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1、wordwe devise strategies and techniques to acplish your business objectives though extensive analysisof your business,industries,marketsand petitors.1. 再定价缺口期限缺口有效期限假设一位名为M.P.Jorgan的政府证券交易商的有关资料如下，阅读后回答如下问题。括号的数字是市场收益率，金额的单位是百万美元。资产负债与股东权益现金$ 10隔夜再回购协议$ 1701个月的国库券(7.05%)757年期固定利率次级债务(8.55%)1503个月的国库
2、券(7.25%)752年期中期国库券(7.50%)508年期中期国库券(8.96%)1005年期市政债券(浮动利率8.20%，每六个月重定一次)25股权资本15总资产$ 335总负债加股东权益$ 335(a) 如果计划期限是30天，那么再定价缺口是多少？91天呢？(提示：现金是一项没有利息收入的资产)(b) 如果所有利率都上升50个根本点，将对未来30的净利息收入有何影响？如果都下降75个根本点呢？参考答案：(a)30天计划期限的利率敏感性资产有：1个月的国库券；30天计划期限的利率敏感性负债有：隔夜再回购协议；所以，计划期限为30的再定价缺口：GAP=资产-负债=75-175=-95.91天
3、计划期限的利率敏感性资产有：1个月的国库券和3个月的国库券；91天计划期限的利率敏感性负债有：隔夜再回购协议；所以，计划期限为91的再定价缺口：GAP=资产-负债=75+75-175=-20.(b)如果所有利率都上升50个根本点，那么未来30的净利息收入变化为：，净利息收入减少0.475如果所有利率都下降75个根本点，那么未来30的净利息收入变化为：，净利息收入增加0.7125以下是County银行按市场价值记账的资产负债表(单位：百万美元，所有利率都是年利率)资产负债与股东权益现金$ 20活期存款$ 10015年期商业贷款(利率为10%，期末还清贷款)1605年期大额可转让存单利率为6%，期
4、末还清贷款21030年期抵押贷款利率为8%，每月分期付款30020年期无抵押债券利率为7%120股权资本50总资产$ 480总负债加股东权益$ 480(a)County银行的期限缺口是多少？(b)如果所有资产和负债的利率都上升1%，那么期限缺口又是多少？参考答案：，(a资产组合的平均期限，其中，。所以。负债组合的平均期限，其中，。所以。(b)如果所有资产和负债的利率都上升1%，那么首先计算各资产、负债的市场价值。，所以Demand deposits = $100CDs = $12.60*PVIFAn=5,i=7% + $210*PVIFn=5,i=7% = $201.39Debentures
5、= $8.4*PVIFAn=20,i=8% + $120*PVIFn=20,i=8% = $108.22ML = 0*100 + 5*201.39 + 20*108.22/(100 + 201.39 + 108.22) = 7.74 years计算一年息票率为10%、到期收益率为14%、价值$1000的两年期债券的有效期限。如果利率下降0.5%，债券价格将如何变化？参考答案：Two-year BondPar value =$1,000 Coupon =0.10Annual paymentsYTM =0.14Maturity =2TimeCash FlowPVIFPV of CFPV*CF*T1
6、$100.00 0.87719$87.72 $87.72 PVIF = 1/(1+YTM)(Time)2$1,100.00 0.76947$846.41 $1,692.83 Price =$934.13 Numerator =$1,780.55 Duration=1.9061= Numerator/PriceExpected change in price = . This implies a new price of $941.94. The actual price using conventional bond price discounting would be $941.99. Th
7、e difference of $0.05 is due to convexity, which was not considered in this solution.2. 日风险收益的计算 Alpha 银行持有AAA级的15年期的零息债券，面值为4亿美元。债券目前在场外市场的收益率为9.5%，请问：如果潜在不利的收益率的变动为25个基点，那么日风险收益是多少？参考答案：a.What is the modified duration of these bonds?Modified duration = (MD) = D/(1 + r) = 15/(1.095) = -13.6986.b.Wh
8、at is the price volatility if the potential adverse move in yields is 25 basis points?Price volatility = (-MD) x (potential adverse move in yield)= (-13.6986) x (.0025) = -0.03425 or -3.425 percent.c.What is the DEAR?Daily earnings at risk (DEAR) = ($ Value of position) x (Price volatility)Dollar va
9、lue of position = 400/(1 + 0.095)15 = $102.5293million. Therefore,DEAR = $102.5293499 million x -0.03425 = -$3.5116 million, or -$3,511,630. d.If the price volatility is based on a 90 percent confidence limit and a mean historical change in daily yields of 0.0 percent, what is the implied standard d
10、eviation of daily yield changes?The potential adverse move in yields (PAMY) = confidence limit value x standard deviation value. Therefore, 25 basis points = 1.65 x s, and s = .0025/1.65 = .001515 or 15.15 basis points.3. 违约概率期限结构的计算利用下面的国债和公司债券(纯折价债券)收益曲线中的即期利率，来计算三年的违约概率期限结构。一定要计算出边际违约概率和累积违约概率。1年
11、即期2年即期3年即期长期国债5.0%6.1%7.2%BBB级债券7.0%8.2%9.3%参考答案：The notation used for implied forward rates is f12 = forward rate from period 1 to period 2.Treasury SecuritiesBBB Graded Debt(1.061)2 = (1.05)(1 + f12)(1.082)2 = (1.07)(1 + f12)f12 = 7.21%f12 = 9.41%(1.07)3 = (1.061)2(1 + f23)(1.093)3 = (1.082)2(1 +
12、f23)f23 = 8.82%f23 = 11.53%Using the implied forward rates, estimate the annual marginal probability of repayment:p01(1.07) = 1.05= p1 = 98.13 percentp12(1.0941) = 1.0721= p2 = 97.99 percentp23(1.1153) = 1.0882= p3 = 97.57 percentUsing marginal probabilities, estimate the cumulative probability of d
13、efault:cp02= 1 - (p1)(p2)= 1 - (.9813)(.9799) = 3.84 percentcp03 = 1 - (p1)(p2)(p3 )= 1 - (.9813)(.9799)(.9757) = 6.18 percent16.Using regression analysis on historical loan losses, a bank has estimated the following:XC = 0.002 + 0.8XL, and Xh = 0.003 + 1.8XLwhere XC = loss rate in the mercial secto
14、r, Xh = loss rate in the consumer (household) sector, XL = loss rate for its total loan portfolio. a.If the banks total loan loss rates increase by 10 percent, what are the increases in the expected loss rates in the mercial and consumer sectors?mercial loan loss rates will increase by 0.002 + 0.8(0
15、.10) = 8.20 percent.Consumer loan loss rates will increase by 0.003 + 1.8(0.10) = 18.30 percent.b.In which sector should the bank limit its loans and why?The bank should limit its loans to the consumer sector because the loss rates are systematically higher than the loss rates for the total loan por
16、tfolio. Loss rates are lower for the mercial sector. For a 10 percent increase in the total loan portfolio, the consumer loss rate is expected to increase by 18.30 percent, as opposed to only 8.2 percent for the mercial sector. 4. 流动性指数的计算Conglomerate公司收购了Acme公司。为了替收购活动融资，Conglomerate公司将出售Acme公司养老基金
17、中的超额局部。下面是将被出售的资产的面值、目前的售价和一年后的售价。出售资产的价值资产面值t=0t=1IBM股票$ 10 000$ 9 900$ 10 500GE债券5 0004 0004 500国债15 00013 00014 000计算出这些证券1年期的流动性指数参考答案：Calculate the 1-year liquidity index for these securities.wherewi = weights of the portfolio,Pi= fire-sale prices,Pi* = fair market value of assetsThusI = (0.333
18、)(9900/10,500) + (0.167)(4,00/4,500) + (0.5)(13,000/14,000) = 0.9275. 净存款外流情况下的资产负债表编制某存款机构的资产负债表如下(单位：百万美元)，其净存款外流预计为1500万美元。资产负债和权益现金10 存款68贷款50权益7证券15总资产75总负债和权益75请列出如下情况下该存款机构的资产负债表：(a) 存款机构购置流动性负债来抵消预期的存款外流(b) 使用储存流动性管理的方法来满足预期的存款外流参考答案：a.The DI purchases liabilities to offset this expected dra
19、in.If the DI purchases liabilities, then the new balance sheet is:Cash$10Deposits$53Loans$50Purchased liabilities$15Securities$15Equity$ 7b.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
20、Deposits$53Securities$10Equity$ 7DIs will most likely use some bination of these two methods.6. 准备金计算期和准备金维持期某地区性银行在最近准备金计算期的日均活期存款余额为2.25亿美元。在准备金维持期，它在美联储的日均准备金余额为1600万美元，在相应计算期，它的日均库存现金为430万美元。（a） 该行在准备金维持期，应该持有的日均准备金余额是多少（b） 该行符合法定准备金要求吗（c） 结转下一期准备金维持期的超额准备金或准备金短缺额是多少参考答案：(a) Reserve requirements
21、 = (0 x $6.0m)+ ($42.1- $6.0)(0.03) + ($225 - $42.1) (0.10) = 0 + $1.083 + $18.29 = $19.373 millionAfter subtracting the average daily balance of vault cash of $4.3 million, the bank needs to maintain a target daily average of $15.073 million ($19.373 million - $4.3 million) during the maintenance p
22、eriod.(b) Yes. The bank has average reserves of $16 million. This amount exceeds the required amount by $0.927 million.(c) A maximum of 4 percent of the required reserves can be carried over to the next maintenance period. Thus, 0.04 x $19.373 million = $0.7749 million can be carried over to the nex
23、t maintenance period.d.If the local bank has an opportunity cost of 6 percent, what is the effect on the ine statement from this reserve period?A total of $0.1521 million (0.927 0.7749) has an opportunity cost of no earnings at the 6 percent rate. Thus the loss would be $0.1521(0.06)(14/365) = $350.
24、04.7. 资本充足率要求第三银行拥有如下资产负债表(单位：百万美元；括号中的数字为风险权重)资产负债和权益现金0%20存款175OECD同业存款20%25次级债务5年3抵押贷款50%70累积优先股(包括限定性的和永久性的)5消费贷款100%70权益2总资产185总资产和权益185此外，该银行有3000万美元的履约备用信用证，400万美元的两年期远期外集合约(目前盈利100万美元)，以与3亿美元的6年期利率互换协议目前亏损200万美元。信用转换系数如下：履约备用信用证 50%1-5年外集合约 5%1-5年利率互换 0.5%5-10年利率互换 1.5%（a） 根据巴塞尔协议的定义，该银行的表风险
25、调整资产是多少（b） 表和表外资产的总资本要多少（c） 该银行的资本能够满足巴塞尔协议的要求吗？参考答案：a.What are the risk-adjusted on-balance-sheet assets of the bank as defined under the Basel Accord?Risk-adjusted assets:Cash0 x 20=$0OECD interbank deposits0.20 x 25=$5Mortgage loans0.50 x 70=$35Consumer loans1.00 x 70=$70Total risk-adjusted asset
26、s=$110= $110b.What is the total capital required for both off- and on-balance-sheet assets?Standby LCs:$30 x 0.50=$15= $15Foreign exchange contracts:Potential exposure$40 x 0.05=$2Current exposurein the money=$0Interest rate swaps:Potential exposure$300 x 0.015=$4.5Current exposureOut-of-the money=$
27、2=$8.5 x0.50= $4.25Total risk-adjusted on- and off-balance-sheet assets= $129.25x 0.08Total capital required= $10.34c.Does the bank have enough capital to meet the Basel requirements? If not, what minimum Tier 1 or total capital does it need to meet the requirement?No, the bank does not have suffici
28、ent capital to meet the Basel requirements. It needs total capital of $10.34, of which Tier 1 must be at least $129.25 x 0.04 = $5.17. Further, since perpetual preferred stock is limited to 25 percent ($1.29 million) of Tier 1, the bank needs at least $3.878 million of equity capital. Thus an additi
29、onal $1.878 million of equity is necessary to satisfy the Tier 1 requirements.If Tier I actually equals $5.17, the required Tier II capital also will be $5.17. Of this amount, the remaining perpetual preferred stock of $3.91?3.71 million is counted, which leaves $1.29 million of subordinated debt th
30、at can be used to satisfy the Tier II requirement. This amount is available and satisfies the limit of 50% of Tier I rule. (Refer to Table 20-8 for explanations of Tier I and Tier II requirements.) A new balance sheet after the issuance of the new required equity is shown below. You will note that t
31、he total capital now seems to exceed the minimum of $10.34 million. However, only a portion of the subordinated debt can be counted, and this portion will decrease as the maturity approaches.New balance sheet:Cash$21.878 Deposits $175OECD interbank deposits $25Subordinated debt (over 5 years)$3Mortgage loans $ 70Cumulative preferred stock$5Consumer loans$70Equity$3.878Total$186.878$186.87815 / 15
