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toffee · 2023年05月23日

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NO.PZ201812020100001202

问题如下:

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


Determine the most appropriate immunization portfolio in Exhibit 2. Justify your decision.


选项:

解释:

Answer:


Justification:

Portfolio 2 is the most appropriate immunization portfolio because it is the only one that satisfies the following two criteria for immunizing a portfolio of multiple 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 possible immunizing portfolios, the portfolio with the lowest convexity that is above the outflow portfolio’s convexity of 135.142 should be selected. The dispersion, as measured by convexity, of the immunizing portfolio should be as low as possible subject to being greater than or equal to the dispersion of the outflow portfolio. This will minimize the effect of non-parallel shifts in the yield curve. Portfolio 3’s convexity of 132.865 is less than the outflow portfolio’s convexity, so Portfolio 3 is not appropriate. Both Portfolio 1 and Portfolio 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 of 147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.

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

portfolio 2 is the most appropriate immunization portfolio.

to immunize multiple liability, three requirements should be met

1、the preset value of portfolio should exceed or equal to the present value of liability

2、the dollar duration of portfolio should be consistent with the dollar duration of liability

3、the convexity of portfolio should exceed the convexity of liability,and minimize the convexity of portfolio

portfolio3 is not suitable due to its lower convexity of 132.865,which is smaller than 135.142

portfolio1 is not suitable due to its larger convexity relative to portfolio2

1 个答案

pzqa31 · 2023年05月23日

嗨,努力学习的PZer你好:


可以把对应三个条件把portfolio2的数字提一下,作为“证据”。

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努力的时光都是限量版,加油!

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NO.PZ201812020100001202 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,有两个问题想请教一下1.这题我觉得答案中还少写了一个点,就是PV(asset)≥ PV(liability)原则,所以我在答案的基础上又多加了一条,不知道是否可以,我加粗标为绿色了,请老师帮忙看一下portfolio 2 is the most approriate immunization portfolio. Reasons are the follows:①market value. Market value of all three possible immunizing portfolios are larger thpresent value of the four future cash flows ($230,372).②Money ration. Money ration of all three possible immunizing portfolios mator closely matthe money ration of the outflow portfolio.③Convexity. The spersion of the immunizing portfolio shoullow possible, subjeto being greater thor equto the spersion of the outflow portfolio. portfolio 3's convexity of 132.865 is less ththe outflow portfolio's convexity, so portfolio 3 is inapproriate. Both portfolio 1 anportfolio 2 have convexity thexcee the convexity of the outflow portfolio, but portfolio 2's convexity is lower thportfolio 1.Therefore, portfolio 2 is the most approriate immunizing portfolio.2.还有一个问题就是上文中标黄的那句话,我对spersion(离散)和versification(分散)做了一个区分,老师请看下我的理解是否正确spersion越大越离散,意味着现金流发生的时间点隔的比较远,convexity会比较大,比如说barbell就是spersion大, convexity高,structrurrisk会比较大。versification高指的是现金流比较分散,就是很多时间点上都有发生现金流,不一定convexity最高,比如说laereportfolio就是versification高,可以更好的用来管理流动性。

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