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我是一条鱼 · 2022年02月23日

BY CZ

NO.PZ2018110601000039

问题如下:

Remington and Montgomery discuss Isabelle Sebastian. During a recent conversation, Sebastian, a long-term client with a $2,900,000 investment portfolio, reminded Remington that she will soon turn age 65 and wants to update her investment goals as follows:

Goal 1: Over the next 20 years, she needs to maintain her living expenditures, which are currently $120,000 per year (90% probability of success). Inflation is expected to average 2.5% annually over the time horizon, and withdrawals take place at the beginning of the year, starting immediately.

Goal 2: In 10 years, she wants to donate $1,500,000 in nominal terms to a charitable foundation (85% probability of success).

Exhibit 2 provides the details of the two sub-portfolios, including Sebastian’s allocation to the sub-portfolios and the probabilities that they will exceed the expected minimum return.


Exhibit 2 Investment Sub-Portfolios & Minimum Expected Return for Success Rate

Assume 0% correlation between the time horizon portfolios.

Using Exhibit 2, which of the sub-portfolio allocations is most likely to meet both of Sebastian’s goals?


选项:

A.

The current sub-portfolio allocation.

B.

A 43% allocation to sub-portfolio BY and a 57% allocation to sub-portfolio CZ.

C.

A 37%allocation to sub-portfolio BY and a 63% allocation to sub-portfolio CZ.

解释:

C is correct.

Goal 1 关键词:90% probability of success,20 years。通过查表,选择CZ portfolio,minimum expected return=5.7%。5.7%是名义利率,当前每年生活费$120,000会以2.5%的通货膨胀率增长,所以实际利率=(1+5.7%)/(1+2.5%)-1=3.12%.(近似法:5.7%-2.5%=3.2%也可行,计算结果影响不大。)

计算CZ的PV:由于第一笔现金流发生在0时刻,所以要使用计算器BGN模式:

输入N=20, I/Y=3.12, FV=0,PMT=120,000,得出PV=1,820,738.

Goal 2 关键词:85% probability of success,10 years。通过查表,选择BY portfolio,minimum expected return=3.6%。

计算BY的PV:将期末的$1.5m折到0时刻,得出PV=1,500,000/1.03610=1,053,158。

CZ占比:1,820,738 / 2,900,000=62.78%

BY占比:1,053,158 / 2,900,000=36.32%

所以最接近选项C。

请问怎么判断BY 和CZ分别是对应那个SUB PORTFOLIO.谢谢

2 个答案

郭静_品职助教 · 2022年03月03日

嗨,爱思考的PZer你好:


选择的标准很简单,先看年限,再看概率,然后横向选收益率高的那个。

例如Goal 1,先找20年,再找90%那一栏,BY 5.2% < CZ 5.7%,就选CZ。

Goal 1: Over the next 20 years,90% probability of success

Goal 2: In 10 years,85% probability of success

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

郭静_品职助教 · 2022年02月24日

嗨,努力学习的PZer你好:


不好意思,不太懂你的问题。BY和CZ就是sub portfolio。题目给出两个portfolio用于基于goal-based的方法构建组合。portfolio 1的名字是BY,portfolio 2的名字是CZ。具体构建的过程如上面的题目解析。还有问题请问的再具体一点,方便讨论,谢谢~

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努力的时光都是限量版,加油!

BAiko · 2022年03月02日

我也没看懂,为什么goal1是选cz,goal2选by?

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NO.PZ2018110601000039 问题如下 Remington anMontgomery scuss Isabelle Sebastian. ring a recentconversation, Sebastian, a long-term client with a $2,900,000 investmentportfolio, reminRemington thshe will soon turn age 65 anwants toupte her investment goals follows:Go1: Over the next 20 years, she nee to maintainher living expentures, whiare currently $120,000 per ye(90% probabilityof success). Inflation is expecteto average 2.5% annually over the timehorizon, anwithawals take plathe beginning of the year, startingimmeately.Go2: In 10 years, she wants to nate $1,500,000 in nomintermsto a charitable fountion (85% probability of success).Exhibit 2 provisthe tails of the two sub-portfolios, inclung Sebastian’s allocation to thesub-portfolios anthe probabilities ththey will exceethe expecteminimumreturn.Exhibit 2 Investment Sub-Portfolios Minimum ExpecteReturnfor Success Rate Assume 0% correlation betweenthe time horizon portfolios.UsingExhibit 2, whiof the sub-portfolio allocations is most likely to meet bothof Sebastian’s goals? A.The current sub-portfolio allocation. A 43% allocation to sub-portfolio ana 57%allocation to sub-portfolio CZ. C.A 37%allocation to sub-portfolio ana 63% allocation to sub-portfolio CZ. C is correct.Go1 关键词90% probability of success,20 years。通过查表,选择portfolio,minimum expectereturn=5.7%。5.7%是名义利率,当前每年生活费$120,000会以2.5%的通货膨胀率增长,所以实际利率=(1+5.7%)/(1+2.5%)-1=3.12%.(近似法5.7%-2.5%=3.2%也可行,计算结果影响不大。)计算CZ的PV由于第一笔现金流发生在0时刻,所以要使用计算器BGN模式输入N=20, I/Y=3.12, FV=0,PMT=120,000,得出PV=1,820,738.Go2 关键词85% probability of success,10 years。通过查表,选择portfolio,minimum expectereturn=3.6%。计算BY的PV将期末的$1.5m折到0时刻,得出PV=1,500,000/1.03610=1,053,158。CZ占比1,820,738 / 2,900,000=62.78%BY占比1,053,158 / 2,900,000=36.32%所以最接近 Go2 用先付年金还是后附年金? why? N=10, FV=1,500,000, PMT=0, I/Y=3.6

2022-08-14 13:30 1 · 回答

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2022-08-03 23:02 3 · 回答

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2022-07-22 22:08 2 · 回答

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2022-07-20 18:20 1 · 回答

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2022-07-11 14:53 1 · 回答