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yan · 2024年09月25日

1.为什么默认goal 1 是CZ，goal 2 是另外一个组合？题干中并没有显示这种对应。2.goal 1 这个包含infl

  1. CFA III
  2. Asset Allocation

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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.


1.为什么默认goal 1 是CZ，goal 2 是另外一个组合？题干中并没有显示这种对应。2.goal 1 这个包含inflation2.5%的公式的知识点出处是在哪里，没看明白这个计算现值的公式

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2 个答案

lynn_品职助教 · 2024年09月27日

嗨，从没放弃的小努力你好：


同学你好：

Goal 1那个公式能解释一下么，没看明

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

运用两者间的计算公式，实际利率=(1+名义利率)/(1+通货膨胀率)-1=（1+5.7%）/（ 1+2.5%）-1=3.12%

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

lynn_品职助教 · 2024年09月26日

嗨，爱思考的PZer你好：


同学你好：

1.为什么默认goal 1 是CZ，goal 2 是另外一个组合？题干中并没有显示这种对应。

我们看题干：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)

根据20年，90%的成功概率，通过查表可以得出选择CZportfolio满足Goal 1，因为BY在这个条件下的minimum expected return为5.2%，而CZ为5.7%，CZ的收益率更高，所以选择CZ。

2.goal 1 这个包含inflation2.5%的公式的知识点出处是在哪里，没看明白这个计算现值的公式

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，这是简化计算。

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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NO.PZ202206210100000206 问题如下 Using Exhibit 2, whiof the sub-portfolio allocations is most likely to meet both of Sebastian’s goals? A.The current sub-portfolio allocation B.A 43% allocation to sub-portfolio ana 57% allocation to sub-portfolio C.A 37% allocation to sub-portfolio ana 63% allocation to sub-portfolio SolutionC is correct. Sebastinee to aust the sub-portfolio allocation to achieve her goals. austing the allocations to 37% × $2,900,000 = $1,073,000 in an63% × $2,900,000 = $1,827,000 in CZ, she will able to achieve both of her goals baseon the confinintervals.Go1: Sebastinee to maintain her current living expenture of $120,000 per yeover 20 years with a 90% probability of success. Inflation is expecteto average 2.5% annually over the time horizon.Sub-portfolio shoulselectebecause it ha higher expectereturn (5.70%) the 90% probability for the 20-yehorizon. Although sub-portfolio hexpecteannureturn of 7.10%, baseon the 90% probability of success requirement, the scount factor is 5.70%. Go1: k = 5.70%; g = 2.50%.termine the inflation-austeannucash flow generatesub-portfolio CZ: $1,827,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$120,432.04 $120,000 Go2: Sebastiwants to contribute $1,500,000 to a charitable fountion in 10 years with 85% probability of success. Sub-portfolio shoulselectebecause it ha higher expectereturn (3.60%) the 85% probability for the 10-yehorizon. Although sub-portfolio hexpecteannureturn of 5.70%, baseon the 85% probability of success requirement, the scount factor is 3.60%.Go2: k = 3.60%.termine the amount neetoy 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, an60% × $2,900,000 = $1,740,000 in CZ.Go1: k= 5.70%; g = 2.50%.termine the inflation-austeannucash flow generatesub-portfolio CZ: $1,740,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$114,697.18 $120,000 Go2: k = 3.60%.termine the amount neetoy in sub-portfolio BY: $1,500,000 1+0.036 10 =$1,053,158.42 $1,160,000 Go1 is not realizebecause the inflation-austeannupayment is below $120,000.Go2 is realizeB is incorrect: 43% × $2,900,000 = $1,247,000 in BY, an57% × $2,900,000 = $1,653,000 in CZ.Go1: k = 5.70%; g = 2.50%.termine the inflation-austeannucash flow generatesub-portfolio CZ: $1,653,000× 0.057−0.025 1− 1+0.025 1+0.057 20 1.057 =$108,962.32 $120,000 Go2: k = 3.60%.termine the amount neetoy in sub-portfolio BY: $1,500,000 1+0.036 10 =$1,053,158.42 $1,247,000 Go1 is not realizebecause the inflation-austeannupayment is below $120,000.Go2 is realize 如题

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