problems26
Note: This is not a proof, but it explains the logicYTM 7%Total investment in bonds 1,000Proportion of bond A in portfolio 30%Proportion of bond B in portfolio 70% #NAME?Dollar amount of A purchased 300 #NAME?Dollar amount of B purchased 700 #NAME?Percentage of face value of A purchased 30.00% #NAME?Percentage of face value of B purchased 49.25% #NAME?Year Ct,A t*Ct,A /(PA*(1+YTM)t) Ct,B1 70 0.0654 1302 70 0.1223 1303 70 0.1714 1304 70 0.2136 1305 70 0.2495 1306 70 0.2799 1307 70 0.3051 1308 70 0.3259 1309 70 0.3427 13010 1070 5.4393 1130Bond price Duration Bond price$ 1,000 7.5152 $ 1,421=NPV(B3,B6:B15)Weighted portfolio durations 6.9820466 #NAME?Note that because we purchase $700 of bond B, which costs $1421, were only purchasing 49.25% of the bonds face value.t*Ct,B /(PB*(1+YTM)t) Portfolio t*Ct,Port /(PPort*(1+YTM)t)0.0855 85.02072 0.0795 0.07945860.1598 85.02072 0.14850.2240 85.02072 0.20820.2791 85.02072 0.25940.3260 85.02072 0.30310.3657 85.02072 0.33990.3987 85.02072 0.37060.4258 85.02072 0.39590.4477 85.02072 0.41624.0413 877.4878 4.4607Duration6.7535 $ 1,000 6.9820=SUM(F6:F15)Note: This is not a proof, but it explains the logicNote that because we purchase $700 of bond B, which costs $1421, were only purchasing 49.25% of the bonds face value.#NAME?注意: 这不是严格的证明，但可以显示本题目逻辑的正确性到期收益率 7%债券组合的总投资额 1,000债券 A 在组合中所占的比例 30%债券 B 在组合中所占的比例 70%购买债券 A 的费用 300购买债券 B 的费用 700购买的债券 A 的面值在组合中所占比例 30.00%购买的债券 B 的面值在组合中所占比例 49.25%年 Ct,A t*Ct,A /(PA*(1+YTM)t) Ct,B1 70 0.0654 1302 70 0.1223 1303 70 0.1714 1304 70 0.2136 1305 70 0.2495 1306 70 0.2799 1307 70 0.3051 1308 70 0.3259 1309 70 0.3427 13010 1070 5.4393 1130债券价格 久期 债券价格$ 1,000 7.5152 $ 1,421=NPV(B3,B6:B15)加权的资产组合久期 6.9820466 - =C25*B6+F25*B7注意：尽管我们买了$700的债券 B,其花费$1421，但其面值只占资产组合面值的49.25%。t*Ct,B /(PB*(1+YTM)t) Portfolio t*Ct,Port /(PPort*(1+YTM)t)0.0855 85.02072 0.0795 0.0794586 - Note that eachindividual term is0.1598 85.02072 0.1485 theweighted average ofthe terms in0.2240 85.02072 0.2082 C14 andF14.0.2791 85.02072 0.25940.3260 85.02072 0.30310.3657 85.02072 0.33990.3987 85.02072 0.37060.4258 85.02072 0.39590.4477 85.02072 0.41624.0413 877.4878 4.4607久期6.7535 $ 1,000 6.9820=SUM(F6:F15)注意: 这不是严格的证明，但可以显示本题目逻辑的正确性- Note that eachindividual term istheweighted average ofthe terms inExercise 2Page 7See fm3_chapter26.xls练习 2 Page 8参见 fm3_chapter26.xlsBASIC IMMUNIZATION EXAMPLE WITH 3 BONDSYield to maturity 6%Bond 1 Bond 2 Bond 3Coupon rate 6.70% 6.988% 5.90%Maturity 10 15 30Face value 1,000 1,000 1,000Bond price $1,051.52 $1,095.96 $986.24Face value equal to $1,000 of market value$ 951.00 $ 912.44 $ 1,013.96Duration #NAME? #NAME? #NAME?Target duration 8.0000Weight of Bond 1 #NAME? Both these portfoliosWeight of Bond 3 #NAME? have the target duration.Weight of Bond 1 #NAME?Weight of Bond 2 #NAME?3 个债券的免疫案例到期收益率 6%债券1 债券2 债券3戏票利率 6.70% 6.988% 5.90%成熟期 10 15 30面值 1,000 1,000 1,000债券价格 $1,051.52 $1,095.96 $986.24等于$1,000市场价值的面值 $ 951.00 $ 912.44 $ 1,013.96久期 #NAME? #NAME? #NAME?目标久期 8.0000债券1所占比例 #NAME? 这两种组合债券3所占比例 #NAME? 都具有我们要求的目标久期债券1所占比例 #NAME?债券2所占比例 #NAME?都具有我们要求的目标久期BASIC IMMUNIZATION EXAMPLE WITH 3 BONDSYield to maturity 6%Bond 1 Bond 2 Bond 3Coupon rate 6.70% 6.988% 5.90%Maturity 10 15 30Face value 1,000 1,000 1,000Bond price $1,051.52 $1,095.96 $986.24Face value equal to $1,000 of market value$ 951.00 $ 912.44 $ 1,013.96Duration #NAME? #NAME? #NAME?Target duration 8.0000Weight of Bond 1 #NAME?Weight of Bond 3 #NAME?Weight of Bond 1 #NAME?Weight of Bond 2 #NAME?New yield to maturity 7%Bond 1 Bond 2 Bond 3Bond price $1,000.00 $999.51 $883.47Reinvested coupons $925.70 $965.49 $815.17Total $1,925.70 $1,965.00 $1,698.64Multiply by percent of face value bought 95.10% 91.24% 101.40%Product $ 1,831.35 $ 1,792.95 $ 1,722.34Bond 1&2 Bond 1&3Data table portfolio Portfolio#NAME? #NAME? - Table header0% #NAME? #NAME?1% #NAME? #NAME?2% #NAME? #NAME?3% #NAME? #NAME?4% #NAME? #NAME?5% #NAME? #NAME?6% #NAME? #NAME?7% #NAME? #NAME?8% #NAME? #NAME?9% #NAME? #NAME?10% #NAME? #NAME?11% #NAME? #NAME?12% #NAME? #NAME?13% #NAME? #NAME?14% #NAME? #NAME?15% #NAME? #NAME?For hedging/immunization, the Bond 1 & 3 portfolio is preferred. It is slightly above the Bond 1 & 2portfolio for all interest rates.2 0 %1 5 %1 0 %5 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 $ 3 ,1 0 0 .0 0 $ 3 ,3 0 0 .0 0 B o n d 1 & 2 p o rtf o lio # N A M E ?B o n d 1 & 3 P o rtf o lio # N A M E ?- Table header2 0 %1 5 %1 0 %5 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 $ 3 ,1 0 0 .0 0 $ 3 ,3 0 0 .0 0 B o n d 1 & 2 p o rtf o lio # N A M E ?B o n d 1 & 3 P o rtf o lio # N A M E ?3 个债券的免疫案例到期收益率 6%债券1 债券2 债券3戏票利率 6.70% 6.988% 5.90%成熟期 10 15 30面值 1,000 1,000 1,000债券价格 $1,051.52 $1,095.96 $986.24等于$1,000市场价值的面值 $ 951.00 $ 912.44 $ 1,013.96久期 #NAME? #NAME? #NAME?目标久期 8.0000债券1所占比例 #NAME?债券3所占比例 #NAME?债券1所占比例 #NAME?债券2所占比例 #NAME?新的到期收益率 7%债券1 债券2 债券3债券价格 $1,000.00 $999.51 $883.47戏票再投资 $925.70 $965.49 $815.17总计 $1,925.70 $1,965.00 $1,698.64乘以购买的面值占$1,000的百分比 95.10% 91.24% 101.40%所得 $ 1,831.35 $ 1,792.95 $ 1,722.34债券1与3 债券1与2数据表 的组合 的组合#NAME? #NAME? - Table header0% $ 1,601.65 $ 1,763.051% $ 1,628.52 $ 1,749.282% $ 1,657.16 $ 1,744.253% $ 1,687.62 $ 1,746.764% $ 1,720.00 $ 1,755.845% $ 1,754.38 $ 1,770.736% $ 1,790.85 $ 1,790.857% $ 1,829.51 $ 1,815.738% $ 1,870.46 $ 1,845.039% $ 1,913.81 $ 1,878.4910% $ 1,959.68 $ 1,915.9111% $ 2,008.18 $ 1,957.1712% $ 2,059.44 $ 2,002.1913% $ 2,113.59 $ 2,050.9414% $ 2,170.77 $ 2,103.4115% $ 2,231.13 $ 2,159.64为了对冲 / 免疫的目的，债券1与2的组合要好一些(其支付在利率的波动范围内显得更加平坦）。2 0 %1 5 %1 0 %5 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 债 券 1 与 3 的 组 合# N A M E ?债 券 1 与 2 的 组 合# N A M E ?0 .1 60 .1 40 .1 20 .10 .0 80 .0 60 .0 40 .0 201 5 0 01 7 0 01 9 0 02 1 0 02 3 0 02 5 0 02 7 0 02 9 0 0债 券 1 与 3 的 组 合1 8 2 9 .5 0 7 2 6 6 3 7 2 9 3债 券 1 与 2 的 组 合1 8 1 5 .7 3 0 7 9 9 7 6 8 3 8- Table header2 0 %1 5 %1 0 %5 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 债 券 1 与 3 的 组 合# N A M E ?债 券 1 与 2 的 组 合# N A M E ?0 .1 60 .1 40 .1 20 .10 .0 80 .0 60 .0 40 .0 201 5 0 01 7 0 01 9 0 02 1 0 02 3 0 02 5 0 02 7 0 02 9 0 0债 券 1 与 3 的 组 合1 8 2 9 .5 0 7 2 6 6 3 7 2 9 3债 券 1 与 2 的 组 合1 8 1 5 .7 3 0 7 9 9 7 6 8 3 8BASIC IMMUNIZATION EXAMPLE WITH 3 BONDSYield to maturity 6%Bond 1 Bond 2 Bond 3Coupon rate 6.70% 6.988% 5.90%Maturity 10 15 30Face value 1,000 1,000 1,000Bond price $1,051.52 $1,095.96 $986.24Face value equal to $1,000 of market value$ 951.00 $ 912.44 $ 1,013.96Duration #NAME? #NAME? #NAME?Target duration 12.0000Weight of Bond 1 #NAME?Weight of Bond 3 #NAME?Weight of Bond 1 #NAME?Weight of Bond 2 #NAME?New yield to maturity 7%Bond 1 Bond 2 Bond 3Bond price $1,000.00 $999.51 $883.47Reinvested coupons $925.70 $965.49 $815.17Total $1,925.70 $1,965.00 $1,698.64Multiply by percent of face value bought 95.10% 91.24% 101.40%Product $ 1,831.35 $ 1,792.95 $ 1,722.34Bond 1&2 Bond 1&3Data table portfolio Portfolio#NAME? #NAME? - Table header0% #NAME? #NAME?1% #NAME? #NAME?2% #NAME? #NAME?3% #NAME? #NAME?4% #NAME? #NAME?5% #NAME? #NAME?6% #NAME? #NAME?7% #NAME? #NAME?8% #NAME? #NAME?9% #NAME? #NAME?10% #NAME? #NAME?11% #NAME? #NAME?12% #NAME? #NAME?13% #NAME? #NAME?14% #NAME? #NAME?15% #NAME? #NAME?1 6 %1 4 %1 2 %1 0 %8 %6 %4 %2 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 $ 3 ,1 0 0 .0 0 $ 3 ,3 0 0 .0 0 B o n d 1 & 2 p o rtfo lio # N A M E ?B o n d 1 & 3 P o rtfo lio # N A M E ?- Table header1 6 %1 4 %1 2 %1 0 %8 %6 %4 %2 %0 %$ 1 ,5 0 0 .0 0 $ 1 ,7 0 0 .0 0 $ 1 ,9 0 0 .0 0 $ 2 ,1 0 0 .0 0 $ 2 ,3 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 2 ,7 0 0 .0 0 $ 2 ,9 0 0 .0 0 $ 3 ,1 0 0 .0 0 $ 3 ,3 0 0 .0 0 B o n d 1 & 2 p o rtfo lio # N A M E ?B o n d 1 & 3 P o rtfo lio # N A M E ?3 个债券的免疫案例到期收益率 6%债券1 债券2 债券3戏票利率 6.70% 6.988% 5.90%成熟期 10 15 30面值 1,000 1,000 1,000债券价格 $1,051.52 $1,095.96 $986.24等于$1,000市场价值的面值 $ 951.00 $ 912.44 $ 1,013.96久期 #NAME? #NAME? #NAME?目标久期 12.0000债券1所占比例 #NAME?债券3所占比例 #NAME?债券1所占比例 #NAME?债券2所占比例 #NAME?新的到期收益率 7%债券1 债券2 债券3债券价格 $1,000.00 $999.51 $883.47戏票再投资 $925.70 $965.49 $815.17总计 $1,925.70 $1,965.00 $1,698.64乘以购买的面值占$1,000的百分比 95.10% 91.24% 101.40%所得 $ 1,831.35 $ 1,792.95 $ 1,722.34债券1与2 债券1与3数据表 的组合 的组合#NAME? #NAME? - 表头0% $ 1,762.72 $ 3,854.261% $ 1,758.83 $ 3,323.552% $ 1,758.41 $ 2,886.973% $ 1,761.42 $ 2,527.714% $ 1,767.83 $ 2,232.215% $ 1,777.64 $ 1,989.546% $ 1,790.85 $ 1,790.857% $ 1,807.47 $ 1,628.968% $ 1,827.54 $ 1,498.049% $ 1,851.09 $ 1,393.3510% $ 1,878.17 $ 1,311.0211% $ 1,908.84 $ 1,247.8912% $ 1,943.16 $ 1,201.3913% $ 1,981.21 $ 1,169.4114% $ 2,023.09 $ 1,150.2315% $ 2,068.90 $ 1,142.461 6 %1 4 %1 2 %1 0 %8 %6 %4 %2 %0 %$ 1 ,5 0 0 .0 0 $ 2 ,0 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 3 ,0 0 0 .0 0 $ 3 ,5 0 0 .0 0 $ 4 ,0 0 0 .0 0 债 券 1 与 2 的 组 合# N A M E ?债 券 1 与 3 的 组 合# N A M E ?0 .1 60 .1 40 .1 20 .10 .0 80 .0 60 .0 40 .0 201 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0债 券 1 与 3 的 组 合1 8 0 7 .4 7 4 6 1 3 8 7 0 1 1债 券 1 与 2 的 组 合1 6 2 8 .9 5 8 1 2 3 9 7 1 2 21 6 %1 4 %1 2 %1 0 %8 %6 %4 %2 %0 %$ 1 ,5 0 0 .0 0 $ 2 ,0 0 0 .0 0 $ 2 ,5 0 0 .0 0 $ 3 ,0 0 0 .0 0 $ 3 ,5 0 0 .0 0 $ 4 ,0 0 0 .0 0 债 券 1 与 2 的 组 合# N A M E ?债 券 1 与 3 的 组 合# N A M E ?0 .1 60 .1 40 .1 20 .10 .0 80 .0 60 .0 40 .0 201 5 0 02 0 0 02 5 0 03 0 0 03 5 0 04 0 0 0债 券 1 与 3 的 组 合1 8 0 7 .4 7 4 6 1 3 8 7 0 1 1债 券 1 与 2 的 组 合1 6 2 8 .9 5 8 1 2 3 9 7 1 2 2
