固定收益证券计算题

计算题题型一：计算普通债券的久期和凸性久期的概念公式：t Nt W t D ∑=⨯=1其中，W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且以上求出的久期是以期数为单位的，还要把它除以每年付息的次数，转化成以年为单位的久期。

久期的简化公式：yy c y c T y y y D T +-+-++-+=]1)1[()()1(1 其中，c 表示每期票面利率，y 表示每期到期收益率，T 表示距到期日的期数。

凸性的计算公式：t Nt W t ty C ⨯++=∑=122)()1(1其中，y 表示每期到期收益率；W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且求出的凸性是以期数为单位的，需除以每年付息次数的平方，转换成以年为单位的凸性。

例一：面值为100元、票面利率为8%的3年期债券，半年付息一次，下一次付息在半年后，如果到期收益率（折现率）为10%，计算它的久期和凸性。

每期现金流：42%8100=⨯=C 实际折现率：%52%10=即，D=5.4351/2=2.7176利用简化公式：4349.5%5]1%)51[(%4%)5%4(6%)51(%5%516=+-+⨯-⨯++-+=D （半年）即，2.7175（年）36.7694/（1.05）2=33.3509 ；以年为单位的凸性：C=33.3509/（2）2=8.3377利用凸性和久期的概念，计算当收益率变动1个基点（0.01%）时，该债券价格的波动①利用修正久期的意义：y D P P ∆⨯-=∆*/5881.2%517175.2*=+=D （年）当收益率上升一个基点，从10%提高到10.01%时，%0259.0%01.05881.2/-=⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0259.0%)01.0(5881.2/=-⨯-≈∆P P 。

②凸性与价格波动的关系：()2*21/y C y D P P ∆∙∙+∆∙-=∆当收益率上升一个基点，从10%提高到10.01%时，%0259.0%)01.0(3377.821%01.05881.2/2-=⨯⨯+⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0676.0%)01.0(3377.821%)01.0(5881.2/2=⨯⨯+-⨯-≈∆P P又因为，债券价格对于收益率的降低比对收益率的上升更加敏感，所以凸性的估计结果与真实价格波动更为接近。

固定收益证券试题及答案

固定收益证券试题及答案一、单项选择题（每题2分，共20分）1. 固定收益证券的主要风险不包括以下哪一项？A. 利率风险B. 信用风险C. 流动性风险D. 汇率风险答案：D2. 以下哪个不是固定收益证券的特点？A. 收益固定B. 投资期限长C. 风险较低D. 价格波动大答案：D3. 债券的票面利率与市场利率的关系是：A. 总是相等的B. 总是不等的C. 有时相等，有时不等D. 以上都不对答案：C4. 如果市场利率上升，而债券的票面利率保持不变，那么债券的：A. 价格上升B. 价格下降C. 价格不变D. 与市场利率无关答案：B5. 以下哪个不是固定收益证券的种类？A. 政府债券B. 企业债券C. 股票D. 金融债券答案：C6. 债券的到期收益率是指：A. 债券的票面利率B. 债券的当前市场价格C. 投资者持有到期的年化收益率D. 债券的发行价格答案：C7. 以下哪个因素不会影响固定收益证券的收益率？A. 发行主体的信用等级B. 债券的期限C. 市场利率水平D. 投资者的风险偏好答案：D8. 债券的久期是指：A. 债券的到期时间B. 债券的加权平均到期时间C. 债券的票面金额D. 债券的发行时间答案：B9. 以下哪个不是影响债券价格的因素？A. 债券的票面利率B. 债券的信用等级C. 债券的发行量D. 市场利率的变化答案：C10. 以下哪个是固定收益证券投资的主要目的？A. 资本增值B. 获得稳定的现金流C. 参与公司决策D. 投机取利答案：B二、多项选择题（每题3分，共15分）11. 固定收益证券的收益来源主要包括哪些？（ACD）A. 利息收入B. 股票升值C. 资本利得D. 再投资收益12. 以下哪些因素会影响固定收益证券的信用风险？（ABD）A. 发行主体的财务状况B. 经济环境的变化C. 投资者的个人偏好D. 法律和政策环境13. 固定收益证券的流动性通常与以下哪些因素有关？（ACD）A. 债券的发行量B. 债券的票面利率C. 市场交易的活跃度D. 债券的到期时间14. 以下哪些措施可以降低固定收益证券的投资风险？（ABD）A. 分散投资B. 选择信用等级较高的债券C. 增加投资金额D. 关注市场利率变动15. 固定收益证券的久期与以下哪些因素有关？（ABC）A. 债券的现金流时间B. 每笔现金流的金额C. 每笔现金流的现值D. 债券的票面利率三、判断题（每题1分，共10分）16. 固定收益证券的风险总是低于股票。

固定收益证券的复习计算题

Fixed-income treasuryPpt31、公式：Practice Question 3.1Suppose currently, 1-year spot rate is 1% and marketexpects that 1-year spot rate next year would be 2%and 1-year spot rate in 2 years would be 3%. Compute today’s2-year spot rate and 3-year spot rate.(已做答案）2、Current YieldCompute the current yield for a 7% 8-year bond whose price is$94.17. How about the current yield if price is $100, $106,respectively?3、Case 3.1Consider a 7% 8-year bond paying coupon semiannually which is sold for $94.17. The present value using various discount rate is:A. What is the YTM for this bond?B. How much is the total dollar return on this bond?C. How much is the total dollar return if you put the same amount of dollars into a deposit account with the same annual yield?4、Forward Rates注：6-month bill spot rate is 3%是年化利率（3%要除以2）1-year bill spot rate is 3.3%是年化利率（3.3%要除以2）Ppt41、Fixed‐Coupon BondsPractice Question 4.2A. What is the value of a 4-year 10% coupon bond that pays interest semiannually assuming that the annual discount rate is 8%? What is the value of a similar 10% coupon bond with an infinite maturity（无期限）?B. What is the value of a 5-year zero-coupon bond with a maturity value of $100 discounted at an 8% interest rate?C. Compute the value par $100 of par value of a 4-year 10% coupon bond, assuming the payments are annual and the discount rate for each year is 6.8%, 7.2%, 7.6% and 8.0%, respectively.Infinite maturityPv=($100*10%/2)/(8%/2)(半年付息）Present Value PropertiesPractice Question 4.4A. Suppose the discount rate for the 4-year 10% coupon bond with a par value of $100 is 8%. Compute its present value.B. One year later, suppose that the discount rate appropriate for a 3-year 10% coupon bond increases from 8% to 9%. Redo your calculation in part A and decompose the price change attributable to moving to maturity and to the increase in the discount rate.（期限与贴现率变化）3、Pricing a Bond between Coupon PaymentsPractice Question 4.6Suppose that there are five semiannual coupon payments remaining for a 10% coupon bond. Also assume the following:①Annual discount rate is 8%② 78 days between the settlement date and the next coupon payment date③182 days in the coupon periodCompute the full price of this coupon bond. What is the clean price of this bond?4、Valuation ApproachCase 4.1A. Consider a 8% 10-year Treasury coupon bond. What is its fair value if traditional approach is used, given yield for the 10-year on-the-run Treasury issue is 8%?B. What is the fair value of above Treasury coupon bond if arbitrage-free approach is used,given the following annual spot rates?C. Which approach is more accurate（准确）?C、Arbitrage-Free Approach is more accuratePpt52、ConvexityConsider a 9% 20-year bond selling at $134.6722 to yield 6%. For a 20 bp change in yield, its price would either increase to $137.5888 or decrease to $131.8439.A. Compute the convexity for this bond.B. What is the convexity adjustment for a change in yield of 200 bps?C. If we know that the duration for this bond is 10.66, what should the total estimated percentage price change be for a 200 bp increase in the yield? How about a 200 bp decrease in the yield?Ppt61、Measuring Yield Curve RiskCase 6.1: Panel AConsider the following two $100 portfolios composed of2-year, 16-year, and 30-year issues, all of which are zero-coupon bonds:For simplicity, assume there are only three key rates—2years, 16 years and 30 years. Calculate the portfolio’s key rate durations at these three points and its effective duration.Case 6.1: Panel BConsider the following three scenarios:Scenario 1: All spot rates shift down 10 basis points.Scenario 2: The 2-year key rate shifts up 10 basis points an the30-year rate shifts down 10 basis points.Scenario 3: The 2-year key rate shifts down 10 basis points andthe 30-year rate shifts up 10 basis points.How would the portfolio value change in each scenario?Ppt7Consider a 6.5% option-free bond with 4 years remaining to maturity. If the appropriate binomial interest rate tree is shown as below, calculate the fair price of this bond.Ppt81、Valuing Callable and Putable BondsCase 8.1: Valuing a callable bond with singlecall priceConsider a 6.5% callable bond with 4 years remaining to maturity, callable in one year at $100. Assume the yield volatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this callable bond.2、Case 8.2: Valuing a callable bond with call scheduleConsider a 6.5% callable bond with 4 years remaining tomaturity, callable in one year at a call schedule as below:Assume the yield volatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this callable bond.3、Case 8.3: Valuing a putable bond Consider a 6.5% putable bond with4 years remaining to maturity, putable in one year at $100. Assume the yieldvolatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this putable bond.Convertible BondsCase 9.1:Suppose that the straight value of a 5.75% ADC convertible bond is $981.9per$1,000 of par value and its market price is $1,065. The market price per share of common stock is $33and the conversion ratio is 25.32shares per $1,000 of parvalue. Also assume that the common stock dividend is $0.90 per share.公式：Minimum Value: the greater of its conversion price and its straight value. Conversion Price = Market price of common stock ×Conversion ratioStraight Value/Investment Value: present value of the bond’s cash flows discounted at the required return on a comparable option-free issue.Market Conversion Price/Conversion ParityPrick= Market price of convertible security ÷Conversion ratioMarket Conversion Premium Per Share= Market conversion price – Market price of common stockMarket Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stock Premium over straight value= (Market price of convertible bond/Straight value) – 1The higher this ratio, the greater downside risk and theless attractive the convertible bond.Premium Payback Period= Market conversion premium per share ÷Favorable income differential per shareFavorable Income Differential Per Share= [Coupon interest – (Conversion ratio × Common stock dividend per share)] ÷Conversion ratioA. What is the minimum value of this convertible bond?B. Calculate its market conversion price, market conversion premium per share and market conversion premium ratio.C. What is its premium payback period?D. Calculate its premium over straight value.Market price of common stock=$33,conversion ratio = 25.32Straight Value=$981.9 ，market price of conversible bond = $1,065common stock dividend = $0.90Coupon rate=5.75%A、Conversion Price = Market price of common stock ×Conversion ratio=$33*25.32=$835.56the minimum value of this convertible bond=max{$835.56,$981.9}=$981.9B、Market Conversion Price/Conversion ParityPrick= Market price of convertible security ÷Conversion ratio=$1065/25.32=$42.06Market Conversion Premium Per Share= Market conversion price – Market price of common stock= $42.06 -$33= $9.06Market Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stock= $9.06/$33=27.5%C、Premium Payback Period= Market conversion premium per share ÷Favorable income differential per shareFavorable Income Differential Per Share= [Coupon interest – (Conversion ratio × Common stock dividend per share)] ÷Conversion ratioCoupon interest from bond = 5.75%×$1,000 =$57.50Favorable income differential per share = ($57.50 –25.32×$0.90) ÷25.32 = $1.37 Premium payback period = $9.06/$1.37 = 6.6 yearsD、Premium over straight value= (Market price of convertible bond/Straight value) – 1=$1,065/$981.5 – 1 =8.5%Ppt10No-Arbitrage Principle:no riskless profits gained from holding a combination of a forward contract position as well as positions in other assets.FP = Price that would not permit profitable riskless arbitrage in frictionless markets, that is:Case 10.1Consider a 3-month forward contrac t on a zero-coupon bond with a face value of $1,000 that is currently quoted at $500, and assume a risk-free annual interest rate of 6%. Determine the price of the forward contract underthe no-arbitrage principle.Solutions.Case 10.2Suppose the forward contract described in case 10.1 is actually trading at $510, which is greater than the noarbitrage price. Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this overpriced forward contrac t and how much the arbitrage profit would be.Case 10.3If the forward contract described in case 10.1 is actually trading at $502, which is smaller than the no-arbitrage price. Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this underpriced forward contract and how much the arbitrage profit would be.Case 10.4:Calculate the price of a 250-day forward contract on a 7% U.S.Treasury bond with a spot price of $1,050 (including accrued interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk-free rate is 6%.Solutions. Remember that T-bonds make semiannual coupon payments, soCase 10.6Solutions.The semiannual coupon on a single, $1,000 face-value7% bond is $35. Abondholder will receive one payment 0.5 years from now (0.7 years left to expiration of futures) and one payment 1 year from now (0.2 yearsuntil expiration). Thus,Ppt11Payoffs and ProfitsCase 11.1Consider a European bond call option with an exercise price of $900. The call premium for this option is $50. At expiration, if the spot price for the underlying bond is $1,000, what is the call option’s payoff as well as its gain/loss? Is this option in the money, out of money, or at the money? Will you exercise this option? How about your answers if the spot price at expiration is $920, and $880, respectively? Solutions.A. If the spot price at expiration is $1,000, the payoff to the call option ismax{0, $1,000 - $900}=$100. So, the call is in the money and it will beexercised with a gain of $50.B. If the spot price at expiration is $920, the payoff to the call option ismax{0, $920 - $900}=$20. So, the call is in the money and it will beexercised with a loss of $30. (why?)C. If the spot price is $880 at expiration, the payoff to the call option ismax{0, $880 - $900}=0. So, the call is out of money and it will not be exercise. The loss occurred would be $50.Case 11.2Consider a European bond put option with an exercise price of $950. The put premium for this option is $50. At expiration, if the spot price for the underlying bond is $1,000, what is the put option’s payoff as well as its gain/loss? Is this option in the money, out of money, or at the money? Will you exercise this option? How about your answers if the spot price at expiration is $920, and $880, respectively?Solutions.A. If the spot price at expiration is $1,000, the payoff to the put option is max{0, $950 - $1,000}=0. So, the put is out of money and it will not be exercised. The loss occurred would be $50.B. If the spot price at expiration is $920, the payoff to the put option is max{0, $950 - $920}=$30. So, the put is in the money and it will be exercised with a loss of $20. (why?)C. If the spot price is $880 at expiration, the payoff to the call option is max{0, $950 - $880}=$70. So, the put is in the money and it will not be exercise with a gain of $20.。

固定收益证券题目及解答

23、假设货币市场期限为3个月、6个月和9个月的债券的实际季度收益率分别为0.75%、1.5%和 2%，再假设该市场上存在期限为3个月和9个月的两种贴现国债，面值都是100元。如果投资者的投资期限是3个月，并假定收益率曲线在未来3
个月里不会变化。请问该投资者应选择哪一种债券投资？
3、一张期限为10年的等额摊还债券，每年等额偿还的金额为100元；另有一张永久债券，每年支付利息为50元。如果市场利率为8%，试比较它们价格的大小。
4、若市场上有下表所示的两个债券，并假设市场利率的波动率是10%，构建一个二期的利率二叉树。
市场债券品种假设
品种 A
到期期限息票利率折现率当前价格
12、考虑票面金额1000元、票面利率为8%、期限为5年的每年付息一次的债券，现有两种情况：到期收益率为7%时，上升1个百分点所引起的债券价格变化率为多少? 到期收益率为8%时，上升1个百分点所引起的债券价格变化率为多少?哪种情况下债券价格变化率大？
13、某投资者购买了10张面值为100元，票面利率为6%、每年付息一次的债券，债券刚付息，持有3年，获得3年末的利息后出售。期间获得的利息可以再投资，假设再投资收益率为4.5%。每份债券购买价为103元，出售价为107元。求该投资者的总收益率。
14、某一次还本付息债券，面值100元，票面利率3.5%，期限3年，2011年12月10日到期。债券交易的全价为99.40元，结算日为2009年9 月15日，试计算其到期收益率。
15、假设有3个不同期限债券，它们的数据
见下表，其中第一个为零息债券，后两个是附
息债券，且都是每年付息一次。试给出1年期
6、设某债券与上题B债券条件相同，但为可回售债券，持有人有权在发行后的第一年末以99.50元的价格向发行人回售，利率二叉树与上题亦相同，试计算该债券的价格。

固定收益证券全书习题

第一章固定收益证券简介三、计算题1．如果债券的面值为1000美元，年息票利率为5%，则年息票额为？答案：年息票额为5%*1000=50美元。

四、问答题1．试结合产品分析金融风险的基本特征。

答案：金融风险是以货币信用经营为特征的风险，它不同于普通意义上的风险，具有以下特征：客观性. 社会性.扩散性. 隐蔽性2．分析欧洲债券比外国债券更受市场投资者欢迎的原因。

答案：欧洲债券具有吸引力的原因来自以下六方面：1）欧洲债券市场部属于任何一个国家，因此债券发行者不需要向任何监督机关登记注册，可以回避许多限制，因此增加了其债券种类创新的自由度与吸引力。

2）欧洲债券市场是一个完全自由的市场，无利率管制，无发行额限制。

3）债券的发行常是又几家大的跨国银行或国际银团组成的承销辛迪加负责办理，有时也可能组织一个庞大的认购集团，因此发行面广4）欧洲债券的利息收入通常免缴所得税，或不预先扣除借款国的税款。

5）欧洲债券市场是一个极富活力的二级市场。

6）欧洲债券的发行者主要是各国政府、国际组织或一些大公司，他们的信用等级很高，因此安全可靠，而且收益率又较高。

3．请判断浮动利率债券是否具有利率风险，并说明理由。

答案：浮动利率债券具有利率风险。

虽然浮动利率债券的息票利率会定期重订，但由于重订周期的长短不同、风险贴水变化及利率上、下限规定等，仍然会导致债券收益率与市场利率之间的差异，这种差异也必然导致债券价格的波动。

正常情况下，债券息票利率的重订周期越长，其价格的波动性就越大。

三、简答题1．简述预期假说理论的基本命题、前提假设、以及对收益率曲线形状的解释。

答案：预期收益理论的基本命题预期假说理论提出了一个常识性的命题：长期债券的到期收益率等于长期债券到期之前人们短期利率预期的平均值。

例如，如果人们预期在未来5年里，短期利率的平均值为10%，那么5年期限的债券的到期收益率为10%。

如果5年后，短期利率预期上升，从而未来20年内短期利率的平均值为11%，则20年期限的债券的到期收益率就将等于11%，从而高于5年期限债券的到期首。

固定收益证券计算题

计算题题型一：计算普通债券的久期和凸性久期的概念公式：t Nt W t D ∑=⨯=1其中，W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且以上求出的久期是以期数为单位的，还要把它除以每年付息的次数，转化成以年为单位的久期。

久期的简化公式：yy c y c T y y y D T +-+-++-+=]1)1[()()1(1 其中，c 表示每期票面利率，y 表示每期到期收益率，T 表示距到期日的期数。

凸性的计算公式：t Nt W t ty C ⨯++=∑=122)()1(1其中，y 表示每期到期收益率；W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且求出的凸性是以期数为单位的，需除以每年付息次数的平方，转换成以年为单位的凸性。

例一：面值为100元、票面利率为8%的3年期债券，半年付息一次，下一次付息在半年后，如果到期收益率（折现率）为10%，计算它的久期和凸性。

每期现金流：42%8100=⨯=C 实际折现率：%52%10=息票债券久期、凸性的计算即，D=5.4351/2=2.7176利用简化公式：4349.5%5]1%)51[(%4%)5%4(6%)51(%5%516=+-+⨯-⨯++-+=D （半年）即，2.7175（年）36.7694/（1.05）2=33.3509 ；以年为单位的凸性：C=33.3509/（2）2=8.3377利用凸性和久期的概念，计算当收益率变动1个基点（0.01%）时，该债券价格的波动①利用修正久期的意义：y D P P ∆⨯-=∆*/5881.2%517175.2*=+=D （年）当收益率上升一个基点，从10%提高到10.01%时，%0259.0%01.05881.2/-=⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0259.0%)01.0(5881.2/=-⨯-≈∆P P 。

②凸性与价格波动的关系：()2*21/y C y D P P ∆••+∆•-=∆当收益率上升一个基点，从10%提高到10.01%时，%0259.0%)01.0(3377.821%01.05881.2/2-=⨯⨯+⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0676.0%)01.0(3377.821%)01.0(5881.2/2=⨯⨯+-⨯-≈∆P P又因为，债券价格对于收益率的降低比对收益率的上升更加敏感，所以凸性的估计结果与真实价格波动更为接近。

固定收益证券题目及答案

二0、假设有一个债券,面值一00元,期限三年, 票面利率五%,每年付息一次,市场利率四%,试计算其凸度.
二一、有一债券面值是一00元,初始到期收益率为八%,修正久期是七.九五年,凸度是八四. 六0,债券价格是八四.九二七八元.当收益率下降一00个基点时,试计算用修正久期预测的债券价格和考虑凸度调整后的债券价格.
一八、试计算面值为一00元,到期收益率为五 %,期限为五年的贴现债券的久期和修正久期.
一九、有一债券,面值一00元,期限二0年,息票利率八%,每年付息一次,到期收益率八%,价格是一00元.当市场利率上升一0个基点时,市场价格是九九.0二五四元；当市场利率下降一0 个基点时,市场价格是一00.九八九二元.求该债券的有效久期.
一五、假设有三个不同期限债券,它们的数据见下表,其中第一个为零息债券,后两个是附息
债券,且都是每年付息一次.试给出一年期到三
年期的即期收益率. 三个不同期限债券的数据
期限[年] 一二三
面值[元] 一00 一00 一00
息票利率[%]
0 五.四二六.七八
市场价格[元] 九五.六0 一0二.三八一0五.五六
二三、假设货币市场期限为三个月、六个月和九个月的债券的实际季度收益率分别为0.七五%、一.五%和二%,再假设该市场上存在期限为三个月和九个月的两种贴现国债,面值都是一00元.如果投资者的投资期限是三个月,并假定收益率曲线在未来三个月里不会变化.请问该投资者应选择哪一种债券投资?
《固定收益证券》课程练习题及答案
一、某投资者在上海证券交易所市场上以六%的年收益率申报买进二00手R00 三,请计算成交后的购回价[小数点后保留三位].
二、设一家公司从员工工作第一年末开始,每年给员工三000元福利存入一个银行账户,连续存四年,三年期存款年复利率为六.五%,二年期存款年复利率为五%,一年期存款年复利率为三%,那么这个年金终值是多少?

固定收益证券作业及答案

固定收益证券作业及答案1.三年后收到的100元现在的价值是多少？分别考虑复利20%、复利100%、复利0%、复利20%（半年计息）、复利20%（季计息）和复利20%（连续计息）的情况。

2.以连续复利方式计息，分别计算复利4%、复利20%（年计息）、复利20%（季计息）和复利100%的利率。

3.考虑以下问题：a。

___在交易日92年9月16日给出了票面利率为91/8's在92年12月31日到期，92年9月17日结算的政府债券，其标价为买入价101：23，卖出价101：25.求该债券的买入和卖出的收益率。

b。

在同一交易日，___对同时在92年12月31日到期和在92年9月17日结算的T-bill报出的买入和卖出折现率分别是2.88%和2.86%。

是否存在套利机会？（“买入”和“卖出”是从交易者的角度出发，你是以“买入价”卖出，以“卖出价”买入）4.在交易日92年9月16日，以10-26的价格买入了一张面值为2000万美元、到期日为2021年11月15日的STRIPs （零息债券）。

求该债券的到期收益率。

5.今天是1994年10月10日，星期一，是交易日。

以下是三种债券的相关信息：发行机构票面利率到期日到期收益___ 10% 8.00% 星期二，1/31/95费城（市政） 9% 7.00% 星期一，12/2/95___（机构） 8.50% 8% 星期五，7/28/95这三种债券的面值均为100美元，每半年付息一次。

注意到上表中最后一列是到期收益，它反映了给定到期日、某种特定债券的标准惯例。

在计算日期时，不考虑闰年，同时也要忽略假期。

回答以下问题时，需要写清楚计算过程，不能只是用计算器计算价格。

a。

计算___发行的国债的报价，假定该国债按照标准结算方式结算。

b。

计算费城发行的城市债券的报价，假定该债券的标准结算期为三天。

c。

计算___发行的机构债券的报价，假定该债券按照标准结算方式结算。

本题需要根据给定的到期收益曲线来计算固定付息债券的全价，以及在曲线上下移动100个基点时的全价。

固定收益证券计算题

精心整理计算题题型一：计算普通债券的久期和凸性久期的概念公式：t Nt W t D ∑=⨯=1付息在半年后，如果到期收益率（折现率）为10%，计算它的久期和凸性。

每期现金流：42%8100=⨯=C 实际折现率：%52%10= 息票债券久期、凸性的计算利用凸性和久期的概念，计算当收益率变动1个基点（0.01%）时，该债券价格的波动利用修正久期的意义：y D P P ∆⨯-=∆*/5881.2%517175.2*=+=D （年）当收益率上升一个基点，从10%提高到10.01%时，%0259.0%01.05881.2/-=⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，题型二：计算提前卖出的债券的总收益率首先，利息+利息的利息=⎦⎤⎢⎣⎡-+⨯111)1(r r C n ；r 1为每期再投资利率；然后，有债券的期末价值=利息+利息的利息+投资期末的债券价格；所以，6年后的期末价值=901.55+1035.46=1937.01元总收益=1937.01-905.53=1031.48元半年期总收益率=%54.6153.90501.193712=-总收益率=（1+6.54%）2-1=13.51%题型三：或有免疫策略（求安全边际）例三：银行有100万存款，5年到期，最低回报率为8%；现有购买一个票面利率为8%，按年付息，3年到期的债券，且到期收益率为10%；求1年后的安全边际。

题型四：求逆浮动利率债券的价格例四（付息日卖出）：已知浮动利率债券和逆浮动利率债券的利率之和为12%，两种债券面值都为1万，3年到期。

1年后卖掉逆浮动利率债券，此时市场折现率（适当收益率）为8%，求逆浮动利率债券的价格。

例五：现有一美国公司债券，息票利率为8%，30年到期，适当收益率为6%，求债券现在的价值？解：因为该债券面值为1000美元，每半年付息一次，所以：60601%)31(1000%)31(40+++=∑=n n P =⎦⎤⎢⎣⎡+-⨯-%3%)31(14060+60%)31(1000+=1276.76元例六：现有一美国公司债券，息票利率为8%，30年到期，假设现在的售价为676.77美元，求债券到期收益率？解：例八：一种美国公司债券，票面利率是10%，2008年4月1日到期。

固定收益证券题目及答案解读

3、一张期限为10年的等额摊还债券，每年等额偿还的金额为100元；另有一张永久债券，每年支付利息为50元。如果市场利率为8%，试比较它们价格的大小。
4、若市场上有下表所示的两个债券，并假设市场利率的波动率是10%，构建一个二期的利率二叉树。市场债券品种假设
品种 A 到期期限息票利率（年）（%） 1 3.50 折现率（%） 3.50 当前价格（元） 100.00
15、假设有3个不同期限债券，它们的数据见下表，其中第一个为零息债券，后两个是附息债券，且都是每年付息一次。试给出1年期到3年期的即期收益率。三个不同期限债券的数据
期限（年） 1 2 3 面值（元） 100 100 100 息票利率（%）市场价格（元） 0 95.60 5.42 102.38 6.78 105.56
18、试计算面值为100元，到期收益率为5%，期限为5年的贴现债券的久期和修正久期。
19、有一债券，面值100元，期限20年，息票利率8%，每年付息一次，到期收益率8%，价格是100元。当市场利率上升10个基点时，市场价格是99.0254元；当市场利率下降10个基点时，市场价格是100.9892元。求该债券的有效久期。
20、假设有一个债券，面值100元，期限3年，票面利率5%，每年付息一次，市场利率4%，试计算其凸度。
21、有一债券面值是100元，初始到期收益率为8%，修正久期是7.95年，凸度是84.60，债券价格是84.9278元。当收益率下降100个基点时，试计算用修正久期预测的债券价格和考虑凸度调整后的债券价格。
9、有一附息债券，一年付息一次，期限5年，票面金额为1000元，票面利率5.2%。某投资者在该债券发行时以998元的发行价购入，持满3年即以1002.20元的价格卖出。请计算该投资者的持有期收益率是多少（可用简化公式）？当期收益率有一企业债券，面值100元，期限3年，票面利率4%，到期一次还本付息，利息所得税税率为20%，请计算持有该债券到期的税后复利到期收益率。

固定收益证券计算题

固定收益证券计算题计算题题型一：计算普通债券的久期和凸性久期的概念公式：t Nt W t D ∑=⨯=1其中，W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且以上求出的久期是以期数为单位的，还要把它除以每年付息的次数，转化成以年为单位的久期。

久期的简化公式：yy c y c T y y y D T +-+-++-+=]1)1[()()1(1 其中，c 表示每期票面利率，y 表示每期到期收益率，T 表示距到期日的期数。

凸性的计算公式：t N t W t t y C ⨯++=∑=122)()1(1其中，y 表示每期到期收益率；W t 是现金流时间的权重，是第t 期现金流的现值占债券价格的比重。

且求出的凸性是以期数为单位的，需除以每年付息次数的平方，转换成以年为单位的凸性。

即，D=5.4351/2=2.7176利用简化公式：4349.5%5]1%)51[(%4%)5%4(6%)51(%5%516=+-+⨯-⨯++-+=D （半年）即，2.7175（年）36.7694/（1.05）2=33.3509 ；以年为单位的凸性：C=33.3509/（2）2=8.3377利用凸性和久期的概念，计算当收益率变动1个基点（0.01%）时，该债券价格的波动①利用修正久期的意义：y D P P ∆⨯-=∆*/5881.2%517175.2*=+=D （年）当收益率上升一个基点，从10%提高到10.01%时，%0259.0%01.05881.2/-=⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0259.0%)01.0(5881.2/=-⨯-≈∆P P 。

②凸性与价格波动的关系：()2*21/y C y D P P ∆••+∆•-=∆当收益率上升一个基点，从10%提高到10.01%时，%0259.0%)01.0(3377.821%01.05881.2/2-=⨯⨯+⨯-≈∆P P ；当收益率下降一个基点，从10%下降到9.99%时，%0676.0%)01.0(3377.821%)01.0(5881.2/2=⨯⨯+-⨯-≈∆P P又因为，债券价格对于收益率的降低比对收益率的上升更加敏感，所以凸性的估计结果与真实价格波动更为接近。

固定收益证券的复习计算题

Fixed-income treasuryPpt31、公式：Practice Question 3.1Suppose currently, 1-year spot rate is 1% and marketexpects that 1-year spot rate next year would be 2%and 1-year spot rate in 2 years would be 3%. Compute today’s2-year spot rate and 3-year spot rate.(已做答案）2、Current YieldCompute the current yield for a 7% 8-year bond whose price is$94.17. How about the current yield if price is $100, $106,respectively?3、Case 3.1Consider a 7% 8-year bond paying coupon semiannually which is sold for $94.17. The present value using various discount rate is:A. What is the YTM for this bond?B. How much is the total dollar return on this bond?C. How much is the total dollar return if you put the same amount of dollars into a deposit account with the same annual yield?4、Forward Rates注：6-month bill spot rate is 3%是年化利率（3%要除以2）1-year bill spot rate is 3.3%是年化利率（3.3%要除以2）Ppt41、Fixed‐Coupon BondsPractice Question 4.2A. What is the value of a 4-year 10% coupon bond that pays interest semiannually assuming that the annual discount rate is 8%? What is the value of a similar 10% coupon bond with an infinite maturity（无期限）?B. What is the value of a 5-year zero-coupon bond with a maturity value of $100 discounted at an 8% interest rate?C. Compute the value par $100 of par value of a 4-year 10% coupon bond, assuming the payments are annual and the discount rate for each year is 6.8%, 7.2%, 7.6% and 8.0%, respectively.Infinite maturityPv=($100*10%/2)/(8%/2)(半年付息）Present Value PropertiesPractice Question 4.4A. Suppose the discount rate for the 4-year 10% coupon bond with a par value of $100 is 8%. Compute its present value.B. One year later, suppose that the discount rate appropriate for a 3-year 10% coupon bond increases from 8% to 9%. Redo your calculation in part A and decompose the price change attributable to moving to maturity and to the increase in the discount rate.（期限与贴现率变化）3、Pricing a Bond between Coupon PaymentsPractice Question 4.6Suppose that there are five semiannual coupon payments remaining for a 10% coupon bond. Also assume the following:①Annual discount rate is 8%② 78 days between the settlement date and the next coupon payment date③182 days in the coupon periodCompute the full price of this coupon bond. What is the clean price of this bond?4、Valuation ApproachCase 4.1A. Consider a 8% 10-year Treasury coupon bond. What is its fair value if traditional approach is used, given yield for the 10-year on-the-run Treasury issue is 8%?B. What is the fair value of above Treasury coupon bond if arbitrage-free approach is used,given the following annual spot rates?C. Which approach is more accurate（准确）?C、Arbitrage-Free Approach is more accuratePpt52、ConvexityConsider a 9% 20-year bond selling at $134.6722 to yield 6%. For a 20 bp change in yield, its price would either increase to $137.5888 or decrease to $131.8439.A. Compute the convexity for this bond.B. What is the convexity adjustment for a change in yield of 200 bps?C. If we know that the duration for this bond is 10.66, what should the total estimated percentage price change be for a 200 bp increase in the yield? How about a 200 bp decrease in the yield?Ppt61、Measuring Yield Curve RiskCase 6.1: Panel AConsider the following two $100 portfolios composed of2-year, 16-year, and 30-year issues, all of which are zero-coupon bonds:For simplicity, assume there are only three key rates—2years, 16 years and 30 years. Calculate the portfolio’s key rate durations at these three points and its effective duration.Case 6.1: Panel BConsider the following three scenarios:Scenario 1: All spot rates shift down 10 basis points.Scenario 2: The 2-year key rate shifts up 10 basis points an the30-year rate shifts down 10 basis points.Scenario 3: The 2-year key rate shifts down 10 basis points andthe 30-year rate shifts up 10 basis points.How would the portfolio value change in each scenario?Ppt7Consider a 6.5% option-free bond with 4 years remaining to maturity. If the appropriate binomial interest rate tree is shown as below, calculate the fair price of this bond.Ppt81、Valuing Callable and Putable BondsCase 8.1: Valuing a callable bond with singlecall priceConsider a 6.5% callable bond with 4 years remaining to maturity, callable in one year at $100. Assume the yield volatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this callable bond.2、Case 8.2: Valuing a callable bond with call scheduleConsider a 6.5% callable bond with 4 years remaining tomaturity, callable in one year at a call schedule as below:Assume the yield volatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this callable bond.3、Case 8.3: Valuing a putable bond Consider a 6.5% putable bond with4 years remaining to maturity, putable in one year at $100. Assume the yieldvolatility is 10% and the appropriate binomial interest rate tree is same as Case 6.4. Calculate the fair price of this putable bond.Convertible BondsCase 9.1:Suppose that the straight value of a 5.75% ADC convertible bond is $981.9per$1,000 of par value and its market price is $1,065. The market price per share of common stock is $33and the conversion ratio is 25.32shares per $1,000 of parvalue. Also assume that the common stock dividend is $0.90 per share.公式：Minimum Value: the greater of its conversion price and its straight value. Conversion Price = Market price of common stock ×Conversion ratioStraight Value/Investment Value: present value of the bond’s cash flows discounted at the required return on a comparable option-free issue.Market Conversion Price/Conversion ParityPrick= Market price of convertible security ÷Conversion ratioMarket Conversion Premium Per Share= Market conversion price – Market price of common stockMarket Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stock Premium over straight value= (Market price of convertible bond/Straight value) – 1The higher this ratio, the greater downside risk and theless attractive the convertible bond.Premium Payback Period= Market conversion premium per share ÷Favorable income differential per shareFavorable Income Differential Per Share= [Coupon interest – (Conversion ratio × Common stock dividend per share)] ÷Conversion ratioA. What is the minimum value of this convertible bond?B. Calculate its market conversion price, market conversion premium per share and market conversion premium ratio.C. What is its premium payback period?D. Calculate its premium over straight value.Market price of common stock=$33,conversion ratio = 25.32Straight Value=$981.9 ，market price of conversible bond = $1,065common stock dividend = $0.90Coupon rate=5.75%A、Conversion Price = Market price of common stock ×Conversion ratio=$33*25.32=$835.56the minimum value of this convertible bond=max{$835.56,$981.9}=$981.9B、Market Conversion Price/Conversion ParityPrick= Market price of convertible security ÷Conversion ratio=$1065/25.32=$42.06Market Conversion Premium Per Share= Market conversion price – Market price of common stock= $42.06 -$33= $9.06Market Conversion Premium Ratio= Market conversion premium per share ÷Market price of common stock= $9.06/$33=27.5%C、Premium Payback Period= Market conversion premium per share ÷Favorable income differential per shareFavorable Income Differential Per Share= [Coupon interest – (Conversion ratio × Common stock dividend per share)] ÷Conversion ratioCoupon interest from bond = 5.75%×$1,000 =$57.50Favorable income differential per share = ($57.50 –25.32×$0.90) ÷25.32 = $1.37 Premium payback period = $9.06/$1.37 = 6.6 yearsD、Premium over straight value= (Market price of convertible bond/Straight value) – 1=$1,065/$981.5 – 1 =8.5%Ppt10No-Arbitrage Principle:no riskless profits gained from holding a combination of a forward contract position as well as positions in other assets.FP = Price that would not permit profitable riskless arbitrage in frictionless markets, that is:Case 10.1Consider a 3-month forward contrac t on a zero-coupon bond with a face value of $1,000 that is currently quoted at $500, and assume a risk-free annual interest rate of 6%. Determine the price of the forward contract underthe no-arbitrage principle.Solutions.Case 10.2Suppose the forward contract described in case 10.1 is actually trading at $510, which is greater than the noarbitrage price. Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this overpriced forward contrac t and how much the arbitrage profit would be.Case 10.3If the forward contract described in case 10.1 is actually trading at $502, which is smaller than the no-arbitrage price. Demonstrate how an arbitrageur can obtain riskless arbitrage profit from this underpriced forward contract and how much the arbitrage profit would be.Case 10.4:Calculate the price of a 250-day forward contract on a 7% U.S.Treasury bond with a spot price of $1,050 (including accrued interest) that has just paid a coupon and will make another coupon payment in 182 days. The annual risk-free rate is 6%.Solutions. Remember that T-bonds make semiannual coupon payments, soCase 10.6Solutions.The semiannual coupon on a single, $1,000 face-value7% bond is $35. Abondholder will receive one payment 0.5 years from now (0.7 years left to expiration of futures) and one payment 1 year from now (0.2 yearsuntil expiration). Thus,Ppt11Payoffs and ProfitsCase 11.1Consider a European bond call option with an exercise price of $900. The call premium for this option is $50. At expiration, if the spot price for the underlying bond is $1,000, what is the call option’s payoff as well as its gain/loss? Is this option in the money, out of money, or at the money? Will you exercise this option? How about your answers if the spot price at expiration is $920, and $880, respectively? Solutions.A. If the spot price at expiration is $1,000, the payoff to the call option ismax{0, $1,000 - $900}=$100. So, the call is in the money and it will beexercised with a gain of $50.B. If the spot price at expiration is $920, the payoff to the call option ismax{0, $920 - $900}=$20. So, the call is in the money and it will beexercised with a loss of $30. (why?)C. If the spot price is $880 at expiration, the payoff to the call option ismax{0, $880 - $900}=0. So, the call is out of money and it will not be exercise. The loss occurred would be $50.Case 11.2Consider a European bond put option with an exercise price of $950. The put premium for this option is $50. At expiration, if the spot price for the underlying bond is $1,000, what is the put option’s payoff as well as its gain/loss? Is this option in the money, out of money, or at the money? Will you exercise this option? How about your answers if the spot price at expiration is $920, and $880, respectively?Solutions.A. If the spot price at expiration is $1,000, the payoff to the put option is max{0, $950 - $1,000}=0. So, the put is out of money and it will not be exercised. The loss occurred would be $50.B. If the spot price at expiration is $920, the payoff to the put option is max{0, $950 - $920}=$30. So, the put is in the money and it will be exercised with a loss of $20. (why?)C. If the spot price is $880 at expiration, the payoff to the call option is max{0, $950 - $880}=$70. So, the put is in the money and it will not be exercise with a gain of $20.。

固定收益证券练习题

固定收益证券练习题第三章1、convert(a)(1+3%/4)4=(1+r/12)12(b)(1+6%/2)2=er2、求以下名义利率的有效利率因为1.109＞1.108＞1.106＞1.105所以，c)选项的利率对投资者最优。

第四章1、所列就是各年期零息债券（面值1000元）的报价期限价格即期利率远期利率0.5年943.412%12%1年898.4711%10%1.5年847.6211.3%12%2年792.1612%14%（1）、恳请核对表空格。

此处均为半年乘数一次的名义利率。

（2）、现金流x=(x0,x0.5,x1,x1.5)为(-1020,85,85,1085)根据上奏排序它的净现值和内部收益率。

答：（1）、如图（2）、该现金流天量现值为：85×0.9434+85×0.89847+1085×0.84762-1020=56.2内部收益率为：1020=85/(1+y/2)+85/(1+y/2)2+1085(1+y/2)3当y=18%p=987.3当y=14%p=1039.36482、附息债券：（-pv,10,10,10,10,110）当yield=5%时，请问第一次付息后，债券市值的下降幅度。

求解：设立附息债券半年还本付息一次，当前价格为p0元，付息一次后价格为p1元。

p0=?t?14510100??134.8437（元）t5(1?5%?2)(1?5%?2)10100??128.2148（元）(1?5%?2)t(1?5%?2)4p1?p0128.2148?134.8437?=-4.92%p0134.8437p1=?t?1市值变化幅度=即为，还本付息一次后市值上升4.92%。

3、有一市政债券，票面利率5.5%，每半年付息一次，面值100元，到期日为12/19/2021,交割日为10/15/2021,到期收益率为4.28%。

上一个付息日为6/19/2021，下一个付息日为12/19/2021。

固定收益证券题目及答案PPT课件

ppt精选版
27
15
13、某投资者购买了10张面值为100元，票面利率为6%、每年付息一次的债券，债券刚付息，持有3年，获得3年末的利息后出售。期间获得的利息可以再投资，假设再投资收益率为4.5%。每份债券购买价为103元，出售价为107元。求该投资者的总收益率。
ppt精选版
16
14、某一次还本付息债券，面值100元，票面利率3.5%，期限3年，2011年12月10日到期。债券交易的全价为99.40元，结算日为2009年9 月15日，试计算其到期收益率。
ppt精选版
7
6、设某债券与上题B债券条件相同，但为可回售债券，持有人有权在发行后的第一年末以99.50元的价格向发行人回售，利率二叉树与上题亦相同，试计算该债券的价格。
ppt精选版
8
7、设某张可转换债券的面值为100元，票面利率为5%，期限5年，转换比例为5。预计2年后的标的股票价格为22元/股，折现率为6%，则该投资者认为该可转换债券的合理价格为多少元？
ppt精选版
11
10、有一企业债券，面值100元，期限3年，票面利率4%，到期一次还本付息，利息所得税税率为20%，请计算持有该债券到期的税后复利到期收益率。
ppt精选版
12
11、某债券的票面金额为1000元，票面利率为6.5%，期限3年，市场利率为6%，每年付息一次，试计算剩余期限从3年到2年债券价格的变化率。
ppt精选版
21
18、试计算面值为100元，到期收益率为5%，期限为5年的贴现债券的久期和修正久期。
ppt精选版
22
19、有一债券，面值100元，期限20年，息票利率8%，每年付息一次，到期收益率8%，价格是100元。当市场利率上升10个基点时，市场价格是99.0254元；当市场利率下降10个基点时，市场价格是100.9892元。求该债券的有效久期。

固定收益证券5套题

1、某8年期债券，第1~3年息票利率为%，第4~5年为7%，第6~7年为%，第8年升为8%，该债券就属于（A 多级步高债券）。

3、固定收益产品所面临的最大风险是（B 利率风险）。

5、目前我国最安全和最具流动性的投资品种是（B 国债）6、债券到期收益率计算的原理是（A 到期收益率是购买债券后一直持有到期的内含报酬率）。

7、在纯预期理论的条件下，下凸的的收益率曲线表示（B 短期利率在未来被认为可能下降）。

9、如果债券嵌入了可赎回期权，那么债券的利差将如何变化？(B 变小)11、5年期，10%的票面利率，半年支付。

债券的价格是1000元，每次付息是（B 50元）。

12、若收益率大于息票率，债券以（A 低于）面值交易；13、贴现率升高时，债券价值（A 降低）14、随着到期日的不断接近，债券价格会不断（C 接近）面值。

15、债券的期限越长，其利率风险（A 越大）。

16、投资人不能迅速或以合理价格出售公司债券，所面临的风险为（B 流动性风险）。

17、投资于国库券时可以不必考虑的风险是（A 违约风险）18、当市场利率大于债券票面利率时，一般应采用的发行方式为（B 折价发行）。

19、下列投资中，风险最小的是（B 购买企业债券）。

20、下面的风险衡量方法中，对可赎回债券风险的衡量最合适的是（B 有效久期）。

26、以下哪项资产不适合资产证券化？(D 股权)27、以下哪一种技术不属于内部信用增级？（C 担保）28、一位投资经理说：“对债券组合进行单期免疫，仅需要满足以下两个条件：资产的久期和债务的久期相等；资产的现值与负债的现值相等。

（B 不对，因为还必须考虑信用风险）固定收益市场上，有时也将（A.零息债券）称为深度折扣债券。

下列哪种情况，零波动利差为零？A.如果收益率曲线为平某人希望在5年末取得本利和20000元，则在年利率为2％，单利计息的方式下，此人现在应当存入银行（、82）元。

在投资人想出售有价证券获取现金时，证券不能立即出售的风险被称为（C.变现力风险）。

固定收益证券作业及答案

作业一1.三年后收到的$100，现在的价值是多少？假设三年期零息债券的利率是：a.复利20%，年计息b.复利100%，年计息c.复利0%，年计息d.复利20%，半年计息e.复利20%，季计息f.复利20%，连续计息2．以连续复利方式计息，下列利率各为多少？a.复利4%，年计息b.复利20%，年计息c.复利20%，季计息d.复利100%，年计息3.考虑下列问题：a.华尔街日报在交易日92年9月16日给出了票面利率为9 1/8’s在92年12月31日到期，92年9月17日结算的政府债券，其标价为买入价101：23，卖出价101：25。

这种债券相应买入和卖出的收益率是多少？b.在同一交易日，华尔街日报对同时在92年12月31日到期和在92年9月17日结算的T-bill报出的买入和卖出折现率分别是2.88%和2.86%（附录A“利率报价和惯例”中的例14中提到的T-bill）,这里面是不是有套利机会？（“买入”和“卖出”是从交易者的角度出发，你是以“买入价”卖出，以“卖出价”买入）。

4.你在交易日92年9月16日以$10-26买入$2，000万票面价值为100的在2021年11月15日到期的STRIPs(零息债券)，这种债券的到期收益率是多少？5.今天是交易日，1994年10月10日，星期一。

这三种债券的面值均为$100,每半年付息一次。

注意到上表中最后一列是到期收益，它反映了给定到期日,某种特定债券的标准惯例。

在计算日期时，不考虑闰年，同时也要忽略假期。

回答这个问题时非常重要的是要写清楚你的运算过程。

不能只是用计算器把价格计算出来。

本题要想得分，必须把计算中的所有步骤都写清楚。

a.计算美国财政部发行的国债的报价，假定此国债是按标准结算方式结算。

b.计算费城发行的城市债券的报价，假定此类债券标准结算期为三天。

c.计算联邦全国抵押协会发行的机构债券的报价，假定此类债券是按标准结算方式结算。

作业二1.考虑一固定付息债券，每年支付利息$1009.09，利息于时期1，2,…20支付。