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👋 · 2022年12月05日

能不能具体解释一下折现率3.12的计算原理

  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.

麻烦具体解释一下折现率3.12的计算原理

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1 个答案

lynn_品职助教 · 2022年12月07日

嗨，努力学习的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。


所以goal 1的折现率是用下面这个公式计算的，I/Y=【（1+5.7%）/（ 1+2.5%）】-1=3.12%


通胀本来是在分子上面，这样是简化计算。知道I/Y，可以直接按计算器了。

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2022-12-15 22:44 1 · 回答