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Amandathink · 2020年01月11日

问一道题: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。

第一个目标和教材例题有相同之处,对于通胀率的考虑在讲课时是说体现在分子--即现金流中的,如果本题一葫芦画瓢,

对每期期初的现金流进行 1,200,0000×(1+2.5%)的n-1的调整,以5.7%折现,也能选出正确选项,只是计算比较繁琐,

考试的话会因为PV差别导致选择错误吗?


另外关于通胀率的问题,将它考虑进现金流(分子),或折现率(分母)有什么规律或者约定吗?

谢谢

1 个答案

Shimin_CPA税法主讲、CFA教研 · 2020年01月12日

嗨,努力学习的PZer你好:


设置选项的时候会考虑计算误差,所以选最接近的答案。

我们在使用计算器第三行的时候,假设PMT是一个固定不变的数值。如果现金流每一期都按 2.5%的通货膨胀率增长,就违反了这一条要求。所以把通胀率考虑进折现率,使得折现率为 (1+5.7%)/(1+2.5%)-1=3.12% ,是为了让每一笔现金流都保持在 120,000 。

你用的方法,对每期期初的现金流进行 1,200,0000×(1+2.5%)的n-1的调整,以5.7%折现,也可以,但N=20,相当于计算器要算20个数值的求和,容易算错,也费时间。如果用了等比数列求和公式,会简化计算流程,但依然不如用计算器第三行快捷。


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


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