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七七 · 2024年07月14日

goal B

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ202212280100004702

问题如下：

B. Construct the overall goals- based asset allocation for the Armstrongs given their three goals and Abbott’s suggestion for investing any excess capital. Show your calculations. （原版书）

选项：

解释：

• The module that should be selected for each goal is the one that offers the highest return given the time horizon and required probability of success.

• Approximately 16.4%, 12.7%, 50.4%, and 20.5% should be invested in Modules A, B, C, and D, respectively.

The appropriate goals- based allocation for the Armstrongs is as follows:

For Goal 1, which has a time horizon of five years and a required probability of success of 85%, Module C should be chosen because its 4.4% expected return is higher than the expected returns of all the other modules. The present value of Goal 1 is calculated as follows:

N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)

So, approximately 50.4% of the total assets of $8 million (= $4.03 million/$8.00 million) should be allocated to Module C.

For Goal 2, which has a time horizon of 10 years and a required probability of success of 99%, Module B should be chosen because its 2.2% expected return is higher than the expected returns of all the other modules. The present value of Goal 2 is calculated as follows:


PV = $1,013,670 (or $1.01 million)

So, approximately 12.7% of the total assets of $8 million (= $1.01 million/$8.00 million) should be allocated to Module B.

For Goal 3, which has a time horizon of 25 years and a required probability of success of 75%, Module D should be chosen because its 7.5% expected return is higher than the expected returns of all the other modules. The present value of Goal 3 is calculated as follows:

N = 25, FV = –10,000,000, I/Y = 7.5%; CPT PV = $1,639,791 (or $1.64 million)

So, approximately 20.5% of the total assets of $8 million (= $1.64 million/$8.00 million) should be allocated to Module D.

Finally, the surplus of $1,315,032 (= $8,000,000 – $4,031,508 – $1,013,670 – $1,639,791), representing 16.4% (= $1.32 million/$8.00 million), should be invested in Module A following Abbott’s suggestion.

annual expenditures应该发生在每年年初，所以本来就应该是先付年金模式，也就是第一笔100,000发生在T=0，第二笔发生在t=1，第十笔发生在t=9。为什么这么理解不对呢

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2 个答案

lynn_品职助教 · 2024年07月23日

嗨，努力学习的PZer你好：


个人IPS那边的算法是独特的，工资也是先付年金。


IPS的原因如下：


因为保险的保费premium是先付年金的形式，所以为了保持统一，协会出的题目要求我们无论是expense or salary，都是按照先付年金来计算。（协会就是这么规定，我们就按照协会的角度来做）


（例如原版书课后题计算【olivia's living expense、children's living expense,、olivia's income】时，尽管这三种明先发生在年末，但还是按照先付年金的形式计算了。所以记住，在这种题型的时候【计算additional insurance】，几乎都是按照先付年金的形式来算。


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

lynn_品职助教 · 2024年07月15日

嗨，爱思考的PZer你好：


不是的哈，除了保险金（premium）是先付的费用，其他只要题目没说都是后付年金。


这道题支付的现金流是后付年金，因为考虑到通胀的问题，所以凑了一个先付年金，方便计算。

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努力的时光都是限量版，加油！

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