIs?
1. What are some of the credit quality problems faced by FIs over the last three decades?
36. Estimate the convexity for each of the following three bonds, all of which trade at a yield to maturity of 8 percent and have face values of $1,000.A seven-year, zero-coupon bond.A seven-year, 10 percent annual coupon bond.A 10-year, 10 percent annual coupon bond that has a duration value of
35. MLK Bank has an asset portfolio that consists of $100 million of 30-year, 8 percent coupon, $1,000 bonds that sell at par.a. What will be the bonds’ new prices if market yields change immediately by ± 0.10 percent? What will be the new prices if market yields change immediately by ± 2.00
34. Consider a $1,000 bond with a fixed-rate 10 percent annual coupon rate and a maturity (N) of 10 years. The bond currently is trading at a yield to maturity (YTM) of 10 percent.a. Complete the following table:b. Use this information to verify the principles of interest rate–price relationships
33. Consider a five-year, 15 percent annual coupon bond with a face value of $1,000. The bond is trading at a yield to maturity of 12 percent.a. What is the price of the bond?b. If the yield to maturity increases 1 percent, what will be the bond’s new price?c. Using your answers to parts (a) and
32. Consider a 12-year, 12 percent annual coupon bond with a required return of 10 percent. The bond has a face value of $1,000.a. What is the price of the bond?b. If interest rates rise to 11 percent, what is the price of the bond?c. What has been the percentage change in price?d. Repeat parts
31. A financial institution has an investment horizon of two years 9.33 months (or 2.777 years). The institution has converted all assets into a portfolio of 8 percent, $1,000 three-year bonds that are trading at a yield to maturity of 10 percent. The bonds pay interest annually. The portfolio
30. In general, what changes have occurred in the financial markets that would allow financial institutions to restructure their balance sheets more rapidly and efficiently to meet desired goals? Why is it critical for an FI manager who has a portfolio immunized to match a desired investment
29. Identify and discuss three criticisms of using the duration gap model to immunize the portfolio of a financial institution.
28. Assume that a goal of the regulatory agencies of financial institutions is to immunize the ratio of equity to total assets, that is,Δ(E/A) = 0. Explain how this goal changes the desired duration gap for the institution. Why does this differ from the duration gap necessary to immunize the total
27. Refer again to the financial institutions in problem 26.a. What is the change in the value of the firm’s assets for a relative upward shift in the entire yield curve of 0.5 percent?b. What is the change in the value of the firm’s liabilities for a relative upward shift in the entire yield
26. The following balance sheet information is available (amounts in thousands of dollars and duration in years) for a financial institution:Treasury bonds are five-year maturities paying 6 percent semiannually and selling at par.a. What is the duration of the T-bond portfolio?b. What is the
25. Hands Insurance Company issued a $90 million, one-year note at 8 percent annual interest (paying one coupon at the end of the year)or with an 8 percent yield. The proceeds, plus $10 million in equity, were used to fund a $100 million, two-year commercial loan with a 10 percent coupon rate and a
24. The balance sheet for Gotbucks Bank Inc. (GBI) is presented below($ millions).Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR (London Interbank Offered Rate) + 4 percent, and page 273 currently LIBOR is 11 percent. Fixed-rate loans have five-year
23. Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par.The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900,000, two-year, 7.25 percent semiannual coupon capital
22. If an FI uses only duration to immunize its portfolio, what three factors affect changes in the net worth of the FI when interest rates change?
21. Two banks are being examined by regulators to determine the interest rate sensitivity of their balance sheets. Bank A has assets composed solely of a 10-year, $1 million loan with a coupon rate and yield of 12 percent. The loan is financed with a 10-year, $1 million CD with a coupon rate and
20. Consider the case in which an investor holds a bond for a period of time longer than the duration of the bond, that is, longer than the original investment horizon.a. If interest rates rise, will the return that is earned exceed or fall short of the original required rate of return? Explain.b.
19. Suppose you purchase a five-year, 15 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000.a. Show that the duration of this bond is equal to four years.b. Show that if interest rates rise to 10 percent within the next year and your
18. Suppose you purchase a six-year, 8 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000.a. Show that the duration of this bond is equal to five years.b. Show that if interest rates rise to 10 percent within the next year and your investment
17. The duration of an 11-year, $1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.9106 years.a. What is the modified duration of the bond? What is the dollar duration of the bond?b. What will be the estimated price change on the bond if interest
16. Calculate the duration of a two-year, $1,000 bond that pays an annual coupon of 10 percent and trades at a yield of 14 percent.What is the expected change in the price of the bond if interest rates fall by 0.50 percent (50 basis points)?
15. What is dollar duration? How is dollar duration different from duration?
14. A 10-year, 10 percent annual coupon, $1,000 bond trades at a yield to maturity of 8 percent. The bond has a duration of 6.994 years.What is the modified duration of this bond? What is the practical value of calculating modified duration? Does modified duration change the result of using the
13. You have discovered that the price of a bond rose from $975 to$995 when the yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of the bond?
12. How is duration related to the interest elasticity of a fixed-income security? What is the relationship between duration and the price of the fixed-income security?
11. You can obtain a loan of $100,000 at a rate of 10 percent for two years. You have a choice of (i) paying the interest (10 percent) each year and the total principal at the end of the second year or (ii)amortizing the loan, that is, paying interest (10 percent) and principal in equal payments
10. An insurance company is analyzing three bonds and is using duration as the measure of interest rate risk. All three bonds trade at a yield to maturity of 10 percent, have $10,000 par values, and have five years to maturity. The bonds differ only in the amount of annual coupon interest they pay:
9. Maximum Pension Fund is attempting to manage one of the bond portfolios under its management. The fund has identified three bonds that have five-year maturities and trade at a yield to maturity of 9 percent. The bonds differ only in that the coupons are 7 percent, 9 percent, and 11 percent.a.
8. What is a consol bond? What is the duration of a consol bond that sells at a yield to maturity of 8 percent? 10 percent? 12 percent?Would a consol bond trading at a yield to maturity of 10 percent have a greater duration than a 20-year zero-coupon bond trading at the same yield to maturity? Why?
7. A six-year, $10,000 CD pays 6 percent interest annually and has a 6 percent yield to maturity. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?
6. Consider three Treasury bonds, each of which has a 10 percent semiannual coupon and trades at par.a. Calculate the duration for a bond that has a maturity of four years, three years, and two years.b. What conclusions can you reach about the relationship between duration and the time to maturity?
5. What is the duration of a five-year, $1,000 Treasury bond with a 10 percent semiannual coupon selling at par? Selling with a yield to maturity of 12 percent? 14 percent? What can you conclude about the relationship between duration and yield to maturity? Plot the relationship. Why does this
4. Two bonds are available for purchase in the financial markets. The first bond is a two-year, $1,000 bond that pays an annual coupon of 10 percent. The second bond is a two-year, $1,000 zero-coupon bond.a. What is the duration of the coupon bond if the current yield to maturity (R) is 8
3. A one-year, $100,000 loan carries a coupon rate and a market interest rate of 12 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and the accrued interest are due at the end of the year.a. What will be the cash
2. What are the two different general interpretations of the concept of duration, and what is the technical definition of this term? How does duration differ from maturity?
1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the two methods? What is marking to market?
1. Is immunizing a bank’s net worth the same as immunizing its net worth-to-assets ratio? If not, why not?
4. Suppose DA = 3 years, DL = 6 years, k = 0.8, and A = $100 million. What is the effect on owners’ net worth if ΔR/(1 + R)rises 1 percent? (ΔE = $1,800,000)
3. How can a manager use information on an FI’s duration gap to restructure, and thereby immunize, the balance sheet against interest rate risk?
2. How is the overall duration gap for an FI calculated?
1. Refer to the example of the insurer in Examples 9–6 through 9–8. Suppose rates fell to 6 percent. Would the FI’s portfolio still be immunized? What if rates rose to 10 percent?
2. How would the formula in equation (6) have to be modified to take into account quarterly coupon payments and monthly coupon payments?
1. What is the relation between the duration of a bond and the interest elasticity of a bond?
3. Do high-coupon bonds have high or low durations?
2. What is the relationship between duration and yield to maturity on a financial security?
1. Which has the longer duration: a 30-year, 8 percent, zerocoupon or discount bond or an 8 percent infinite maturity consol bond?
5. What feature is unique about a consol bond compared with other bonds?
4. What is the duration of a zero-coupon bond?
3. Calculate the duration of a one-year, 8 percent coupon, 10 percent yield bond that pays coupons quarterly.
2. What does the numerator of the duration equation measure?
1. What does the denominator of the duration equation measure?
2. When is the duration of an asset equal to its maturity?
1. Why is duration considered a more complete measure of an asset’s or liability’s interest rate sensitivity than maturity?
3. What is the impact over the next year on net interest income if interest rates on RSAs increase 60 basis points and on RSLs increase 40 basis points?
2. What is the impact over the next six months on net interest income if interest rates on RSAs increase 60 basis points and on RSLs increase 40 basis points?
1. What is the repricing gap if the planning period is 30 days? 6 months? 1 year? 2 years? 5 years?
39. You note the following yield curve in The Wall Street Journal.According to the unbiased expectations hypothesis, what is the oneyear forward rate for the period beginning two years from today, 2f1?Maturity Yield One day 2.00%One year 5.50 Two years 6.50 Three years 9.00
38. The Wall Street Journal reports that the rate on three-year Treasury securities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-year interest rate expected in year 4, E(4r1), is 6.10 percent. According to the liquidity premium hypothesis, what is the
37. Based on economists’ forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:R = 5.65% == E(21) 6.75% L = 0.05% E()=6.85% E(31) 6.85% L = 0.10% E(41)=7.15% L = 0.12% L4 Using the liquidity premium hypothesis, plot the
36. How does the liquidity premium theory of the term structure of interest rates differ from the unbiased expectations theory? In a normal economic environment, that is, an upward-sloping yield curve, what is the relationship of liquidity premiums for successive years into the future? Why?
35. The Wall Street Journal reports that the rate on three-year Treasury securities is 5.60 percent and the rate on four-year Treasury securities is 5.65 percent. According to the unbiased expectations hypothesis, what does the market expect the one-year Treasury rate to be in year 4, E(4r1)?
34. The Wall Street Journal reported interest rates of 6 percent, 6.35 percent, 6.65 percent, and 6.75 percent for three-year, four-year, five-year, and six-year Treasury notes, respectively. According to the unbiased expectations theory, what are the expected one-year rates for years 4, 5, and 6?
33. The current one-year Treasury bill rate is 5.2 percent and the expected one-year rate 12 months from now is 5.8 percent.According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security?
32. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:R = 6% E)=7% E(ar)= 7.5% E(41)= 7.85%Using the unbiased expectations theory, calculate the current (longterm)rates
31. What are the weaknesses of the maturity gap model?The following questions and problems are based on material in Appendix 8B to the chapter.
30. EDF Bank has a very simple balance sheet. Assets consist of a twoyear,$1 million loan that pays an interest rate of London Interbank Offer Rate (LIBOR) plus 4 percent annually. The loan is funded with a two-year deposit on which the bank pays LIBOR plus 3.5 percent interest annually. LIBOR
29. Scandia Bank has issued a one-year, $1 million CD paying 5.75 percent to fund a one-year loan paying an interest rate of 6 percent.The principal of the loan will be paid in two installments: $500,000 in six months and the balance at the end of the year.a. What is the maturity gap of Scandia
28. Gunnison Insurance has reported the following balance sheet (in thousands):All securities are selling at par equal to book value. The 2-year notes are yielding 5 percent and the 15-year munis are yielding 9 percent. The 1-year commercial paper pays 4.5 percent and the 5-year notes pay 8
27. The following is a simplified FI balance sheet:The average maturity of loans is four years and the average maturity of deposits is two years. Assume that loan and deposit balances are reported as book value, zero-coupon items.a. Assume that the interest rate on both loans and deposits is 9
26. An insurance company has invested in the following fixed-income securities: (a) $10,000,000 of 5-year Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7 percent interest with a par value of $6,000,000, and(c) $6,200,000 of 20-year
25. If a bank manager is certain that interest rates are going to increase within the next six months, how should the bank manager adjust the bank’s maturity gap to take advantage of this anticipated increase? What if the manager believes rates will fall? Would your suggested adjustments be
24. County Bank has the following market value balance sheet (in millions, all interest at annual rates). All securities are selling at par equal to book value.a. What is the maturity gap for County Bank?b. What will be the maturity gap if the interest rates on all assets and liabilities increase 1
23. Nearby Bank has the following balance sheet (in millions):What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or a decrease in interest rates? Explain why. Assets Liabilities and Equity Cash $ 60 Demand deposits 5-year Treasury notes 60 1-year certificates $140
22. What is a maturity gap? How can the maturity model be used to immunize an FI’s portfolio? What is the critical requirement that allows maturity matching to have some success in immunizing the balance sheet of an FI?
21. What are some of the weaknesses of the repricing model? How have large banks solved the problem of choosing the optimal time period for repricing? What is runoff cash flow, and how does this amount affect the repricing model’s analysis?The following questions and problems are based on
20. A bank has the following balance sheet:Suppose interest rates rise such that the average yield on ratesensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points.a. Calculate the bank’s repricing GAP.b. Assuming the bank does
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