商業(yè)銀行管理 ROSE 7e 課后答案chapter_07

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1、CHAPTER 7 ASSET-LIABILITY MANAGEMENT： DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS Goals of This Chapter： The purpose of this chapter is to explore the options bankers have today for dealing with risk – especially the risk of loss due to changing

2、interest rates – and to see how a bank's management can coordinate the management of its assets with the management of its liabilities in order to achieve the institution’s goals。 Key Topic In This Chapter · Asset， Liability， and Funds Management · Market Rates and Interest Rate Risk · The Goal

3、s of Interest Rate Hedging · Interest Sensitive Gap Management · Duration Gap Management · Limitations of Hedging Techniques Chapter Outline I. Introduction： The Necessity for Coordinating Bank Asset and Liability Management Decisions II。 Asset/Liability Management Strategies A. Asset Managem

4、ent Strategy B。 Liability Management Strategy C. Funds Management Strategy III。 Interest Rate Risk： One of the Greatest Asset-Liability Management Strategy Challenges A。 Forces Determining Interest Rates B. The Measurement of Interest Rates 1. Yield to Maturity 2。 Bank Discount Rate C. The

5、 Components of Interest Rates 1. Risk Premiums 2. Yield Curves 3。 The Maturity Gap and the Yield Curve D。 Response to Interest Rate Risk IV。 One of the Goals of Interest-Rate Hedging A. The Net Interest Margin B. Interest-Sensitive Gap Management 1。 Asset-Sensitive Position 2. Liability—Sen

6、sitive Position 3. Dollar Interest-Sensitive Gap 4。 Relative Interest Sensitive Gap 5。 Interest Sensitivity Ratio 6。 Computer-Based Techniques 7。 Cumulative Gap 8. Strategies in Gap Management C. Duration Gap Management V. The Concept of Duration A. Definition of Duration B. Calculati

7、on of Duration C. Net Worth and Duration D. Price Risk and Duration E. Convexity and Duration VI. Using Duration to Hedge Against Interest—Rate Risk A. Duration Gap 1. Dollar Weighted Duration of Assets 2. Dollar Weighted Duration of Liabilities 3. Positive Duration Gap 4。 Negative Duration

8、 Gap B. Change in the Bank’s Net Worth VII. The Limitations of Duration Gap Management VIII。 Summary of the Chapter Concept Checks 7—1. What do the following terms mean： Asset management? Liability management? Funds management? Asset management refers to a banking strategy where management has

9、 control over the allocation of bank assets but believes the bank's sources of funds (principally deposits) are outside its control. Liability management is a strategy of control over bank liabilities by varying interest rates offered on borrowed funds. Funds management combines both asset and lia

10、bility management approaches into a balanced liquidity management strategy。 7—2。 What factors have motivated financial institutions to develop funds management techniques in recent years？ The necessity to find new sources of funds in the 1970s and the risk management problems encountered with trou

11、bled loans and volatile interest rates in the 1970s and 1980s led to the concept of planning and control over both sides of a bank’s balance sheet —— the essence of funds management。 7-3. What forces cause interest rates to change？ What kinds of risk do financial firms face when interest rates chan

12、ge？ Interest rates are determined, not by individual banks， but by the collective borrowing and lending decisions of thousands of participants in the money and capital markets。 They are also impacted by changing perceptions of risk by participants in the money and capital markets, especially the

13、risk of borrower default， liquidity risk, price risk, reinvestment risk, inflation risk, term or maturity risk, marketability risk, and call risk. Financial institutions can lose income or value no matter which way interest rates go. Rising interest rates can lead to losses on security instruments

14、 and on fixed—rate loans as the market values of these instruments fall. Falling interest rates will usually result in capital gains on fixed-rate securities and loans but an institution will lose income if it has more rate—sensitive assets than liabilities. Rising interest rates will also cause a

15、 loss to income if an institution has more rate-sensitive liabilities than rate—sensitive assets。 7—4. What makes it so difficult to correctly forecast interest rate changes？ Interest rates cannot be set by an individual bank or even by a group of banks； they are determined by thousands of investo

16、rs trading in the credit markets. Moreover, each market rate of interest has multiple components-—the risk—free interest rate plus various risk premia。 A change in any of these rate components can cause interest rates to change. To consistently forecast market interest rates correctly would requi

17、re bankers to correctly anticipate changes in the risk—free interest rate and in all rate components. Another important factor is the timing of the changes. To be able to take full advantage of their predictions, they also need to know when the changes will take place。 7-5. What is the yield curv

18、e and why is it important for bankers to know about its shape or slope? The yield curve is a graphical description of the distribution of market interest rates by maturity of financial instrument. The slope of the yield curve determines the spread between long-term and short—term interest rates.

19、In banking most of the long-term rates apply to loans and securities (i.e。, bank assets) and most of the short—term interest rates are attached to bank deposits and money market borrowings. Thus， the shape or slope of the yield curve has a profound influence on a bank's net interest margin or sprea

20、d between asset revenues and liability costs。 7—6。 What is it that a lending institution’s wishes to protect from adverse movements in interest rates? A financial institution wishes to protect both the value of assets and liabilities and the revenues and costs generated by both assets and liabilit

21、ies from adverse movements in interest rates. 7—7。 What is the goal of hedging？ The goal of hedging in banking is to freeze the spread between asset returns and liability costs and to offset declining values on certain assets by profitable transactions so that a target rate of return is assured。

22、7—8。 First National Bank of Bannerville has posted interest revenues of $63 million and interest costs of ＄42 million。 If this bank possesses $700 million in total earning assets， what is First National’s net interest margin? Suppose the bank’s interest revenues and interest costs double, while i

23、ts earning assets increase by 50 percent. What will happen ti its net interest margin？ Net Interest = ＄63 mill。 - $42 mill. = 0。03 or 3 percent Margin $700 mill. If interest revenues and interest costs double while earning assets grow by 50 percent， the net interest margin will change as

24、 follows: （$63 mill。 — $42 mill.) * 2 = 0.04 or 4 percent $700 mill. ＊ (1。50） Clearly the net interest margin increases—-in this case by one third。 7—9. Can you explain the concept of gap management？ Gap management involves determining the maturity distribution and the repricing schedule for

25、 a bank’s assets and liabilities。 When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa， the bank has a GAP between assets and liabilities and is exposed to loss from adverse interest-rate movements based on the gap’s size and direction。

26、7—10 When is a financial institution asset sensitive？ Liability sensitive？ A financial institution is asset sensitive when it has more interest—rate sensitive assets maturing or subject to repricing during a specific time period than rate-sensitive liabilities. A liability sensitive position, in c

27、ontrast， would find the financial institution having more interest-rate sensitive deposits and other liabilities than rate-sensitive assets for a particular planning period. 7-11. Commerce National Bank reports interest—sensitive assets of ＄870 million and interest sensitive liabilities of ＄625 mi

28、llion during the coming month. Is the bank asset sensitive or liability sensitive? What is likely to happen to the banks net interest margin if interest rates rise？ If they fall? Because interest—sensitive assets are larger than liabilities by ＄245 million the bank is asset sensitive。 If inter

29、est rates rise， the bank’s net interest margin should rise as asset revenues increase by more than the resulting increase in liability costs. On the other hand， if interest rates fall， the bank's net interest margin will fall as asset revenues decline faster than liability costs. 7—12. Peoples' Sa

30、vings Bank, a thrift institution, has a cumulative gap for the coming year of + ＄135 million and interest rates are expected to fall by two and a half percentage points。 Can you calculate the expected change in net interest income that this thrift institution might experience? What change will o

31、ccur in net interest income if interest rates rise by one and a quarter percentage points？ For the decrease in interest rates： Expected Change in = $135 million ＊ (—0。025) = -＄3。38 million Net Interest Income For the increase in interest rates: Expected Change in Net

32、 Interest = ＄135 million * （+0.0125） = +$1。69 million Income 7-13 How do you measure the dollar interest-sensitive gap? The relative interest—sensitive gap？ What is the interest-sensitivity ratio？ The dollar interest-sensitive gap is measured by taking the repriceable （interest-sensitiv

33、e) assets minus the repriceable (interest—sensitive) liabilities over some set planning period. Common planning periods include 3 months, 6 months and 1 year. The relative interest—sensitive gap is the dollar interest-sensitive gap divided by some measure of bank size （often total assets). The in

34、terest—sensitivity ratio is just the ratio of interest—sensitive assets to interest sensitive liabilities. Regardless of which measure you use， the results should be consistent。 If you find a positive （negative） gap for dollar interest-sensitive gap, you should also find a positive （negative） rela

35、tive interest-sensitive gap and an interest sensitivity ratio greater (less) than one。 7—14 Suppose Carroll Bank and Trust reports interest-sensitive assets of ＄570 million and interest-sensitive liabilities of $685 million。 What is the bank’s dollar interest-sensitive gap？ Its relative interest—

36、sensitive gap and interest—sensitivity ratio？ Dollar Interest-Sensitive Gap = Interest-Sensitive Assets – Interest Sensitive Liabilities = ＄570 - ＄685 = -$115 Relative Gap = $ IS Gap = —$115 = -0。2018 or —20。18 percent Bank Size $570 Interest-Sensitivity = Interest—Sensitiv

37、e Assets = $570 = 。8321 Ratio Interest-Sensitive Liabilities ＄685 7-15 Explain the concept of weighted interest-sensitive gap。 How can this concept aid management in measuring a financial institution’s real interest-sensitive gap risk exposure? Weighted interest-sensitive gap is base

38、d on the idea that not all interest rates change at the same speed. Some are more sensitive than others。 Interest rates on bank assets may change more slowly than interest rates on liabilities and both of these may change at a different speed than those interest rates determined in the open market

39、。 In the weighted interest-sensitive gap methodology， all interest—sensitive assets and liabilities are given a weight based on their speed （sensitivity） relative to some market interest rate. Fed Funds loans， for example, have an interest rate which is determined in the market and which would hav

40、e a weight of 1。 All other loans， investments and deposits would have a weight based on their speed relative to the Fed Funds rate。 To determine the interest-sensitive gap， the dollar amount of each type of asset or liability would be multiplied by its weight and added to the rest of the interest—

41、sensitive assets or liabilities. Once the weighted total of the assets and liabilities is determined， a weighted interest-sensitive gap can be determined by subtracting the interest—sensitive liabilities from the interest—sensitive assets. This weighted interest—sensitive gap should be more accura

42、te than the unweighted interest-sensitive gap. The interest-sensitive gap may change from negative to positive or vice versa and may change significantly the interest rate strategy pursued by the bank。 7-16。 What is duration？ Duration is the weighted average time at which the cash flows on a secu

43、rity are received. It is a direct measure of price risk. 7-17. How is a financial institution’s duration gap determined? A bank’s duration gap is determined by taking the difference between the duration of a bank’s assets and the duration of its liabilities。 The duration of the bank’s assets can

44、 be determined by taking a weighted average of the duration of all of the assets in the bank’s portfolio. The weight is the dollar amount of a particular type of asset out of the total dollar amount of the assets of the bank。 The duration of the liabilities can be determined in a similar manner。

45、The duration of the liabilities is then adjusted to reflect that the bank has fewer liabilities than assets。 7-18。 What are the advantages of using duration as an asset—liability management tool as opposed to interest—sensitive gap analysis? Interest—sensitive gap only looks at the impact of chang

46、es in interest rates on the bank's net income。 It does not take into account the effect of interest rate changes on the market value of the bank’s equity capital position. In addition， duration provides a single number which tells the bank their overall exposure to interest rate risk. 7—19. How c

47、an you tell you are fully hedged using duration gap analysis? You are fully hedged when the dollar weighted duration of the assets portfolio of the bank equals the dollar weighted duration of the liability portfolio。 This means that the bank has a zero duration gap position when it is fully hedged

48、。 Of course, because the bank usually has more assets than liabilities the duration of the liabilities needs to be adjusted by the ratio of total liabilities to total assets to be entirely correct. 7-20. What are the principal limitations of duration gap analysis？ Can you think of some ways of r

49、educing the impact of these limitations？ There are several limitations with duration gap analysis。 It is often difficult to find assets and liabilities of the same duration to fit into the bank’s portfolio。 In addition， some accounts such as deposits and others don’t have well defined patterns of

50、 cash flows which makes it difficult to calculate duration for these accounts。 Duration is also affected by prepayments by customers as well as default。 Finally, duration analysis works best when interest rate changes are small and short and long term interest rates change by the same amount。 If

51、this is not true， duration analysis is not as accurate. 7—21。 Suppose that a thrift institution has an average asset duration of 2.5 years and an average liability duration of 3.0 years。 If the bank holds total assets of $560 million and total liabilities of $467 million， does it have a significant

52、 duration gap? If interest rates rise, what will happen to the value of the bank’s net worth? Duration Gap = DA – DL * = 2。5 yrs。 – 3.0 yrs. = 2.5 years – 2.5018 years = -0。018 years This bank has a very slight negative duration gap； so small in fact that we could consider it insignificant

53、. If interest rates rise, the bank's liabilities will fall slightly more in value than its assets， resulting in a small increase in net worth。 7-22. Stilwater Bank and Trust Company has an average asset duration of 3。25 years and an average liability duration of 1。75 years. Its liabilities amount

54、 to $485 million, while its assets total $512 million。 Suppose that interest rates were 7 percent and then rise to 8 percent。 What will happen to the value of the Stilwater Bank’s net worth as a result of a decline in interest rates？ First， we need an estimate of Stilwater's duration gap. This is：

55、 Duration Gap = 3.25 yrs。 – 1。75 yrs ＊ = + 1。5923 years Then, the change in net worth if interest rates rise from 7 percent to 8 percent will be： Change in NW = = —$7。62 million。 Problems 7-1。 A government bond is currently selling for ＄900 and pays ＄75 per year in interest for nine years

56、when it matures. If the redemption value of this bond is $1，000, what is its yield to maturity if purchased today for ＄900? The yield to maturity equation for this bond would be: Using a financial calculator the YTM = 9。72% 7-2. Suppose the government bond described in problem 1 above is held fo

57、r three years and then the thrift institution acquiring the bond decides to sell it at a price of ＄950. Can you figure out the average annual yield the thrift institution will have earned for its 3—year investment in the bond？ $900 = + + + Using a financial calculator, the HPY is 10.56％ 7—3。

58、 U。S。 Treasury bills are available for purchase this week at the following prices （based upon ＄100 par value) and with the indicated maturities： a。 $98。25, 182 days。 b。 $97.25， 270 days. c. ＄99。25， 91 days. Calculate the bank discount rate (DR） on each bill if it is held to maturity. What is

59、the equivalent yield to maturity （sometimes called the bond—equivalent or coupon equivalent yield） on each of these Treasury Bills? The discount rates and equivalent yields to maturity (bond—equivalent or coupon-equivalent yields) on each of these Treasury bills are： Discount Rates Equivalent Y

60、ields to Maturity a. b. c. 7—4。 The First State Bank of Gregsville reports a net interest margin of 2.5 percent in its most recent financial report with total interest revenues of ＄88 million and total interest costs of ＄72 million。 What volume of earning assets must the bank hold? Su

61、ppose the bank’s interest revenue rises by 8 percent and its interest costs and earnings assets increase by 9 percent。 What will happen to Gregsville's net interest margin? The relevant formula is: Net Interest Margin = .025 = Then Earning Assets = ＄640 million. If revenues rise by 8 percent a

62、nd costs and earnings assets rise by 9 percent net interest margin is: Net Interest Margin = = = 0.0237 or 2.37 percent. 7—5。 If a bank's net interest margin, which was 2.5 percent, increases 70 percent and its total assets， which stood originally at ＄545 million， rise by 40 percent, wha

63、t change will occur in the bank's net interest income? The correct formula is： .025 ＊ （1+.7）= or Net Interest Income = 0。0425 * $763 million = ＄32。4275 million。 7—6. The cumulative interest—rate gap of Commonwealth Federal Savings and Loan increases 60 percent from an initial figure of $4

64、0 million。 If market interest rates rise by 25 percent from an initial level of 6 percent， what change will occur in this thrift’s net interest income? The key formula here is： Change in the Bank’s = Change in interest rates （in percentage points) ＊ cumulative gap Net Interest = 0。06 * 。2

65、5 x (＄40 mill.) ＊ (1+.6） Income = 。96 Thus， the bank's net interest income will drop by 4 percent。 7-7。 Old Misers State Bank has recorded the following financial data for the past three years (dollars in millions）： Current Year Previous Year Two Years Ago Interest revenues ＄8

66、8 $84 ＄80 Interest expenses 79 77 74 Loans (Excluding nonperforming） 415 400 390 Investments 239 197 174 Total deposits 487 472 467 Money market borrowings 143 118 96 What has been happening to the bank's net interest margin？ What do you think caused the changes you have observed? Do you have any recommendations for Old Misers’ management team？ Net interest margin （NIM） = Net Interest Income/Earning Assets, where Net Interest Income = Net Interest Revenues - Net Intere