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小马8926 · 2022年06月11日

这类goal-based题目的I/Y用哪个

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。

No.PZ2018110601000039 (选择题)

来源: Mock

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?

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.


解析

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。


两个I/Y为什么不是5.7和7.1,而要用probability里面的?是题目里哪句话的特殊要求,还是以后这类题目统一都用对应时间对应概率的收益率做折现率?谢谢

1 个答案

lynn_品职助教 · 2022年06月13日

嗨,努力学习的PZer你好:


同学注意到了这个细节很好,po出来的两道题是一样的,不过应该都是同一类型的题目吧。goal-based中的折现用的是minimum expectation,这个知识点在基础班The Characteristics of Goals-Based Asset Allocations 2倍速04:20处有讲到。

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