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Amandathink · 2020年01月11日

问一道题：NO.PZ2018110601000039

  1. CFA III
  2. Asset Allocation

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

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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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