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Spencer · 2022年12月28日

老师可以解释一下37%和63%是如何计算的吗？

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ202206210100000206

问题如下：

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：

Solution

C is correct. Sebastian needs to adjust the sub-portfolio allocation to achieve her goals. By adjusting the allocations to 37% × $2,900,000 = $1,073,000 in BY and 63% × $2,900,000 = $1,827,000 in CZ, she will be able to achieve both of her goals based on the confidence intervals.

Goal 1: Sebastian needs to maintain her current living expenditure of $120,000 per year over 20 years with a 90% probability of success. Inflation is expected to average 2.5% annually over the time horizon.

Sub-portfolio CZ should be selected because it has a higher expected return (5.70%) at the 90% probability for the 20-year horizon. Although sub-portfolio CZ has an expected annual return of 7.10%, based on the 90% probability of success requirement, the discount factor is 5.70%.

Goal 1: k = 5.70%; g = 2.50%.

Determine the inflation-adjusted annual cash flow generated by sub-portfolio CZ:

$1,827,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$120,432.04>$120,000

Goal 2: Sebastian wants to contribute $1,500,000 to a charitable foundation in 10 years with an 85% probability of success.

Sub-portfolio BY should be selected because it has a higher expected return (3.60%) at the 85% probability for the 10-year horizon. Although sub-portfolio BY has an expected annual return of 5.70%, based on the 85% probability of success requirement, the discount factor is 3.60%.

Goal 2: k = 3.60%.

Determine the amount needed today in sub-portfolio BY:

$1,500,000 1+0.036 10 =$1,053,158.42<$1,073,000

A is incorrect: 40% × $2,900,000 = $1,160,000 in BY, and 60% × $2,900,000 = $1,740,000 in CZ.

Goal 1: k= 5.70%; g = 2.50%.

Determine the inflation-adjusted annual cash flow generated by sub-portfolio CZ:

$1,740,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$114,697.18<$120,000

Goal 2: k = 3.60%.

Determine the amount needed today in sub-portfolio BY:

$1,500,000 1+0.036 10 =$1,053,158.42<$1,160,000

Goal 1 is not realized because the inflation-adjusted annual payment is below $120,000.

Goal 2 is realized

B is incorrect: 43% × $2,900,000 = $1,247,000 in BY, and 57% × $2,900,000 = $1,653,000 in CZ.

Goal 1: k = 5.70%; g = 2.50%.

Determine the inflation-adjusted annual cash flow generated by sub-portfolio CZ:

$1,653,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$108,962.32<$120,000

Goal 2: k = 3.60%.

Determine the amount needed today in sub-portfolio BY:

$1,500,000 1+0.036 10 =$1,053,158.42<$1,247,000

Goal 1 is not realized because the inflation-adjusted annual payment is below $120,000.

Goal 2 is realized.

老师可以解释一下37%和63%是如何计算的吗？我只知道20 year投资CZ，10 year投资BY

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2 个答案
已采纳答案

lynn_品职助教 · 2022年12月28日

嗨，努力学习的PZer你好：


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%近似63%

BY占比：1,053,158 / 2,900,000=36.32%近似37%（因为另一个是63%）

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加油吧，让我们一起遇见更好的自己！

FionaFang · 2024年08月08日

老师输入N=20, I/Y=3.12, FV=0,PMT=120,000，PV算出来不是1820哦

lynn_品职助教 · 2024年08月09日

嗨，努力学习的PZer你好：


BGN模式哦

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努力的时光都是限量版，加油！

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