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歪fine朱 · 2019年11月12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。

本题理解：对于存在通货膨胀的goal 1来说，在probability=90%下的折旧率为annualized minimun expected return (5.7%)。该利率为求goal 1在目前需要多少资金投入（PV）的名义折旧率，用（1+nominal discount rate）/（1+inflation rate）-1 可以求出真实的折现率，快速的带入PMT, I/Y(真实折现），N， FV(=0), 求出PV。

这种做法可以解决很多期PMT的问题


问题：然而，这种方法在原版书课后题reading 13 的Q18中不能够适用。原版书这道题也存在有多期的PMT，这个时候的折旧率为annualized minimun expected return 却小于通胀，那么就得求出所有的PMT (Cash flows）再带入I/Y (名义折旧率）求NPV。

求问：是否解题应该先判断annualized minimun expected return 与通胀率的大小，再进行方法选择？

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Shimin_CPA税法主讲、CFA教研 · 2019年11月13日

嗨，爱思考的PZer你好：


这种题目把现金流画出来就清楚了。reading 13 的Q18 goal 2有这样一句话： assuming annual inflation of 3% from Year 2 onward，所以乘以(1+inf)是从第二笔现金流开始的，计算过程比这道题难一些，因为分子分母的变化不是对应的。只有分子分母的次方数相同，才可以用(1+nominal rate)/(1+real rate)-1的方法。

reading 13 的Q18在原版书课后题讲解中有提到这一点，可以结合视频讲解，进一步理解。以下为两道题的大致思路：


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


歪fine朱 · 2019年11月13日

好的 谢谢～ 看来这题不能简单的用通胀调整折现率简化来做，还是老老实实算10年通胀下的现金流求NPV

Shimin_CPA税法主讲、CFA教研 · 2019年11月13日

对，我的建议是先画现金流的图，符合分子分母次方数相同，就可以简化来做。

歪fine朱 · 2019年11月14日

好的 很清晰 谢谢啦

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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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