关于MV和duration

NO.PZ2018120301000036 问题如下 Chaopraya is investment aisor forhigh-net-worth invials. One of her clients, Schuylkill, plans to funhergranon’s college ecation anconsirs two options:Option 1 Contribute a lump sum of $300,000 in 10 years.Option 2 Contribute four level annupayments of $76,500 starting in 10 years.The granon will start college in 10years. Schuylkill seeks to immunize the contribution toy. For Option 1, Chaopraya calculates thepresent value of the $300,000 $234,535. To immunize the future single outfow,Chaopraya consirs three bonportfolios given thno zero- coupon governmentbon are available. The three portfolios consist of non-callable,fi­xerate, coupon-bearing government bon consirefree of fault risk.Chaopraya prepares a comparative analysis of the three portfolios, presenteinExhibit 1.Chaopraya evaluates the three bonortfolios anselects one to recommento Schuylkill.Recommenhe portfolio in Exhibit 1 thwoulbest achieve the immunization.Justify your response Justification:PortfolioA is the most appropriate portfolio because it is the only one thsatisfiesthe three criteria for immunizing a single future outflow (liability), givenththe cash flow yiel are sufficiently close in value: 1. Market Value: Portfolio A’s initimarketvalue of $235,727 excee the outflow’s present value of $234,535. Portfolio Bis not appropriate because its market value of $233,428 is less ththepresent value of the future outflow of $234,535. A bonportfolio structuretoimmunize a single liability must have initimarket value thequals or exceethe present value of the liability.2. Macaulration: Portfolio A’s Macaulayration of 9.998 closely matches the 10-yehorizon of the outflow. PortfolioC is not appropriate because its Macaulration of 9.503 is furthest awayfrom the investment horizon of 10 years. 3. Convexity: Although Portfolio C hthelowest convexity 108.091, its Macaulration es not closely mattheoutflow amount. Of the remaining two portfolios, Portfolio A hthe lowerconvexity 119.055; this lower convexity will minimize structurrisk.fault risk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero.faultrisk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero. 就是B和C都小于234535，我就直接选A了，这个我虽然选对了，但是我看答案那么多，我这是不是有蒙对的嫌疑。

NO.PZ2018120301000036 问题如下 Chaopraya is investment aisor forhigh-net-worth invials. One of her clients, Schuylkill, plans to funhergranon’s college ecation anconsirs two options:Option 1 Contribute a lump sum of $300,000 in 10 years.Option 2 Contribute four level annupayments of $76,500 starting in 10 years.The granon will start college in 10years. Schuylkill seeks to immunize the contribution toy. For Option 1, Chaopraya calculates thepresent value of the $300,000 $234,535. To immunize the future single outfow,Chaopraya consirs three bonportfolios given thno zero- coupon governmentbon are available. The three portfolios consist of non-callable,fi­xerate, coupon-bearing government bon consirefree of fault risk.Chaopraya prepares a comparative analysis of the three portfolios, presenteinExhibit 1.Chaopraya evaluates the three bonortfolios anselects one to recommento Schuylkill.Recommenhe portfolio in Exhibit 1 thwoulbest achieve the immunization.Justify your response Justification:PortfolioA is the most appropriate portfolio because it is the only one thsatisfiesthe three criteria for immunizing a single future outflow (liability), givenththe cash flow yiel are sufficiently close in value: 1. Market Value: Portfolio A’s initimarketvalue of $235,727 excee the outflow’s present value of $234,535. Portfolio Bis not appropriate because its market value of $233,428 is less ththepresent value of the future outflow of $234,535. A bonportfolio structuretoimmunize a single liability must have initimarket value thequals or exceethe present value of the liability.2. Macaulration: Portfolio A’s Macaulayration of 9.998 closely matches the 10-yehorizon of the outflow. PortfolioC is not appropriate because its Macaulration of 9.503 is furthest awayfrom the investment horizon of 10 years. 3. Convexity: Although Portfolio C hthelowest convexity 108.091, its Macaulration es not closely mattheoutflow amount. Of the remaining two portfolios, Portfolio A hthe lowerconvexity 119.055; this lower convexity will minimize structurrisk.fault risk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero.faultrisk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero. portfolio A is best achieve the immunization.the requirements of immunization for single liability shoulmeet1、the present value of portfolio shoulexceeor equto the present value of liability2、the macaulration of portfolio equto the investment horizon of liability，whiis e te of liability3、minimize the convexity of portfolioportfolio B is not suitable e to its smaller present value 233428 th234,535；portfolio C is not suitable e to smaller macaulration th10 years

NO.PZ2018120301000036 问题如下 Chaopraya is investment aisor forhigh-net-worth invials. One of her clients, Schuylkill, plans to funhergranon’s college ecation anconsirs two options:Option 1 Contribute a lump sum of $300,000 in 10 years.Option 2 Contribute four level annupayments of $76,500 starting in 10 years.The granon will start college in 10years. Schuylkill seeks to immunize the contribution toy. For Option 1, Chaopraya calculates thepresent value of the $300,000 $234,535. To immunize the future single outfow,Chaopraya consirs three bonportfolios given thno zero- coupon governmentbon are available. The three portfolios consist of non-callable,fi­xerate, coupon-bearing government bon consirefree of fault risk.Chaopraya prepares a comparative analysis of the three portfolios, presenteinExhibit 1.Chaopraya evaluates the three bonortfolios anselects one to recommento Schuylkill.Recommenhe portfolio in Exhibit 1 thwoulbest achieve the immunization.Justify your response Justification:PortfolioA is the most appropriate portfolio because it is the only one thsatisfiesthe three criteria for immunizing a single future outflow (liability), givenththe cash flow yiel are sufficiently close in value: 1. Market Value: Portfolio A’s initimarketvalue of $235,727 excee the outflow’s present value of $234,535. Portfolio Bis not appropriate because its market value of $233,428 is less ththepresent value of the future outflow of $234,535. A bonportfolio structuretoimmunize a single liability must have initimarket value thequals or exceethe present value of the liability.2. Macaulration: Portfolio A’s Macaulayration of 9.998 closely matches the 10-yehorizon of the outflow. PortfolioC is not appropriate because its Macaulration of 9.503 is furthest awayfrom the investment horizon of 10 years. 3. Convexity: Although Portfolio C hthelowest convexity 108.091, its Macaulration es not closely mattheoutflow amount. Of the remaining two portfolios, Portfolio A hthe lowerconvexity 119.055; this lower convexity will minimize structurrisk.fault risk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero.faultrisk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero. 我这边的判断标准是首先A L, 所以只剩下 c可选, 再看一下十年期, 两个的ration都很接近十年期, 所以无法判断, 最后看convexity发现c的convexity最小, 符合单个负债的免疫条件, 所以选但详解却说ration更重要, 这怎么理解

NO.PZ2018120301000036问题如下 Chaopraya is investment aisor forhigh-net-worth invials. One of her clients, Schuylkill, plans to funhergranon’s college ecation anconsirs two options:Option 1 Contribute a lump sum of $300,000 in 10 years.Option 2 Contribute four level annupayments of $76,500 starting in 10 years.The granon will start college in 10years. Schuylkill seeks to immunize the contribution toy. For Option 1, Chaopraya calculates thepresent value of the $300,000 $234,535. To immunize the future single outfow,Chaopraya consirs three bonportfolios given thno zero- coupon governmentbon are available. The three portfolios consist of non-callable,fi­xerate, coupon-bearing government bon consirefree of fault risk.Chaopraya prepares a comparative analysis of the three portfolios, presenteinExhibit 1.Chaopraya evaluates the three bonortfolios anselects one to recommento Schuylkill.Recommenhe portfolio in Exhibit 1 thwoulbest achieve the immunization.Justify your response Justification:PortfolioA is the most appropriate portfolio because it is the only one thsatisfiesthe three criteria for immunizing a single future outflow (liability), givenththe cash flow yiel are sufficiently close in value: 1. Market Value: Portfolio A’s initimarketvalue of $235,727 excee the outflow’s present value of $234,535. Portfolio Bis not appropriate because its market value of $233,428 is less ththepresent value of the future outflow of $234,535. A bonportfolio structuretoimmunize a single liability must have initimarket value thequals or exceethe present value of the liability.2. Macaulration: Portfolio A’s Macaulayration of 9.998 closely matches the 10-yehorizon of the outflow. PortfolioC is not appropriate because its Macaulration of 9.503 is furthest awayfrom the investment horizon of 10 years. 3. Convexity: Although Portfolio C hthelowest convexity 108.091, its Macaulration es not closely mattheoutflow amount. Of the remaining two portfolios, Portfolio A hthe lowerconvexity 119.055; this lower convexity will minimize structurrisk.fault risk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero.faultrisk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero. multiple的话，ration不作为判断条件，对不

NO.PZ2018120301000036 问题如下 Chaopraya is investment aisor forhigh-net-worth invials. One of her clients, Schuylkill, plans to funhergranon’s college ecation anconsirs two options:Option 1 Contribute a lump sum of $300,000 in 10 years.Option 2 Contribute four level annupayments of $76,500 starting in 10 years.The granon will start college in 10years. Schuylkill seeks to immunize the contribution toy. For Option 1, Chaopraya calculates thepresent value of the $300,000 $234,535. To immunize the future single outfow,Chaopraya consirs three bonportfolios given thno zero- coupon governmentbon are available. The three portfolios consist of non-callable,fi­xerate, coupon-bearing government bon consirefree of fault risk.Chaopraya prepares a comparative analysis of the three portfolios, presenteinExhibit 1.Chaopraya evaluates the three bonortfolios anselects one to recommento Schuylkill.Recommenhe portfolio in Exhibit 1 thwoulbest achieve the immunization.Justify your response Justification:PortfolioA is the most appropriate portfolio because it is the only one thsatisfiesthe three criteria for immunizing a single future outflow (liability), givenththe cash flow yiel are sufficiently close in value: 1. Market Value: Portfolio A’s initimarketvalue of $235,727 excee the outflow’s present value of $234,535. Portfolio Bis not appropriate because its market value of $233,428 is less ththepresent value of the future outflow of $234,535. A bonportfolio structuretoimmunize a single liability must have initimarket value thequals or exceethe present value of the liability.2. Macaulration: Portfolio A’s Macaulayration of 9.998 closely matches the 10-yehorizon of the outflow. PortfolioC is not appropriate because its Macaulration of 9.503 is furthest awayfrom the investment horizon of 10 years. 3. Convexity: Although Portfolio C hthelowest convexity 108.091, its Macaulration es not closely mattheoutflow amount. Of the remaining two portfolios, Portfolio A hthe lowerconvexity 119.055; this lower convexity will minimize structurrisk.fault risk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero.faultrisk (cret risk) is not consirebecause the portfolios consist ofgovernment bon thpresumably have fault probabilities approaching zero. 在不同plans中，是convexity越大越好还是越小越好？伴随着什么特点？现金流的分散程度？