为什么计算Goal 2的时候不用考虑通货膨胀？当是Goal 1的时候要考虑呢？-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

为什么计算Goal 2的时候不用考虑通货膨胀？当是Goal 1的时候要考虑呢？

* 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:

$\frac{$ 1, 827, 000 \times (0.057 - 0.025)}{[1 - {(\frac{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:

$\frac{$ 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:

$\frac{$ 1, 740, 000 \times (0.057 - 0.025)}{[1 - {(\frac{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:

$\frac{$ 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:

$\frac{$ 1, 653, 000 \times (0.057 - 0.025)}{[1 - {(\frac{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:

$\frac{$ 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.

老师能否帮忙厘清一下整体的解题思路，看了步骤大概能明白，但是整体思路有点浆糊

嗨，爱思考的PZer你好：

Goal 1: Over the next 20 years, she needs to maintain her living expenditures,

maintain living expenditures的意思是包含了要保持购买力。

Goal 2: In 10 years, she wants to donate $1,500,000 in nominal terms to a charitable foundation (85% probability of success).

说明这1.5m是名义金额，不需要经过通货膨胀调整直接使用即可。

老师能否帮忙厘清一下整体的解题思路，看了步骤大概能明白，但是整体思路有点浆糊

其实这类题就是翻译（找条件），找合适的sub-portfolio，计算年金就结束了。

第一步翻译其实挺关键的，像同学的疑问就是读题要解决的“翻译”问题，多做几道题总结一下就可以了

同学可以看一看smith的例题，虽然答案不正确，单丝很有代表性。

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为什么计算Goal 2的时候不用考虑通货膨胀？当是Goal 1的时候要考虑呢？

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