商業(yè)銀行管理ROSE7e課后答案chapter_07

1、CHAPTER 7ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTERESTRATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPSGoals 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 interest

2、 ratesand 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 Man ageme nt? Market Rates and In terest Rate Risk? The Goals of In terest Ra

3、te Hedg ing? In terest Sen sitive Gap Man ageme nt? Duratio n Gap Man ageme nt? Limitati ons of Hedg ing Tech niq uesChapter Outl ineI. In troducti on: The Necessity for Coord in ati ng Bank Asset and Liability Man ageme nt Decisi onsII. Asset/Liability Man ageme nt StrategiesA. Asset Man ageme nt S

4、trategyB. Liability Man ageme nt StrategyC. Funds Man ageme nt StrategyIII. In terest Rate Risk: One of the Greatest Asset-Liability Man ageme nt Strategy Challe ngesA. Forces Determi ning In terest RatesB. The Measureme nt of In terest Rates1. Yield to Maturity2. Bank Disco unt RateC. The Comp onen

5、ts of In terest Rates1. Risk Premiums2. Yield Curves3. The Maturity Gap and the Yield CurveD. Response to Interest Rate RiskIV. One of the Goals of Interest-Rate HedgingA. The Net Interest MarginB. Interest-Sensitive Gap Management1. Asset-Sensitive Position2. Liability-Sensitive Position精品3. Dollar

6、 In terest-Se nsitive Gap4. Relative In terest Sen sitive Gap5. In terest Sen sitivity Ratio6. Computer-Based Tech niq ues7. Cumulative Gap8. Strategies in Gap Man ageme ntC. Duratio n Gap Man ageme ntV. The Con cept of Durati onA. Defin iti on of Durati onB. Calculatio n of Durati onC. Net Worth an

7、d DurationD. Price Risk and Duratio nE. Conv exity and Durati onVI. Using Durati on to Hedge Aga inst In terest-Rate RiskA. Duratio n Gap1. Dollar Weighted Duratio n of Assets2. Dollar Weighted Duratio n of Liabilities3. Positive Durati on Gap4. Negative Durati on GapB. Change inthe Bank s Net Worth

8、VII. The Limitati ons of Durati on Gap Man ageme ntVIII. Summary of the ChapterCon cept Checks7-1. What do the followi ng terms mean: Asset man ageme nt? Liability man ageme nt? Funds man ageme nt?Asset man ageme nt refers to a banking strategy where man ageme nt has con trol over the allocati on of

9、 bank assets but believes the banks 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 fun ds. Funds man ageme nt comb ines both asset and liability man ageme nt approaches

10、 into a bala need liquidity man ageme nt strategy.7-2. What factors have motivated finan cial in stituti ons to develop funds man ageme nt tech niq ues in rece nt years?The necessity to find new sources of funds in the 1970s and the risk management problems encountered with troubled loans and volati

11、le interest rates in the 1970s and 1980s led to the concept of pla nning and con trol over both sides of a ban ks bala nee sheet - the esse nee of funds man ageme nt.7-3.What forces cause in terest rates to cha nge? What kinds of risk do finan cial firms face whe nin terest rates cha nge?Interest ra

12、tes 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 risk of borrower d

13、efault, 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 and on fixed-rate lo

14、ans 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 loss to income if an i

15、nstitution 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 investors trading in the credit ma

16、rkets. 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 require bankers to correctly anticip

17、ate 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 curve and why is it important for banke

18、rs 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. In banking most of the long-term rates

19、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 banks net interest margin or spread between asset revenues and liability co

20、sts.7-6. What is it that a lending institution s wishes to protect from adverse movements inrates?A financial institution wishes to protect both the value of assets and liabilities and the revenues and costs generated by both assets and liabilities from adverse movements in interest rates.7-7. What

21、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.7-8. First Nati onal Bank of Bann erville has posted in teres

22、t reve nues of $63 millio n and in terest 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 coswhile its earning assets in crease by 50 perce nt. What will happe n ti its

23、net in terest margi n?Net In terest =$63 mill. - $42 mill. = 0.03 or 3 perce ntMargin$700 mill.If in terest reve nues and in terest costs double while earning assets grow by 50 perce nt, the netin terest margin will cha nge as follows:($63 mill. - $42 mill.) * 2= 0.04 or 4 perce nt$700 mill. *(1.50)

24、Clearly the net in terest margin in creases-i n this case by one third.7-9. Can you expla in the con cept of gap man ageme nt?Gap management invoIves determining the maturity distribution and the repricing schedule for a banks assets and liabilities. When more assets are subject to repricing or will

25、 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 in terest-rate moveme nts based on the gaps size and directi on.7-10 When is a financial institution asset sensitive? Liability sensitive?A financia

26、l 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 contrast, would find the financial institution having more interest-rate sensitive depos

27、its and other liabilities than rate-sensitive assets for a particular planning period.7-11. Commerce Natio nal Bank reports in terest-se nsitive assets of $870 millio n andin terest sen sitive liabilities of $625 milli on duri ng the coming mon th. Is the bank asset sen sitive or liability sen sitiv

28、e? What is likely to happe n to the banks net in terest margin if in terest rates rise? If they fall?Because interest-sensitive assets are larger than liabilities by $245 million the bank is asset sensitive.If interest rates rise, the banks net interest margin should rise as asset revenues increase

29、by more than the resulting increase in liability costs. On the other hand, if interest rates fall, the banks net interest margin will fall as asset revenues decline faster than liability costs.7-12. Peoples Savings Bank, a thrift institution, has a cumulative gap for the coming year of + $135 millio

30、n 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 cha nge will occur in net in terest in come if in terest rates rise by one and a quarter perce ntage poin ts?

31、For the decrease in in terest rates:ExpectedCha nge in= $135 millio n * (-0.025) = -$3.38 millio nNet In terest In comeFor the in crease in in terest rates:=$135 million * (+0.0125) = +$1.69 millionExpected Change in Net In terestIn come7-13 How do you measure the dollar in terest-se nsitive gap? Th

32、e relative in terest-se nsitive gap? What is the interest-sensitivity ratio?The dollar in terest-se nsitive gap is measured by tak ing the repriceable (in terest-se nsitive) assets minus the repriceable (in terest-se nsitive) liabilities over some set pla nning period. Common pla nning periods in cl

33、ude 3 mon ths, 6 mon ths and 1 year. The relative in terest-se nsitive gap is the dollar in terest-se nsitive gap divided by some measure of bank size (ofte n total assets). The interest-sensitivity ratio is just the ratio of interest-sensitive assets to interest sensitive liabilities. Regardless of

34、 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) relative in terest-se nsitive gap and an in terest sen sitivity ratio greater (less) tha n one.7-14 Suppose Carroll Bank and T

35、rust reports in terest-se nsitive assets of $570 millio n and in terest-se nsitive liabilities of $685 milli on. What is the bank-se nsitive gap? stdollar in terestrelative in terest-se nsitive gap and in terest-se nsitivity ratio?Dollar In terest-Se nsitive Gap = In terest-Se nsitive Assets In tere

36、st Sen sitive Liabilities=$570 - $685 = -$115Relative Gap =$ IS Gap =Bank Size-$115= -0.2018 or -20.18 perce ntIn terest-Se nsitivity =In terest-Se nsitive Assets=$570= .8321RatioInterest-Sensitive Liabilities$6857-15 Explain the concept of weighted interest-sensitive gap. How can this concept aid m

37、anagement in measuring a financial institution-sensitivesgraepalriisnkteerxepstosure?精品Weighted interest-sensitive gap is based 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 ra

38、tes on liabilities and both of these may change at a different speed than those interest rates determined in the open market. 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 marke

39、t interest rate. Fed Funds loans, for example, have an interest rate which is determined in the market and which would have 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 d

40、ollar amount of each type of asset or liability would be multiplied by its weight and added to the rest of the interest-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 interes

41、t-sensitive liabilities from the interest-sensitive assets. This weighted interest-sensitive gap should be more accurate 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 p

42、ursued by the bank.7-16. What isduration?Duration is the weighted average time at which the cash flows on a security are received. It is a direct measure of price risk.7-17. How is a financial institution s duration gap determined?A banks duration gap is determined by taking the difference between t

43、he duration of a banks assets and the duration of its liabilities. The duration of the bankrmined by takinsgaassets can be deweighted average of the duration of all of the assets in the bank s portfolio. Thedollar amount of a particular type of asset out of the total dollar amount of the assets of t

44、he bank. The duration of the liabilities can be determined in a similar manner. 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-sen

45、sitive gap analysis?Interest-sensitive gap only looks at the impact of changes in interest rates on the bank income. It does not take into account the effect of interest rate changes on the market value of the bank s equity capital position. aInddition, duration provides a single number which tells

46、the bank their overall exposure to interest rate risk.7-19. How can 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

47、 bank has a zero duration gap position when it is fully hedged. 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

48、of duration gap analysis? Can you think of some ways of reducing 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 acdeposits and othe

49、rs dont have well definedqaatfteflowofwhich makes it difficult tocalculate duratio n for these acco un ts. Durati on is also affected by prepayme nts by customers as well as default. Finally, duration analysis works best when interest rate changes are small and short and long term interest rates cha

50、nge by the same amount. If 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, d

51、oes it have a significant duration gap? If interest rates rise, what will happen to the value of the ban ks net worth?Durati on Gap = DaDlLiabilitie sAssets=2.5 yrs. - 3.0 yrs.$467 million$560 million=2.5 years- 2.5018 years=-0.018 yearsThis bank has a very slight negative duration gap; so small in

52、fact that we could consider it in sig nifica nt. If in terest rates rise, the ban ks liabilities will fall slightly more in value tha n its assets, result ing in a small in crease in net worth.7-22. Stilwater Bank and Trust Compa ny has an average asset durati on of 3.25 years and an average liabili

53、ty duration of 1.75 years. Its liabilities amount 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 Banks net worth as a result of a decline in interest rates?First, we need an e

54、stimate of Stilwaters duration gap. This is: $485 mill.Duration Gap = 3.25 yrs. - 1.75 yrs * -= + 1.5923 years$512 mill.Then, the change in net worth if interest rates rise from 7 percent to 8 percent will be:x$485mill.01 01Change in NW = -3.25yrS. x (x $512涮-Syrs.x=-$7.62 millio n.Problems7-1. A go

55、ver nment bond is curre ntly selli ng for $900 and pays $75 per year in in terest for nine years 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 equati on for this bond would be:$80 $80 $80 $80 $80 $80 $

56、80 $80 $1080$900?23456789(17)1(1?)2(1?)3(1?)4(1?)5(1 ?)6(1?)7(1?)8(1?)9Using a financial calculator the YTM = 9.72% 7-2. Suppose the gover nment bond described in problem 1 above is held for three years and the n the thrift institution acquiring the bond decides to sell it at a price of $950. Can yo

57、u figure out the average annual yield the thrift institution will have earned for its 3-year investment in the bond?$900 =$80+$80+$80+$950(1 HPY)1(1 HPY)2(1 HPY)3(1 HPY)3Using a financial calculator, the HPY is 10.56%7-3. U.S. Treasury bills are available for purchase this week at the following pric

58、es (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 disco unt rate (DR) on each bill if it is held to maturity. What is the equivale nt yield to maturity (sometimes called the bon d-equivale nt or coup on equivale nt yield) on each of these Treasury Bills?The dis