为何Convexity要从比outflow portfolio convexity大的portfolio中选择convexity小的

NO.PZ2018120301000037 问题如下 SchuylkillanChaopraya now scuss Option 2. Chaopraya estimates the present value ofthe four future cash flows $230,372, with a money ration of $2,609,700 anonvexity of 135.142. She consirs three possible portfolios to immunize thefuture payments, presentein Exhibit 2.terminethe most appropriate immunization portfolio in Exhibit 2. Justify yourcision. Answer:Justification:Portfolio2 is the most appropriate immunization portfolio because it is the only onethsatisfies the following two criteria for immunizing a portfolio ofmultiple future outflows: Money ration: Money rations of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio. Matching money rations is useful because the market values ancash flow yiel of the immunizing portfolio anthe outflow portfolio are not necessarily equal.Convexity:Given ththe money ration requirement is met all three possibleimmunizing portfolios, the portfolio with the lowest convexity this abovethe outflow portfolio’s convexity of 135.142 shoulselecte Thespersion, measureconvexity, of the immunizing portfolio shoulaslow possible subjeto being greater thor equto the spersion of theoutflow portfolio. This will minimize the effeof non-parallel shifts in theyielcurve. Portfolio 3’s convexity of 132.865 is less ththe outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 anortfolio 2 have convexities thexceethe convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower thPortfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.Theimmunizing portfolio nee to greater ththe convexity (anspersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio shoulbeminimizein orr to minimize spersion anrestructurrisk 提示在Matmultiple liabilities时，虽然要求是Asset money ration (BPV) = Liability money ration (BPV)，但是在做题目时，并不会出现严格相等的情况。一般的情形是，给的待选3个Portfolio的BPV是近似地等于负债的Money ration，或多或少都无所谓，只要Portfolio资产的BPV不要差负债的BPV太多，我们就认为从BPV这个角度上是满足免疫条件的。至于BPV的差距多少才能接受？这点是需要对比着看的，如本题3个Portfolio，虽然Portfolio 3的BPV离负债BPV最近，但其Convexity不满足条件，所以Portfolio 3肯定不能选。那剩下的Portfolio 1,2的BPV与负债BPV的差异我们认为就是可以接受的，且Portfolio 1与2的BPV差不多都离负债的BPV差200多，所以从BPV这个角度看，3个组合都满足要求。在BPV近似的情况下，资产的BPV可以大于负债BPV，也可以小于BPV，只要差异不过大即可。在BPV满足条件的情况下，接下来我们需要按照Convexity的条件，进一步选出最佳的组合。 我理解是因为convexity太小，现金流太集中，虽然BPV差不多，所以不行，这么理解对吗？

NO.PZ2018120301000037问题如下 SchuylkillanChaopraya now scuss Option 2. Chaopraya estimates the present value ofthe four future cash flows $230,372, with a money ration of $2,609,700 anonvexity of 135.142. She consirs three possible portfolios to immunize thefuture payments, presentein Exhibit 2.terminethe most appropriate immunization portfolio in Exhibit 2. Justify yourcision. Answer:Justification:Portfolio2 is the most appropriate immunization portfolio because it is the only onethsatisfies the following two criteria for immunizing a portfolio ofmultiple future outflows: Money ration: Money rations of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio. Matching money rations is useful because the market values ancash flow yiel of the immunizing portfolio anthe outflow portfolio are not necessarily equal.Convexity:Given ththe money ration requirement is met all three possibleimmunizing portfolios, the portfolio with the lowest convexity this abovethe outflow portfolio’s convexity of 135.142 shoulselecte Thespersion, measureconvexity, of the immunizing portfolio shoulaslow possible subjeto being greater thor equto the spersion of theoutflow portfolio. This will minimize the effeof non-parallel shifts in theyielcurve. Portfolio 3’s convexity of 132.865 is less ththe outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 anortfolio 2 have convexities thexceethe convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower thPortfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.Theimmunizing portfolio nee to greater ththe convexity (anspersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio shoulbeminimizein orr to minimize spersion anrestructurrisk 有没有一个门槛比例之类可以界定，我感觉200多又不算相差的少，但是答案有这么写，想怎么都是按照答案来倒推，下次遇见类似的还是拿不准

NO.PZ2018120301000037 问题如下 SchuylkillanChaopraya now scuss Option 2. Chaopraya estimates the present value ofthe four future cash flows $230,372, with a money ration of $2,609,700 anonvexity of 135.142. She consirs three possible portfolios to immunize thefuture payments, presentein Exhibit 2.terminethe most appropriate immunization portfolio in Exhibit 2. Justify yourcision. Answer:Justification:Portfolio2 is the most appropriate immunization portfolio because it is the only onethsatisfies the following two criteria for immunizing a portfolio ofmultiple future outflows: Money ration: Money rations of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio. Matching money rations is useful because the market values ancash flow yiel of the immunizing portfolio anthe outflow portfolio are not necessarily equal.Convexity:Given ththe money ration requirement is met all three possibleimmunizing portfolios, the portfolio with the lowest convexity this abovethe outflow portfolio’s convexity of 135.142 shoulselecte Thespersion, measureconvexity, of the immunizing portfolio shoulaslow possible subjeto being greater thor equto the spersion of theoutflow portfolio. This will minimize the effeof non-parallel shifts in theyielcurve. Portfolio 3’s convexity of 132.865 is less ththe outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 anortfolio 2 have convexities thexceethe convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower thPortfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.Theimmunizing portfolio nee to greater ththe convexity (anspersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio shoulbeminimizein orr to minimize spersion anrestructurrisk 老师好，我怎么判断ration接近呢？我感觉portfolio2 ration低所以不行啊

NO.PZ2018120301000037 问题如下 SchuylkillanChaopraya now scuss Option 2. Chaopraya estimates the present value ofthe four future cash flows $230,372, with a money ration of $2,609,700 anonvexity of 135.142. She consirs three possible portfolios to immunize thefuture payments, presentein Exhibit 2.terminethe most appropriate immunization portfolio in Exhibit 2. Justify yourcision. Answer:Justification:Portfolio2 is the most appropriate immunization portfolio because it is the only onethsatisfies the following two criteria for immunizing a portfolio ofmultiple future outflows: Money ration: Money rations of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio. Matching money rations is useful because the market values ancash flow yiel of the immunizing portfolio anthe outflow portfolio are not necessarily equal.Convexity:Given ththe money ration requirement is met all three possibleimmunizing portfolios, the portfolio with the lowest convexity this abovethe outflow portfolio’s convexity of 135.142 shoulselecte Thespersion, measureconvexity, of the immunizing portfolio shoulaslow possible subjeto being greater thor equto the spersion of theoutflow portfolio. This will minimize the effeof non-parallel shifts in theyielcurve. Portfolio 3’s convexity of 132.865 is less ththe outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 anortfolio 2 have convexities thexceethe convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower thPortfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.Theimmunizing portfolio nee to greater ththe convexity (anspersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio shoulbeminimizein orr to minimize spersion anrestructurrisk Multiple Liability——ration matching的第三个条件不是Convexity convexityL吗，为什么选最接近的呢？

NO.PZ2018120301000037 问题如下 SchuylkillanChaopraya now scuss Option 2. Chaopraya estimates the present value ofthe four future cash flows $230,372, with a money ration of $2,609,700 anonvexity of 135.142. She consirs three possible portfolios to immunize thefuture payments, presentein Exhibit 2.terminethe most appropriate immunization portfolio in Exhibit 2. Justify yourcision. Answer:Justification:Portfolio2 is the most appropriate immunization portfolio because it is the only onethsatisfies the following two criteria for immunizing a portfolio ofmultiple future outflows: Money ration: Money rations of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio. Matching money rations is useful because the market values ancash flow yiel of the immunizing portfolio anthe outflow portfolio are not necessarily equal.Convexity:Given ththe money ration requirement is met all three possibleimmunizing portfolios, the portfolio with the lowest convexity this abovethe outflow portfolio’s convexity of 135.142 shoulselecte Thespersion, measureconvexity, of the immunizing portfolio shoulaslow possible subjeto being greater thor equto the spersion of theoutflow portfolio. This will minimize the effeof non-parallel shifts in theyielcurve. Portfolio 3’s convexity of 132.865 is less ththe outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 anortfolio 2 have convexities thexceethe convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower thPortfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.Theimmunizing portfolio nee to greater ththe convexity (anspersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio shoulbeminimizein orr to minimize spersion anrestructurrisk 在market value 满足的前提下，应该选择最精确的money ration匹配吧？这里三个portfolio 都满足了market value 大于 PV of liability ;然后Portfolio 3 的money ration is 2609 707 ，the money ration of the liability is 2609700；在money ration 匹配的基础上，再最后考虑凸度的匹配吧？凸度只是二阶导的影响，所以影响力没有money ration来的重要；为什么放着money ration能精确匹配的不选，要选择近似匹配的其他；