Chap金融機(jī)構(gòu)管理課后題答案

1、Chapter EightInterest Rate Risk IChapter OutlineIntroductionThe Central Bank and Interest Rate RiskThe Repricing Model· Rate-Sensitive Assets· Rate-Sensitive Liabilities· Equal Changes in Rates on RSAs and RSLs· Unequal Changes in Rates on RSAs and RSLsWeaknesses of the Repricing

2、 Model· Market Value Effects· Overaggregation· The Problem of Runoffs· Cash Flows from Off-Balance Sheet ActivitiesThe Maturity Model· The Maturity Model with a Portfolio of Assets and LiabilitiesWeakness of the Maturity ModelSummaryAppendix 8A: Term Structure of Interest Ra

3、tes· Unbiased Expectations Theory· Liquidity Premium Theory· Market Segmentation TheorySolutions for End-of-Chapter Questions and Problems: Chapter Eight1.What was the impact on interest rates of the borrowed reserves targeting regime used by the Federal Reserve from 1982 to 1993?The

4、volatility of interest rates was significantly lower than under the nonborrowed reserves target regime used in the three years immediately prior to 1982. Figure 8-1 indicates that both the level and volatility of interest rates declined even further after 1993 when the Fed decided that it would targ

5、et primarily the fed funds rate as a guide for monetary policy.2.How has the increased level of financial market integration affected interest rates?Increased financial market integration, or globalization, increases the speed with which interest rate changes and volatility are transmitted among cou

6、ntries. The result of this quickening of global economic adjustment is to increase the difficulty and uncertainty faced by the Federal Reserve as it attempts to manage economic activity within the U.S. Further, because FIs have become increasingly more global in their activities, any change in inter

7、est rate levels or volatility caused by Federal Reserve actions more quickly creates additional interest rate risk issues for these companies.3.What is the repricing gap? In using this model to evaluate interest rate risk, what is meant by rate sensitivity? On what financial performance variable doe

8、s the repricing model focus? Explain.The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar value of liabilities that will reprice within a specific time period, where reprice means the potential to receive a new interest rate. Rate sensi

9、tivity represents the time interval where repricing can occur. The model focuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive ne

10、w interest rates.4.What is a maturity bucket in the repricing model? Why is the length of time selected for repricing assets and liabilities important when using the repricing model? The maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. The leng

11、th of the repricing period determines which of the securities in a portfolio are rate-sensitive. The longer the repricing period, the more securities either mature or need to be repriced, and, therefore, the more the interest rate exposure. An excessively short repricing period omits consideration o

12、f the interest rate risk exposure of assets and liabilities are that repriced in the period immediately following the end of the repricing period. That is, it understates the rate sensitivity of the balance sheet. An excessively long repricing period includes many securities that are repriced at dif

13、ferent times within the repricing period, thereby overstating the rate sensitivity of the balance sheet. 5.Calculate the repricing gap and the impact on net interest income of a 1 percent increase in interest rates for each of the following positions:· Rate-sensitive assets = $200 million. Rate

14、-sensitive liabilities = $100 million.Repricing gap = RSA RSL = $200 $100 million = +$100 million. DNII = ($100 million)(.01) = +$1.0 million, or $1,000,000.· Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.Repricing gap = RSA RSL = $100 $150 million = -$50 milli

15、on. DNII = (-$50 million)(.01) = -$0.5 million, or -$500,000.· Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.Repricing gap = RSA RSL = $150 $140 million = +$10 million. DNII = ($10 million)(.01) = +$0.1 million, or $100,000.a.Calculate the impact on net interes

16、t income on each of the above situations assuming a 1 percent decrease in interest rates.· DNII = ($100 million)(-.01) = -$1.0 million, or -$1,000,000.· DNII = (-$50 million)(-.01) = +$0.5 million, or $500,000.· DNII = ($10 million)(-.01) = -$0.1 million, or -$100,000.b.What conclusio

17、n can you draw about the repricing model from these results?The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap) while the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the lowest interest rate risk exposure since the absolute val

18、ue of the repricing gap is the lowest, while the opposite is true for part (1). 6.What are the reasons for not including demand deposits as rate-sensitive liabilities in the repricing analysis for a commercial bank? What is the subtle, but potentially strong, reason for including demand deposits in

19、the total of rate-sensitive liabilities? Can the same argument be made for passbook savings accounts?The regulatory rate available on demand deposit accounts is zero. Although many banks are able to offer NOW accounts on which interest can be paid, this interest rate seldom is changed and thus the a

20、ccounts are not really sensitive. However, demand deposit accounts do pay implicit interest in the form of not charging fully for checking and other services. Further, when market interest rates rise, customers draw down their DDAs, which may cause the bank to use higher cost sources of funds. The s

21、ame or similar arguments can be made for passbook savings accounts.7.What is the gap ratio? What is the value of this ratio to interest rate risk managers and regulators?The gap ratio is the ratio of the cumulative gap position to the total assets of the bank. The cumulative gap position is the sum

22、of the individual gaps over several time buckets. The value of this ratio is that it tells the direction of the interest rate exposure and the scale of that exposure relative to the size of the bank.8.Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?91

23、-day U.S. Treasury billsYes1-year U.S. Treasury notesYes20-year U.S. Treasury bondsNo20-year floating-rate corporate bonds with annual repricingYes30-year floating-rate mortgages with repricing every two yearsNo30-year floating-rate mortgages with repricing every six monthsYesOvernight fed fundsYes9

24、-month fixed rate CDsYes1-year fixed-rate CDsYes5-year floating-rate CDs with annual repricingYesCommon stockNo9.Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):AssetsLiabilities and EquityFloating-rate mortgages Demand deposits(currently 10% annually)$50(currently 6%

25、 annually)$7030-year fixed-rate loansTime deposits(currently 7% annually)$50(currently 6% annually$20Equity$10Total Assets$100Total Liabilities & Equity$100a.What is WatchoverUs expected net interest income at year-end?Current expected interest income:$5m + $3.5m = $8.5m. Expected interest expen

26、se:$4.2m + $1.2m = $5.4m. Expected net interest income:$8.5m $5.4m = $3.1m.b.What will be the net interest income at year-end if interest rates rise by 2 percent? After the 200 basis point interest rate increase, net interest income declines to: 50(0.12) + 50(0.07) 70(0.08) 20(.06) = $9.5m $6.8m = $

27、2.7m, a decline of $0.4m.c.Using the cumulative repricing gap model, what is the expected net interest income for a 2 percent increase in interest rates? Wachovias' repricing or funding gap is $50m $70m = $20m. The change in net interest income using the funding gap model is ($20m)(0.02) = $.4m.

28、d. What will be the net interest income at year-end if interest rates increase 200 basis points on assets, but only 100 basis points on liabilities? Is it reasonable for changes in interest rates to affect balance sheet in an uneven manner? Why?After the unbalanced rate increase, net interest income

29、 will be 50(0.12) + 50(0.07) 70(0.07) 20(.06) = $9.5m $6.1m = $3.4m, an increase of $0.3m. It is not uncommon for interest rates to adjust in an uneven manner over two sides of the balance sheet because interest rates often do not adjust solely because of market pressures. In many cases the changes

30、are affected by decisions of management. Thus you can see the difference between this answer and the answer for part a.10.What are some of the weakness 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

31、 does this amount affect the repricing models analysis?The repricing model has four general weaknesses:(1)It ignores market value effects. (2)It does not take into account the fact that the dollar value of rate sensitive assets and liabilities within a bucket are not similar. Thus, if assets, on ave

32、rage, are repriced earlier in the bucket than liabilities, and if interest rates fall, FIs are subject to reinvestment risks.(3)It ignores the problem of runoffs, that is, that some assets are prepaid and some liabilities are withdrawn before the maturity date.(4)It ignores income generated from off

33、-balance-sheet activities.Large banks are able to reprice securities every day using their own internal models so reinvestment and repricing risks can be estimated for each day of the year.Runoff cash flow reflects the assets that are repaid before maturity and the liabilities that are withdrawn uns

34、uspectedly. To the extent that either of these amounts is significantly greater than expected, the estimated interest rate sensitivity of the bank will be in error.11.Use the following information about a hypothetical government security dealer named M.P. Jorgan. Market yields are in parenthesis, an

35、d amounts are in millions. AssetsLiabilities and EquityCash$10Overnight Repos$1701 month T-bills (7.05%)75Subordinated debt3 month T-bills (7.25%)757-year fixed rate (8.55%1502 year T-notes (7.50%)508 year T-notes (8.96%)1005 year munis (floating rate)(8.20% reset every 6 months) 25Equity 15Total As

36、sets$335Total Liabilities & Equity$335a.What is the funding or repricing gap if the planning period is 30 days? 91 days? 2 years? Recall that cash is a noninterest-earning asset.Funding or repricing gap using a 30-day planning period = 75 170 = $95 million.Funding gap using a 91-day planning per

37、iod = (75 + 75) 170 = -$20 million.Funding gap using a two-year planning period = (75 + 75 + 50 + 25) 170 = +$55 million.b.What is the impact over the next 30 days on net interest income if all interest rates rise 50 basis points? Decrease 75 basis points? Net interest income will decline by $475,00

38、0. DNII = FG(DR) = 95(.005) = $0.475m.Net interest income will increase by $712,500. DNII = FG(DR) = 95(.0075) = $0.7125m.c. The following one-year runoffs are expected: $10 million for two-year T-notes, and $20 million for eight-year T-notes. What is the one-year repricing gap?Funding or repricing

39、gap over the 1-year planning period = (75 + 75 + 10 + 20 + 25) 170 = +$35 million.d.If runoffs are considered, what is the effect on net interest income at year-end if interest rates rise 50 basis points? Decrease 75 basis points?Net interest income will increase by $175,000. DNII = FG(DR) = 35(0.00

40、5) = $0.175m.Net interest income will decrease by $262,500, DNII = FG(DR) = 35(-0.0075) = -$0.2625m.12.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

41、 to market?Book value accounting reports assets and liabilities at the original issue values. Current market values may be different from book values because they reflect current market conditions, such as interest rates or prices. This is especially a problem if an asset or liability has to be liqu

42、idated immediately. If the asset or liability is held until maturity, then the reporting of book values does not pose a problem. For an FI, a major factor affecting asset and liability values is interest rate changes. If interest rates increase, the value of both loans (assets) and deposits and debt

43、 (liabilities) fall. If assets and liabilities are held until maturity, it does not affect the book valuation of the FI. However, if deposits or loans have to be refinanced, then market value accounting presents a better picture of the condition of the FI. The process by which changes in the economi

44、c value of assets and liabilities are accounted is called marking to market. The changes can be beneficial as well as detrimental to the total economic health of the FI.13.Why is it important to use market values as opposed to book values when evaluating the net worth of an FI? What are some of the

45、advantages of using book values as opposed to market values?Book values represent historical costs of securities purchased, loans made, and liabilities sold. They do not reflect current values as determined by market values. Effective financial decision-making requires uptodate information that inco

46、rporates current expectations about future events. Market values provide the best estimate of the present condition of an FI and serve as an effective signal to managers for future strategies.Book values are clearly measured and not subject to valuation errors, unlike market values. Moreover, if the

47、 FI intends to hold the security until maturity, then the security's current liquidation value will not be relevant. That is, the paper gains and losses resulting from market value changes will never be realized if the FI holds the security until maturity. Thus, the changes in market value will

48、not impact the FI's profitability unless the security is sold prior to maturity.14.Consider a $1,000 bond with a fixed-rate 10 percent annual coupon (Cpn %) and a maturity (N) of 10 years. The bond currently is trading to a market yield to maturity (YTM) of 10 percent. Complete the following tab

49、le.From Par, $From Par, %NCpn %YTMPriceChange in PriceChange in Price810%9%$1,055.35$55.355.535%910%9%$1,059.95$59.955.995%1010%9%$1,064.18$64.186.418%1010%10%$1,000.001010%11%$941.11-$58.89-5.889%1110%11%$937.93-$62.07-6.207%1210%11%$935.07-$64.93-6.493%Use this information to verify the principles

50、 of interest rate-price relationships for fixed-rate financial assets.Rule One: Interest rates and prices of fixed-rate financial assets move inversely. See the change in price from $1,000 to $941.11 for the change in interest rates from 10 percent to 11 percent, or from $1,000 to $1,064.18 when rat

51、es change from 10 percent to 9 percent.Rule Two: The longer is the maturity of a fixed-income financial asset, the greater is the change in price for a given change in interest rates. A change in rates from 10 percent to 11 percent has caused the 10-year bond to decrease in value $58.89, but the 11-

52、year bond will decrease in value $62.07, and the 12-year bond will decrease $64.93. Rule Three: The change in value of longer-term fixed-rate financial assets increases at a decreasing rate. For the increase in rates from 10 percent to 11 percent, the difference in the change in price between the 10

53、-year and 11-year assets is $3.18, while the difference in the change in price between the 11-year and 12-year assets is $2.86.Rule Four: Although not mentioned in the text, for a given percentage (±) change in interest rates, the increase in price for a decrease in rates is greater than the de

54、crease in value for an increase in rates. Thus for rates decreasing from 10 percent to 9 percent, the 10-year bond increases $64.18. But for rates increasing from 10 percent to 11 percent, the 10-year bond decreases $58.89. 15.Consider a 12-year, 12 percent annual coupon bond with a required return

55、of 10 percent. The bond has a face value of $1,000.a.What is the price of the bond?PV = $120*PVIFAi=10%,n=12 + $1,000*PVIFi=10%,n=12 = $1,136.27b.If interest rates rise to 11 percent, what is the price of the bond?PV = $120*PVIFAi=11%,n=12 + $1,000*PVIFi=11%,n=12 = $1,064.92c.What has been the perce

56、ntage change in price? DP = ($1,064.92 - $1,136.27)/$1,136.27 = -0.0628 or 6.28 percent.d.Repeat parts (a), (b), and (c) for a 16-year bond.PV = $120*PVIFAi=10%,n=16 + $1,000*PVIFi=10%,n=16 = $1,156.47PV = $120*PVIFAi=11%,n=16 + $1,000*PVIFi=11%,n=16 = $1,073.79DP = ($1,073.79 - $1,156.47)/$1,156.47

57、 = -0.0715 or 7.15 percent.e.What do the respective changes in bond prices indicate?For the same change in interest rates, longer-term fixed-rate assets have a greater change in price.16.Consider a five-year, 15 percent annual coupon bond with a face value of $1,000. The bond is trading at a market yield to maturity of 12 percent.a.What is the price of the bond?PV = $150*PVIFAi=12%,n=5 + $1,000*PVIFi=12%,n=5 = $1,108.14b.If the market