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Zoe邹 · 2025年02月28日

请问这道题为什么不用上面的EXPECTED RETURN折现而用下面的minimum expected return折现呢?

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NO.PZ201803130100000602

问题如下:

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.

Show your calculations.

选项:

解释:

Guideline Answer:
■ The module that should be selected for each goal is the one that o
ers 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:


Supporting calculations:
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=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10

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.

请问这道题为什么不用上面的EXPECTED RETURN折现而用下面的minimum expected return折现呢?什么时候需要用expected return,什么时候要用minimum expected return,请老师解答一下。

1 个答案

Lucky_品职助教 · 2025年02月28日

嗨,从没放弃的小努力你好:


同学你好:


在 goal-based 投资分析里,选择折现率的关键在于与投资目标的匹配度。当以确定性目标为导向,如本题中不同目标都有特定成功概率要求时,应选用在相应时间期限和成功概率下能实现目标的预期最小回报率,这一回报率能保障在给定条件下达成投资目标。

例如在计算目标 1 时,因要实现 5 年后以 85% 概率购买价值 500 万美元度假屋的目标,所以选用 5 年期、85% 成功概率下各模块的预期回报率进行比较,模块 C 的 4.4% 预期回报率最高,故选择该回报率计算现值。目标 2 和目标 3 同理,分别依据 10 年期 99% 成功概率、25 年期 75% 成功概率下各模块的预期回报率,选择模块 B 的 2.2%、模块 D 的 7.5% 来计算现值。

若投资决策重点关注长期平均收益表现,不涉及特定成功概率要求,在对资产未来现金流进行估值或评估投资组合潜在收益时,可采用预期回报率;当投资者风险承受能力极低,更关心投资可能出现的最差收益情况,避免资产大幅缩水时,年化最小预期回报率就可用于评估投资风险,衡量投资是否能满足基本收益要求 。

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NO.PZ201803130100000602问题如下Construtheoverall goals-baseasset allocation for the Armstrongs given their three goalsanAbbott’s suggestion for investing any excess capital. Show yourcalculations.Show your calculations. Guiline Answer:■ The mole thshoulselectefor eagois the one thoffers the highest return given the time horizon anrequireprobability of success.■ Approximately 16.4%, 12.7%, 50.4%, an20.5% shoulinvestein Moles an respectively. The appropriate goals-baseallocation for the Armstrongs is follows:Supporting calculations:For Go1, whiha time horizon of five years ana requireprobability of success of 85%, Mole C shoulchosen because its 4.4% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1 is calculatefollows: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 totassets of $8 million (= $4.03 million/$8.00 million) shoulallocateto Mole For Go2, whiha time horizon of 10 years ana requireprobability of success of 99%, Mole B shoulchosen because its 2.2% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2 is calculatefollows:PV=$100,000/(1.022)1+$100,000(1.03)1/(1.022)2+$100,000(1.03)2/(1.022)3+...+$100,000(1.03)9/(1.022)10PV = $1,013,670 (or $1.01 million)So, approximately 12.7% of the totassets of $8 million (= $1.01 million/$8.00 million) shoulallocateto Mole For Go3, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole shoulchosen because its 7.5% expectereturn is higher ththe expectereturns of all the other moles. The present value ofGo3 is calculatefollows: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 totassets of $8 million (= $1.64 million/$8.00 million) shoulallocateto Mole 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), shoulinvestein Mole A following Abbott’s suggestion. 请问考试中需要像解析里写出计算器按键过程吗?例如N = 5, FV = –5,000,000, I/Y = 4.4%; CPT PV = $4,031,508 (or $4.03 million)

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