开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

尚好的青春 · 2024年06月12日

相差要多少算近似相等

  1. CFA III
  2. Fixed Income

NO.PZ2018120301000037

问题如下：

Schuylkilland Chaopraya now discuss Option 2. Chaopraya estimates the present value ofthe four future cash flows as $230,372, with a money duration of $2,609,700 andconvexity of 135.142. She considers three possible portfolios to immunize thefuture payments, as presented in Exhibit 2.


Determinethe most appropriate immunization portfolio in Exhibit 2. Justify yourdecision.

解释：

Answer:

Justification:

Portfolio2 is the most appropriate immunization portfolio because it is the only onethat satisfies the following two criteria for immunizing a portfolio ofmultiple future outflows:

  • Money Duration: Money durations of all three possible immunizing portfolios match or closely match the money duration of the outflow portfolio. Matching money durations is useful because the market values and cash flow yields of the immunizing portfolio and the outflow portfolio are not necessarily equal.
  • Convexity:Given that the money duration requirement is met by all three possibleimmunizing portfolios, the portfolio with the lowest convexity that is abovethe outflow portfolio’s convexity of 135.142 should be selected. Thedispersion, as measured by convexity, of the immunizing portfolio should be aslow as possible subject to being greater than or equal to the dispersion of theoutflow portfolio. This will minimize the effect of non-parallel shifts in theyield curve. Portfolio 3’s convexity of 132.865 is less than the outflowportfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 andPortfolio 2 have convexities that exceed the convexity of the outflow portfolio,but Portfolio 2’s convexity of 139.851 is lower than Portfolio 1’s convexity of147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.

Theimmunizing portfolio needs to be greater than the convexity (and dispersion) ofthe outflow portfolio. But, the convexity of the immunizing portfolio should beminimized in order to minimize dispersion and reduce structural risk

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，想怎么解释都是按照答案来倒推，下次遇见类似的还是拿不准

添加评论
1 个答案

发亮_品职助教 · 2024年06月12日

嗨，从没放弃的小努力你好：


这块原版书还真没有一个严格的标准。但就回到做题而言，一定是可以选出来的。

因为总有几个Portfolio的几个指标比较离谱，满足不了immunization的要求，所以可以通过排除法选择出来一个最佳的。


因为这里是在几个Portfolio里面选出相对而言最佳的，几个组合之间一比较就有了分析的相对标准benchmark，所以还是比较容易选出来的。后面碰到其他题目，mock题和经典题就会有感觉，其实就是几个Portfolio之间的数据比较着选出最优的，不存在一个严格的标准直接判断出答案。


像这道题分析思路是这样：

负债的Money duration=$2,609,700，三个组合的Money duration分别是

Portfolio 1 = 2609,981，Portfolio 2 = 2609,442，Portfolio 3=2609,770


Portfolio 3的Money duration最接近，其他两个差不多，所以Portfolio 3有潜力是最佳，现在要通过其他条件验证portfolio 3能不能选，观察convexity，负债的convexity = 135.142，Portfolio 3的convexity = 132.865，Portfolio 3的convexity不满足大于的条件，所以直接排除。


剩下Portfolio 1和2的BPV基本和liability的BPV差不多，两个Portfolio和Liability的BPV差异差不多大，无法根据BPV选择出最佳，所以都是备选。观察convexity指标，Portfolio 2的convexity在大于liability convexity的基础上，又相对更小，所以Portfolio 2更好，本题选Portfolio 2.


几个Portfolio之间就是用这种比较着分析的方法找到最佳组合的，并不存在一个严格的标准直接选出最优的。

----------------------------------------------
努力的时光都是限量版，加油！

  • 1

    回答

  • 0

    关注

  • 176

    浏览
相关问题

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？

2024-11-04 15:08 1 · 回答

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

2024-04-24 11:47 1 · 回答

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？

2023-12-30 10:27 1 · 回答

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；

2023-12-17 11:11 1 · 回答