《固定收益证券分析》作业三

1 固定收益证券分析固定收益证券分析 作业三作业三 1 Which of the following two bonds is more price sensitive to changes in interest rates 1 A par value band X with a 5 year to maturity and a 10 coupon rate 2 A zero coupon bond Y with a 5 year to maturity and a 10 yield to maturity A Bond X because of the higher yield to maturity B Bond X because of the longer time to maturity C Bond Y because of the longer duration D Both have the same sensitivity because both have the same yield to maturity E None of the above 解答 解答 C C PricePrice sensitivesensitive 理解成价格绝对值变化 那么选择理解成价格绝对值变化 那么选择 E E 问题 问题 很多同学选很多同学选B B 2 For a bond trading at par value the ratio of the price value of a basis point divided by modified duration would be approximately A 1 00 B 0 01 C 0 10 D 2 00 解答 解答 B dp D dy p 当 dy 1bp 则 dp pvbp 所以 pvbp duration 0 01 100 所以大 致为 0 01 注 面值理解成 1000 应该是 0 1 答案为 C 问题 问题 选 A 和 C 3 The modified duration of a perpetuity with a yield of 8 is A 13 50 B 12 50 C 12 11 D 6 66 E none of the above 解答 B 2 4 For a coupon paying bond which is most likely to be greater in absolute value terms modified duration or Macaulay duration Which of these is more appropriate when embedded options are present C A Greater Macaulay duration More appropriate when options are present modified duration B Greater modified duration More appropriate when options are present Macaulay duration C Greater Macaulay duration More appropriate when options are present neither is more appropriate D Greater modified duration More appropriate when options are present neither is more appropriate 解答 解答 修正久期要小于 Mauclay 久期 但有期权时 必须使用有效久期 5 Janet Meer is a fixed income portfolio manager Noting that the current shape of the yield curve is flat she considers the purchase of a newly issued option free corporate bond priced at par the bond is described in Exhibit 1 Exhibit 1 7 Option free Bond Maturity 10 years Change in Yields Up 10 Basis PointsDown 10 Basis Points Price99 29100 71 Convexity Measure35 00 A Calculate the duration of the bond described in Exhibit 1 Show your calculations Duration 100 71 99 29 2 100 0 0012 100 0 001 7 17 1 Meer is also considering the purchase of a second newly issued option free corporate bond which is described in Exhibit 2 She wants to evaluate this second bond s price sensitivity to an instantaneous downward parallel shift in the yield curve of 200 basis points Exhibit 2 7 25 Option free Bond Maturity 12 years Original Issue PricePar value to yield 7 25 Modified Duration at original price 7 90 Convexity Measure41 55 B Estimate the total percentage price change for the bond described in Exhibit 2 if the yield curve experiences an instantaneous downward parallel shift of 200 basis points Show your calculations Percentage price change using duration 7 90 7 90 0 02 15 800 02 15 80 3 Percentage price change using convexity adjustment 0 02 2 41 551 0 0166 Total estimated percentage price change 17 46 注 1 凸性的公式为 1 2 0 02 2 41 551 0 0083 Total estimated percentage price change 15 808 2 凸性的符号 都是正面影响 凸性的符号 都是正面影响 6 请为如下的5年期现金流给出免疫方案 每年都需要支付1000元现金流 可以选 择的债券有两种 一是票面利率为10 每年付息一次的10年期债券 二是票面利 率为5 每年付息一次的2年期债券 另外假设市场上的利率期限结构如下 Term 年 spot rate discount fct 18 50560 9216 2 8 67530 8467 3 8 83770 7756 4 8 99270 7086 5 9 14040 6458 6 9 28070 5871 7 9 41360 5327 8 9 53910 4824 9 9 6570 4362 10 9 76750 3938 11 9 87050 3551 12 9 96590 3198 13 10 05370 2878 14 10 1340 2589 15 10 20670 2327 16 10 27180 2092 17 10 32920 1880 18 10 3790 1691 19 10 42120 1521 20 10 45570 1368 解答 1 负债的现值和久期 现值 3898 35 Macaulay 久期 11005 24 3898 35 2 8231 YTM 8 9140 2 资产的现值和久期 10年期债券 现值 102 6850 Macaulay 久期 693 5901 102 6850 6 7545 YTM 9 5710 2年