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徐威廉 · 2022年08月14日

Goal 2 用先付年金还是后附年金？ why？

  1. CFA III
  2. Asset Allocation

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。

Goal 2 用先付年金还是后附年金？ why？ N=10, FV=1,500,000, PMT=0, I/Y=3.6

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lynn_品职助教 · 2022年08月14日

嗨，爱思考的PZer你好：


后付

一般默认期间现金流都发生在期末。如果题目有特别交代，比方说收入或者支出发生在期初或者年初，才应该把相应PV或者FV计算调成BGN模式。比如goal1题干中就有一句话withdrawals take place at the beginning of the year, starting immediately. 0时候就有现金流，算完期初现金流流入的情况，一定要记得把模式调回END。

另外在计算insurance相关题目时，注意如果提到premium一般为先付，提到dividend时一般为后付年金。这一点也非常好记忆，联想自己买保险的情况，总要在期初先交保费，保险公司才给你提供保险服务；而总是要在期末保险公司盈利了，才会给你分红。

主要是看题干，会说清楚的。

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