固定收益证券估值与分析
固定收益证券的估值、定价与计算 课件 (9)
在前一步骤的基础上进行业绩评估
调整组合结构
债券组合的管理是一个持续不断的过程 组合管理者随时根据当前的形势判断是否应该调整组合以便与外部的变化协 调一致
债券组合管理概述
债券组合管理的内容
债券组合管理的前提是对风险的预防与处理，包括风险因子的辨别、度 量以及对促使风险因子变化的市场环境的认知。
债券组合管理概述
债券组合
债券组合是投资者按照一定的投资目标设立的一组债券以及相关的债券 衍生品的集合
债券组合管理
债券组合管理是根据事先确立的管理目标，通过一定的技术手段对组合 进行维护、调节与控制，以便实现预定投资目标的过程 债券组合管理的主要内容涉及组合风险因子的辨别与处理、市场时机选 择、资产配置（包括部类配置与券种选择）以及组合业绩评价
7.5%
7.5%
138.83
终值
0.09*6133.7+0.91*305.4
289．8 9
HRR
2[（289.89/138.84）1/20- 7.5%
债券A、债券B以及债券组合10年的表现（市场利率为5.5%）
Bond A（4%,20,MD=11.78,D=12.22） 现金流 计算过程 金额 52.36 30.46 58.13 140.9 8 2[（133.71/64.04）1/201] Bond B（12%,20,MD=9.43,D=9.78） 现金流 计算过程 金额 157.18 91.36 58.13 306.67 2[（306.67/146.24） 1/20-1]
根据免疫法管理的债券组合可以在指定的时间内获得确定的、不受利率 变化影响的收益率。 这一管理方法在两个层面上得以运用：
一是在组合构造时使债券组合的久期等于负债的久期，并且使债券组合的初 始价值等于负债的初始价值。这样，当利率发生变化时，资产价值与负债价 值大致同等变化，相互抵消，组合管理者的总体财务状况不受利率波动的影 响；
CIIA复习宝典_固定收益证券估值与分析_部分幻灯片_鲁衡军
今天
折现
未来某日
1元钱
？？
¾单利计算
求终值
例2-1 F = S ×（1+ i）× n
单利
¾复利计算 例2-2
复利
F = S ×（1+ i）×（1+i）×iii= S × (1+ i)n连续复利
¾连续复利计算 例2-8
F
=
S × er×t
15
第二章 货币的时间价值
¾年金的概念
9年金的概念:在金融理财部分非常重要 99公重式要：是现标理值系准解数年其an =金概∑t=n1期念(1+1i)末涵n = 支义1−iv付，n 现考值试系时数候；会标给准出年公金式终期值末系数支Sn付= ∑t终n=−01 (1值+ i)系t = 数(1+；ii)n −1
付息方式多样：年，半年，季度 无特殊说明，一般为年利率
10
第一章 基础知识
¾标价方式
◆中长期国债的百分比报价与美国传统的价格标价法
例1-2 例1-3
标价
=
交易价格 面值
×100
=
4335 5000
×100
=
86.70
89-16
=
1000
×
⎛ ⎜⎝
89
+
16 32
⎞ ⎟⎠
=
895
◆短期票据和短期国债的收益率报价法和指数报价法
美式复利计算
YTMA =2 × YTMS
18
第二章 货币的时间价值
两付息日之间的到期收益率
P
f 上次付息
现在
1-f 下次付息
f 理解成如0.2，0.3之类的比例数值 债券价格报价一般采用净价，总价格=净价P+ f×票面利息C 折现可以先折现到上次付息时间，然后右推到现在时间点
固定收益证券投资分析和估值(一)_真题-无答案
固定收益证券投资：分析和估值(一)(总分53,考试时间90分钟)单项选择题The investor would prefer the municipal bond because the taxable-equivalent yield is greater than the yield on the corporate bond: 6.4%＞6.375%.1. Assume a city issues a $ 5 million bond to build a new arena. The bond pays 8 percent semiannual interest and will mature in 10 years. Current interest rates are 9 percent. What is the pres ent value of this bond and what will the bond's value be in seven years from today? Present Value Value in 7 Years from Today ①A. 4674802 4931276 ②B. 5339758 4871053 ③C. 4674802 4871053 A. ①B. ②C. ③2. An investor has the following options available to them:They can buy a 10% semi annual coupon, 10 - year bond for $1000.The coupons can be reinvested at 12%.They estimate the bond will be sold in 3 years $1050.Based on this information, what would be the average annual rate of return over the 3 years?A. 11.5%. B. 13.5%. C. 10.0%.3. A bond has a par value of $1000, a time to maturity of 20 years, a coupon rate of 10 percent with interest paid annually, a current price of $ 850, and a yield to maturity (YTM) of 12 percent. If the interest payments are reinvested at 10 percent, the **pounded yield on this bond is:A.10.00%. B. 12.0%. C. 10.9%.4. A non-callable bond with 18 years remaining maturity has an annual coupon of 7 percent and a $1000 par value. The current yield to maturity on the bond is 8 percent. Which of the following is closest to the effective duration of the bond?A. 9.63. B.11.89. C. 8.24.5. If a bond has a convexity of 120 and a modified duration of 10, what is the convexity adjustment associated with a 25 basis point interest rate decline?A. -2.875%. B. -2.125%. C. +0.075%.6. If interest rates fall, the:A. callable bond's price rises faster than that of a noncallable but otherwise identical bond. B. callable bond's price rises more slowly than that of a noncallable but otherwise identical bond. C. value of call option embedded in the callable bond fails.7. For an option-flee bond, if yields increase by 200 basis points, the parts of the total estimatedpercentage price change attributable to duration and the convexity adjustment, respectively, will most likely be: Part of the total estimated percentage price change attributable to duration Part of the total estimated percentage price change attributable to the convexity adjustment ①A. Negative Positive ②B. Negative Negative ③C. Positive Positive A. ①B. ②C. ③8. An investor gathered the following information about two 7 percent annual-pay, option-free bonds:Bond R has 4 years to maturity and is priced to yield 6 percentBond S has 7 years to maturity and is priced to yield 6 percentBoth bonds have a par value of $1000.Given a 50 basis point parallel upward shift in interest rates, what is the value of the two-bond portfolio?A. $2044. B. $2030. C. $2086.9. The six-month Treasury bill has a yield to maturity of 5 percent. The one-year Treasury bill, with zero coupon, has a yield to maturity of 6 percent. If a Treasury note with a maturity of 1.5 years and a coupon rate of 6 percent is priced at 97.32, what's the implied spot rate of 1.5 years?A.7.00%. B. 7.50%. C. 8.00%.10. Which of the following statements concerning arbitrage-free bond prices is FALSE?A. The riskier the bond, the greater is its credit spread. B. It is not possible to strip coupons from U. S. Treasuries and resell them. C. The determination of spot rates is usually done using risk-free securities.11. Consider a $ 1000 - face value, 12 - year, 8% , semiannual coupon bond with a YTM of 10.45%. The change in value for a decrease in yield of 38 basis points is:A. $21.18 B. $22.76. C. $23.06.12. If a $1000 bond has a 14 percent coupon rate and a current market price of 950, what is the current market yield?A. 14.74%. B. 14.00%. C. 15.36%.13. If market rates do not change, as time passes the price of a zero-coupon bond will:A. approach zero. B. approach the purchase price.C. approach par.14. The 3-year annual spot rate is 7%, the 4-year annual spot rate is 7.5%, and the 5-year annual spot rate is 8%. Based on the pure expectations theory of interest rates, the 1-year implied forward rate in four years is closest to:A. 10.00%. B. 7.75%. C. 9.00%.15. A bond with an 8 percent semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5 percent. If the yield declines to 9 percent, the bond's price will increase to $934.96, and if the yield increases to 10 percent, the bond's price will decrease to $875.38. Estimate the percentage price change for a 100 basis point change in rates.A. 4. 35%. B. 2. 13%. C. 6.58%.16. A bond with a 12 percent coupon, 10 years to maturity and selling at 88 has a YTM of:A.between 10% and 12%. B. between 13% and 14%. C. over 14%.17. Consider a 10 percent, 10 - year bond sold to yield 8 percent. One year passes and interest rates remained unchanged (8 percent). What will have happened to the bond's price during this period?A. It will have decreased. B. It will have increased. C. It will have remained constant.18. Why should effective duration, rather than modified duration, be used when bonds contain embedded options?A. Effective duration considers expected changes in cash flows. B. Modified duration considers expected changes in cash flows. C. Either could be used if the bond has embedded options.19. Which of the following statements concerning the current yield is CORRECT? It:A. is of great interest to conservative bond investors seeking current income. B. is of great interest to aggressive bond investors seeking capital gains. C. shows the rate of return an investor will receive by holding a bond to maturity.20. Three years ago, at the advice of her financial planner, an investor purchased a $1000 face, 4.50%, semiannual coupon bond with seven years to maturity priced to yield 6.50% for $888.94. The reinvestment income that must be generated over the life of the bond for the investor to realize a yield of 6.5% is closest to:A. $72. B. $76. C. $80.21. Suppose you have a three-security portfolio containing bonds A, B and C. The effective portfolio duration is 5.9. The market values of bonds A, B and C are $60, $25 and $80, respectively.The durations of bonds A and C are 4. 2 and 6.2, respectively. Which of the following amounts is closest to the duration of bond B?A. 9.0. B. 1.4. C. 7.1.22. Consider a bond , par value $100 , that pays an annual coupon of 5 percent and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6 percent. How much does the bond price change if the term structure of interest rates shifts down by 1 percent instantaneously?A. -2.67. B. 2.67. C. 0.00.23. What is the duration of a floating rate bond that has six years remaining to maturity and has semi-annual coupon payments. Assume a flat-term structure of 6 percent. Which of the following is closest to the correct duration?A. 0.500. B. 6.000. C.12.000.24. One of the **monly used yield spread measures is the nominal spread. Which of the following is a limitation of nominal spread? The nominal spread assumes:A. an upward sloping yield curve. B. a downward sloping yield curve. C. a flat yield curve.25. A semiannual-pay bond is callable in five years at $1080. The bond has an 8% coupon and 15 years to maturity. If an investor pays $ 895 for the bond today, what are the yield to call (YTC)and the yield to maturity (YTM), respectively? YTC YTM ①A. 10.77% 9.31% ②B.12.07% 9.31% ③C. 10.77% 10.21% A. ①B. ②C. ③26. Which of the following statements about a bond's cash flows is TRUE? The appropriate discount rate is a function of:A. the risk-free rate plus the return on the market. B. the risk-free rate plus the risk premium. C. only the risk premium.27. What is the probable change in price of a 30-year semiannual 6.5 percent coupon, $1000 par value bond yielding 8 percent when the nominal risk-free rate changes from 5 percent to 4 percent?A. $106.34. B. $107.31. C. $102.57.28. Assume that an option-free 5 percent coupon bond with annual coupon payments has two years to maturity. A callable bond that is the same in every respect as the option-free bond is priced at 91.76. With the term structure flat at 6 percent, what is the value of the embedded call option?A. -8.24. B. 4.58. C. 6.41.29. Consider the following two statements about put-able bonds:Statement 1: As yields fall, the price of put-able bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option.Statement 2: As yields rise, the price of put-able bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option.You should:A. agree with statement 1 and disagree with statement 2. B. agree with statement 1 and agree with statement 2. C. disagree with statement 1 and disagree with statement 2.30. You are considering the purchase of a three-year annual coupon bond with a par value of $1000 and a coupon rate of 5.5 percent. You have determined that the spot rate for year 1 is 5.2 percent, the spot rate for year two is 5.5 percent, and the spot rate for year three is 5.7 percent. What would you be willing to pay for the bond now?A. $937.66. B. $995.06. C. $1000.00.31. Bond is selling at a discount relative to its par value. Which of the following relationships holds?A. yield to maturity ＜coupon rate ＜current yield. B. current yield ＜coupon rate ＜yield to maturity. C. coupon rate ＜current yield ＜yield to maturity.32. Current spot rates are as follows:1- Year: 6.5%2 - Year: 7.0%3 - Year: 9.2%Which of the following is TRUE?A. For a 3 - year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond's arbitrage-free value. B. The yield to maturity for 3 - year annual pay coupon bond can be found by taking the arithmetic average of the 3 spot rates. C. For a 3 - year annual pay coupon bond, the first coupon can be discounted at 6.5%, thesecond coupon can be discounted at 7.0% , and the third coupon plus maturity value can be discounted at 9.2% to find the bond's arbitrage-free value.33. All else held equal, the duration of bonds selling at higher **pared to bonds selling at lower yields will be:A. greater. B. lower. C. equal.34. Calculate the current yield and the Yield-to-first Call on a bond with the following characteristics: 5 years to maturity $1000 face value 8.75% semi-annual coupon Priced to yield 9.25% = Callable at $1025 in two years Current Yield Yield-to-Call ①A. 8.93% 11.02% ②B. 9.83% 19.80% ③C. 12.67% 11.02% A. ①B. ②C. ③35. Which of the following characteristics would create the least difficulty in estimating a bond's cash flows?A. Variable coupon rate. B. Put-able bond. C. Non-callable bond.36. An 11 percent coupon bond with annual payments and 10 years to maturity is callable in 3 years at a call price of $1100. If the bond is selling today for 975, the yield to call is:A.14.97%. B. 10.26%. C. 10.00%.37. Answering an essay question on a midterm examination, a finance student writes these two statements: Statement 1: The value of a fixed income security is the sum of the present values of all its expected future coupon payments. Statement 2: The steps in the bond valuation process are to estimate the bond's cash flows, determine the appropriate discount rate, and calculate the present value of the expected cash flows. Should the instructor mark these statements correct or incorrect? Statement 1 Statement 2 ①A. Correct Correct ②B. Correct Incorrect ③C. Incorrect Correct A. ①B. ②C. ③38. An investor gathered the following information on three zero-coupon bonds:1 - year, $600 par, zero-coupon bond valued at $5712 - year, $600 par, zero-coupon bond valued at $5443 - year, $10600 par, zero-coupon bond valued at $8901Given the above information, how much should an investor pay tbr a $10000 par, 3 - year, 6 percent, annual-pay coupon bond?A. $10000. B. $10600. C. $10016.39. The one-year spot rate is 6 percent and the one-year forward rates starting in one, two and three years respectively are 6.5 percent, 6.8 percent and 7 percent. What is the four-year spot rate?A. 6.51%. B. 6.58%. C. 6.57%.40. Which of the following statements about duration is TRUE?A. The result of the formula for effective duration is for a 0.01% change in interest rates. B. A bond's percentage change in price and dollar change in price are both tied to the underlying price volatility. C. The formula for effective duration is: (price when yields fall - price when yields rise)/(initial price × change in yield expressed as a decimal).41. Given a required yield to maturity of 6 percent, what is the intrinsic value of a semi-annual paycoupon bond with an 8 percent coupon and 15 years remaining until maturity?A. $1196. B. $1202. C. $1095.42. What value would an investor place on a 20 - year, $1000 face value, 10 percent annual coupon bond, if the investor required a 9 percent rate of return?A. $879. B. $920. C. $1091.43. What is the present value of a 7 percent semi-annual pay corporate bond with a $1000 face value and 20 years to maturity if it is yielding 6. 375 percent?? If a municipal bond is yielding 4.16 percent and an investors marginal tax rate is 35 percent, would the investor prefer the corporate bond or the municipal bond? Value Investor preference ①A. $1121.23 municipal bond ②B. $1070.09 corporate bond ③C. $1070.09 municipal bondA. ①B. ②C. ③44. An analyst has gathered the following information:Bond A is an 11 percent annual coupon bond currently trading at 106. 385 and matures in 3 years. The yield-to-maturity (YTM) for Bond A is 8.50 percent.The YTM for a Treasury bond that matures in 3 - years is 7.65 percent. 1, 2, and 3 - year spot rates are 5.0 percent, 6.5 percent and 8.25 percent, respectively. Which of the following statements regarding spreads on bond A is TRUE?A. The nominal spread is approximately 85 basis points. B. The Z-spread is approximately 85 basis points. C. The option-adjusted spread is approximately 75 basis points.45. Which of the following is a limitation of the cash flow yield measure? The cash flow yield measure:A. uses a 360-day year. B. assumes that the projected cash flows are reinvested at the cash flow yield. C. assumes a flat yield curve.46. Which of the following statements about duration is FALSE?A. There is a direct relationship between yield to maturity and duration. B. There is an inverse relationship between coupon and duration. C. There is a direct relationship between duration and maturity.47. Which is the bond-equivalent yield given if the monthly yield is equal to 0.7 percent?A.8.40%. B. 8.58%. C. 8.55%.48. Yield to call is a less conservative yield measure than the yield to maturity whenever the price of a callable bond is quoted at a value:A. equal to par value less one year's interest. B. equal to par value. C. more than par.49. A coupon bond pays annual interest, has a par value of $1000, matures in 4 years, has a annual coupon of $100, and a yield to maturity of 12 percent. The current yield on this bond is:A.9.50%. B. 10.65%. C. 11.25%.50. At 1 January, 2008, an option-free 8 percent annual coupon bond, with 10 years to maturity and a par value of $1000, had a discount rate of 9 percent. On 1 January 2009, the discount rate had decreased to 8.5 percent because of an upgrade in the bond's rating. If interest is paidannually, the portions of the bond's price change from 2008 to 2009 attributable to the passage of time and the rating upgrade respectively, are closet to: Passage of time Rating upgrade ①A. -$4.23 $29.35 ②B. -$4.23 $33.58 ③C. $4.23 $29.35 A. ①B. ②C. ③51. An investor purchased a 10 - year zero-coupon bond with a yield to maturity of 10 percent anda par value of $1000. What would her rate of return be at the end of the year if she sells the bond? Assume the yield to maturity on the bond is 9 percent at the time it is sold and **pounding periods are used.A. 16.00%. B. 17.63%. C. 19.42%.52. In capital markets, stock dividends and bond coupons generally provide what is referred to as:A. current yield. B. capital gain yield. C. internal yield.53. Which of the following statements about duration and convexity is FALSE?A. duration to first call is longer than duration to maturity. B. convexity of a callable bond is always lower than that of a noncallable bond when rates fall. C. callable bonds' convexity can be negative.。
固定收益证券的估值定价与计算
固定收益证券的估值定价与计算固定收益证券是指具有固定利率和到期日的债务工具，包括国债、企业债、可转换债券等。
这些证券的估值定价非常重要，因为它关系到投资者购买和持有这些证券的决策。
下面将详细介绍固定收益证券的估值定价与计算方法。
一、债券的估值定价要素债券的估值定价主要涉及以下几个要素：1.本金（面值）：债券的本金是债券发行时债务人承诺归还给债权人的金额，也被称为面值。
本金通常是固定的，一般情况下以100元计。
2.利率：债券的利率是债券发行时债务人承诺向债权人支付的利息。
利率可以是固定利率，也可以是浮动利率。
利率对于债券的定价影响很大。
3.期限（到期日）：债券的期限是债权人持有债券的时间，也被称为到期日。
期限的长短对债券的定价有一定影响。
4.利息支付方式：债券的利息支付可以是按年、按半年或按季度支付等不同方式，不同的支付方式也会对债券的定价产生影响。
5.市场利率：债券的估值定价还需要考虑市场利率的影响，市场利率是指当前时间点上同期限、同等级债券的市场利率水平。
二、债券的估值定价方法根据债券的估值定价要素，常用的债券估值定价方法有以下几种：1.毛收益率法：毛收益率法是根据债券的票面利率、到期日、发行价格、市场利率等要素，来计算债券的估值价格。
具体计算公式如下所示：估值价格=每年应付利息/（1+市场利率）+本金/（1+市场利率）^n 其中，每年应付利息=面值*票面利率如果债券的估值价格高于发行价格，则被认为是高估；反之，被认为是低估。
2.净现值法：净现值法是根据债券的未来现金流量的现值与购买价格的差额来计算债券的估值价格。
具体计算公式如下所示：净现值=票面利息*折现系数/（1+市场利率）^n+赎回价格/（1+市场利率）^n其中，票面利息=面值*票面利率折现系数=（1-（1+市场利率）^(-n)）/市场利率如果净现值为正，则债券被认为是低估；反之，被认为是高估。
3.收益率法：收益率法是根据债券的票面利率、到期日、估值价格等要素，来计算债券的收益率。
CIIA最终考试II问题翻译
试卷II:固定收益证券估值与分析衍生品估值与分析投资组合管理问题最终考试2013年9月问题1 ：固定收益证券估值与分析（41分）作为一名固定收益证券方面的金融工程师，你面对以下三种证券：所有债券面值都是100。
1bps: 0.01%；收益率天数惯例：30/360。
a)在考虑一些结构化投资机会前，你需要完成一些基本的计算并回答下列问题：a1) 根据上面给出的表格，计算三种债券的价格①, ②和③。
【为了计算②, 假设刚刚确定6个月期a2) 根据上面给出的表格，计算三个修正久期④, ⑤和⑥。
【假设刚刚确定6个月期Euribor是0.35%（每年）。
】（6 分）a3) 给定的三种债券，哪种凸性最高? （不需要计算，简要给出理由）（3分）b)你的投资者需要一种称为“逆浮动利率债券（inverse floater）”的产品，此产品需要每半年支付“12%减去6个月期EURIBOR”的票息。
b1)原则上，你如何利用上面表格中给出的债券构造该“逆浮动利率债券”？（不需要严格计算，只是简单解释一下将持有何种债券、每种债券的数量以及是空头头寸还是多头头寸）（5分）b2) 此“逆浮动利率债券”的价格是多少？【如果没能解出问题a1），可以假设给出的三种债券的价格分别是106%、100% 和99%。
】（5分）b3) 计算此“逆浮动利率债券”的修正久期。
【如果没有解出问题a2），可假设三种债券的修正久期分别为0.97、0.5 和0.99，债券的价格则使用问题b2）中的数值】（5分）c)最后，要求你估计该“逆浮动利率债券”内在的风险暴露：c1) 简要指出这项投资的三种主要的风险因素。
（3分）c2) 你如何估计该“逆浮动利率债券”的利率风险？（不需要计算，只需做出简要解释）（4分）c3) 你能使用何种对冲手段来减少该“逆浮动利率债券”的利率风险？（3分）问题2：固定收益/ 衍生品/ 投资组合管理(38 分)作为跨国银行XYZ的结构化产品部门的领导，你当前的项目是为银行XYZ发行一款信用联结票据（CLN），其参照主体是汽车公司ABC，主要特征如下：注：Euribor：欧元区银行间同业拆借利率；“bps”= “基点”：1 bps = 0.01%；收益率天数惯例：30/360。
固定收益证券的估值、定价与计算 课件 (4)
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收益率曲线和利率期限结构
利率期限结构形状及变化的几种理论解释
预期理论(The expectation theory)
假如当前1年期利率为6%，市场普遍预期1年后的利率为7%，那么，2年期的 即期利率应该是[（1+6%）（1+7%）]1/2-1≈6.5%。 如果2年期市场利率低于这一水平，比如6.2%，即 [（1+6%）（1+7%）]1/2-1＞6.2% 2年期借款利率便宜，1年期借款利率昂贵，借款者势必放弃1年期借款而转向2 年期借款，而贷款者则愿意放弃2年期贷款转向1年期贷款，结果是1年期贷 款利率下降，2年期贷款利率上升，最后市场重新回到均衡。
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收益率曲线和利率期限结构
利率期限结构形状及变化的几种理论解释
市场分割理论（market segmentation theory）
如果长期资金供求曲线交叉点利率＞中期资金供求曲线交叉点利率＞短期资 金供求曲线交叉点利率，期限结构呈上升趋势；反之，则呈下降趋势；如果 三者相等，则呈现平行形状。
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原曲线
到期时间
固定收益证券估值和分析
固定收益证券估值和分析债券按照发行主体不同分类：省或州债券是由次级国家行政区发行的证券政府机构证券是由与政府相关联的机构或政府发起的公司（GSE ）发行的债券超国家机构债券是由少数几个主权国家共同拥有的实体（通常是银行）来发行的债券 政府担保证券是由政府担保偿付的其他机构发行的债券 公司债券是由一些上市或者非上市公司发行的债券 抵押债券是由发行人的特定资产来担保偿付的债券资产担保债券是抵押债券的一种，金融机构常发行资产担保债券融资无担保债券即无抵押债券，是指没有以发行人的有形资产或者金融资产做担保的债券 债券的价格=债券报价+应计利息 其中应计利息的计算有：瑞士债券，德国国内债券的计算公式： 应计利息=C dm *360*30+C 为息票利率；m 为整月数；d 为零头天数 美元长期国债应计利息=2*C际天数两次利息支付之间的实际天数距离上次付息之后的实现值和未来值简单单利折现和单利累计=(1)+年数未来值现值年化利率=()(1)⋅+年数未来值现值年化利率年金年金的现值计算式111(1)(1)Nt N t CF CF R R R =⎛⎫==⋅-⎪++⎝⎭∑现值 此处CF 稳定的现金流R 折现率，假定是一直稳定的 N 现金分配的次数 年金的未来值计算式(1)1 N R CF R ⎛⎫+-=⋅ ⎪⎝⎭未来值此处CF 稳定的现金流R 折现率，假定是一直稳定的N 现金分配的次数 连续的复利折现和复利累计=e⋅年数年化复利利率未来值现值=()e ⋅⋅年数年化复利利率未来值现值债券收益计量 当前收益=每年票息当前收益率价格零息债券不付息，当期收益率为零其他条件不变时，随着到期的临近，折价债券的当期收益率逐步下降 到期收益率（债券到期之前全部现金流的现值等于债券当前市场价格的贴现率） 债券价格作为到期收益率的函数，其计算式如下()()()()Nit Nt t Ni t iY CF Y CF Y CF Y CF P++++++=+=∑=1 (1112)1211对于一个一年付息一次的债券，在两个付息日之间，债券价格计算式为()()()()⎥⎥⎦⎤⎢⎢⎣⎡+++++++=⋅+=N N f f ex f cum Y CF Y CF Y CF Y C f P P 1 (11122)11,, 此处P cum, f 当前支付的债券价格（包括应计利息） P ex ，f 债券的标定价格 Y 到期收益率f 上一次付息日距今年数CF i 在t i 时刻收到的现金（息票利息） CF N 最终现金流（利息加本金） N 现金分配的次数到期收益率是即期利率的复杂平均。
固定收益证券估值和分析
固定收益证券估值和分析固定收益证券是一种具有固定利率或固定收益的证券，如债券、优先股等。
在金融市场中，固定收益证券是重要的投资工具，具有一定的估值和分析方法。
本文将探讨固定收益证券的估值和分析，包括债券估值和债券分析，以及其他固定收益证券的特点和评估方法。
债券估值是指确定债券的市场价值，一般采用贴现法计算。
贴现法的基本思想是将债券的未来现金流折现到当前时点，以确定债券的市场价值。
具体的计算方法为将每一期的现金流按照相应的市场利率进行折现，并相加得到债券的现值。
常见的市场利率包括市场基准利率、预期回报率等。
债券分析是指对债券的风险和收益进行评估，以确定是否值得投资。
债券的风险主要包括信用风险、利率风险和流动性风险。
信用风险是指发行机构无法按时偿付债券的本金和利息；利率风险是指债券价格受到市场利率波动的影响；流动性风险是指债券在二级市场上的买卖性质。
债券分析的方法主要包括财务分析、信用分析和市场分析。
财务分析主要通过分析企业的财务状况、偿债能力和盈利能力等指标来评估债券的风险和收益；信用分析主要评估债券发行人的信用状况和还债能力；市场分析主要通过分析市场的供求关系、竞争关系和技术指标等来预测债券价格的走势。
二、其他固定收益证券的特点和评估方法除了债券，还有其他固定收益证券，如优先股、可转债等。
这些证券具有一些特点和估值方法。
优先股是一种具有固定股息的股票，它的收益和风险介于债券和普通股票之间。
优先股的特点是具有优先分红权和清偿权，但没有表决权。
优先股的估值方法主要包括财务分析、市场分析和股息贴现法。
财务分析主要评估企业的盈利能力和偿债能力；市场分析主要通过分析市场的需求和供给关系来预测优先股的价格；股息贴现法是将优先股的股息按照一定的折现率进行折现，以确定其市场价值。
可转债是一种具有转股权的债券，可以按照一定的比例转换为普通股票。
可转债的特点是具有债券和股票的特性，既可以获得固定收益，又可以获得股票的增值收益。
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固定收益证券估值与分析
固定收益证券估值与分析是金融领域中一项重要的技术，它涉及到对固定收益证券的评估和预测。
固定收益证券是指一种承诺在未来一些时间支付固定利息或本金的金融资产，包括债券、国债、定期存款等。
通过对这些金融资产的估值与分析，可以帮助投资者做出更明智的投资决策。
首先，票面利率是固定收益证券上标明的年利率，也称为固定利率。
该利率与债券的价格具有直接的关系，利率越高，价格越低，反之亦然。
其次，市场利率是指当前市场上可获得的利率。
当市场利率高于固定收益证券的票面利率时，固定收益证券的价格会下降。
因为投资者可以购买市场上更高利率的债券来获取更高的回报。
第三，到期时间是指固定收益证券的还款期限。
一般来说，到期时间越长，固定收益证券的价格越高。
因为长期债券的风险较高，需要提供更高的回报才能吸引投资者购买。
第四，流动性是指固定收益证券的市场交易性。
流动性较高的固定收益证券通常价格较高，因为投资者更容易买入和卖出这些证券。
最后，信用风险是指固定收益证券发行机构的违约风险。
如果发行机构的信用状况较差，投资者要求更高的回报来补偿风险。
基于这些关键因素，可以采用不同的估值模型来评估固定收益证券的价格。
其中，最常用的模型是现金流模型和折现模型。
现金流模型根据固定收益证券的未来现金流量来估算其价格。
该模型假设投资者持有证券直到到期，并收取所有利息和本金。
根据预期的现金
流量和利率，可以计算出证券的价值。
这个模型适用于没有违约风险的证券。
而折现模型是基于固定收益证券的现金流量和投资回报率来计算证券
的价格。
该模型认为投资者可能在未来将证券出售，因此考虑了证券的市
场交易性。
该模型也考虑了违约风险，以及不同投资者对风险的不同偏好。
综上所述，固定收益证券的估值与分析涉及到多方面的因素，包括票
面利率、市场利率、到期时间、流动性和信用风险。
通过合理运用现金流
模型和折现模型等估值方法，可以对固定收益证券的价格进行评估和预测，帮助投资者做出更明智的投资决策。