开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

1111 · 2025年01月18日

何时用mathematic expected return的数据进行计算呢？

  1. CFA III
  2. Asset Allocation

NO.PZ2022122801000045

问题如下：

Sarzi also advises James and Karen Rozeer, a married couple who recently retired with total assets of USD 10 million. The Rozeers have two goals they wish to achieve during their retirement:

Goal 1: The Rozeers wish to have an 85% chance of transferring USD 7.5 million to their children in 10 years.

Goal 2: The Rozeers wish to have a 75% chance of being able to donate USD 15 million to a charitable organization in 25 years.

Sarzi recommends implementing a goals-based approach to construct a portfolio. He develops a set of sub-portfolio modules, which are presented in Exhibit 3. Sarzi suggests investing any excess capital in Module A.

Exhibit 3 “Highest Probability-and Horizon-Adjusted Return” Sub-Portfolio Modules under Different Horizon and Probability Scenarios

C. Construct the overall goals-based asset allocation for the Rozeers given their two goals and Sarzi’s suggestion for investing any excess capital. Show your calculations. (2018 Q9)

Note: The answer should be the percentage of total assets to be invested in each module.

选项：

解释：

The appropriate goals-based allocation for the Rozeers is as follows:

Goal 1 has a time horizon of 10 years and a required probability of success of 85%. As a result, Module B should be chosen because its 5.0% expected return is higher than the expected returns of all the other modules. The present value of Goal 1, discounted using the 5.0% expected return, is calculated as:

N = 10, FV = –USD 7,500,000, I/Y = 5.0%; PV = USD 4,604,349 (or USD 4.60 million)

So, approximately 46.0% of the total assets of USD 10 million (= USD 4.60 million / USD 10.00 million) should be allocated to Module B.

For Goal 2, which has a time horizon of 25 years and a required probability of success of 75%, Module C should be chosen because its 6.9% expected return is higher than the expected returns of all the other modules. The present value of Goal 2, discounted using the 6.9% expected return, is calculated as:

N = 25, FV = –USD 15,000,000, I/Y = 6.9%; PV = USD 2,829,102 (or USD 2.83 million)

So, approximately 28.3% of the total assets of USD 10 million (= USD 2.83 million / USD 10.00 million) should be allocated to Module C.

Finally, the surplus of USD 2,566,549 (= USD 10,000,000 – USD 4,604,349 – USD 2,829,102), representing 25.7% (= USD 2.57 million / USD 10.00 million), should be invested in Module A following Sarzi’s suggestion.

请问计算什么的时候才会用到各module的mathematic expected return呢？（第一个表格中的expected return的数据）可以举个例子吗谢谢

添加评论
1 个答案

Lucky_品职助教 · 2025年01月20日

嗨，从没放弃的小努力你好：


同学你好：


你所说的mathematic expected return是考虑了各种可能结果及其发生概率的加权平均回报。它是一种基于概率分布的预期值计算，假设投资有多种可能的回报情况，每种情况都有相应的发生概率，mathematic expected return就是将每种回报乘以其概率后相加得到的结果。

例如，一个投资项目有 50% 的概率获得 20% 的回报，有 30% 的概率获得 10% 的回报，还有 20% 的概率亏损 5%，那么其mathematic expected return为：

0.5x20% +0.3x10% +0.2x(-5%)=10%+3%-1%=12%

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

  • 1

    回答

  • 0

    关注

  • 4

    浏览
相关问题

NO.PZ2022122801000045 问题如下 Sarzi also aises JamesanKaren Rozeer, a marriecouple who recently retirewith totassets ofUS10 million. The Rozeers have two goals they wish to achieve ring theirretirement:Go1: The Rozeers wish to have 85% chanoftransferring US7.5 million to their chilen in 10 years.Go2: The Rozeers wish to have a 75% chanof being able tonate US15 million to a charitable organization in 25 years.Sarzi recommenimplementing a goals-baseapproato construa portfolio. He velops a setof sub-portfolio moles, whiare presentein Exhibit 3. Sarzi suggestsinvesting any excess capitin Mole A.Exhibit 3 “Highest Probability-anHorizon-AusteReturn”Sub-Portfolio Moles unr fferent Horizon anProbability ScenariosC.Construthe overall goals-baseasset allocation for the Rozeers given theirtwo goals anSarzi’s suggestion for investing any excess capital. Show yourcalculations. (2018 Q9)Note: The answershoulthe percentage of totassets to investein eamole. The appropriate goals-baseallocation for the Rozeers is follows:Go1 ha time horizon of 10 years ana requireprobability of success of 85%. a result, Mole B shoulchosen because its 5.0% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1, scounteusing the 5.0% expectereturn, is calculateas:N = 10, FV = –US7,500,000, I/Y = 5.0%; PV = US4,604,349 (or US4.60 million)So, approximately 46.0% of the totassets of US10 million (= US4.60 million / US10.00 million) shoulallocateto Mole B.For Go2, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole C shoulchosen because its 6.9% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2, scounteusing the 6.9% expectereturn, is calculateas:N = 25, FV = –US15,000,000, I/Y = 6.9%; PV = US2,829,102 (or US2.83 million)So, approximately 28.3% of the totassets of US10 million (= US2.83 million / US10.00 million) shoulallocateto Mole C.Finally, the surplus of US2,566,549 (= US10,000,000 – US4,604,349 – US2,829,102), representing 25.7% (= US2.57 million / US10.00 million), shoulinvestein Mole A following Sarzi’s suggestion. 根据No.PZ2022122801000046题老师的讲解，surplus要投expectereturn高的portfolio，那本题剩余的2.57为什么不投在moleC （expectereturn=8.3%，最高）?

2024-02-02 14:30 1 · 回答

NO.PZ2022122801000045 问题如下 Sarzi also aises JamesanKaren Rozeer, a marriecouple who recently retirewith totassets ofUS10 million. The Rozeers have two goals they wish to achieve ring theirretirement:Go1: The Rozeers wish to have 85% chanoftransferring US7.5 million to their chilen in 10 years.Go2: The Rozeers wish to have a 75% chanof being able tonate US15 million to a charitable organization in 25 years.Sarzi recommenimplementing a goals-baseapproato construa portfolio. He velops a setof sub-portfolio moles, whiare presentein Exhibit 3. Sarzi suggestsinvesting any excess capitin Mole A.Exhibit 3 “Highest Probability-anHorizon-AusteReturn”Sub-Portfolio Moles unr fferent Horizon anProbability ScenariosC.Construthe overall goals-baseasset allocation for the Rozeers given theirtwo goals anSarzi’s suggestion for investing any excess capital. Show yourcalculations. (2018 Q9)Note: The answershoulthe percentage of totassets to investein eamole. The appropriate goals-baseallocation for the Rozeers is follows:Go1 ha time horizon of 10 years ana requireprobability of success of 85%. a result, Mole B shoulchosen because its 5.0% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go1, scounteusing the 5.0% expectereturn, is calculateas:N = 10, FV = –US7,500,000, I/Y = 5.0%; PV = US4,604,349 (or US4.60 million)So, approximately 46.0% of the totassets of US10 million (= US4.60 million / US10.00 million) shoulallocateto Mole B.For Go2, whiha time horizon of 25 years ana requireprobability of success of 75%, Mole C shoulchosen because its 6.9% expectereturn is higher ththe expectereturns of all the other moles. The present value of Go2, scounteusing the 6.9% expectereturn, is calculateas:N = 25, FV = –US15,000,000, I/Y = 6.9%; PV = US2,829,102 (or US2.83 million)So, approximately 28.3% of the totassets of US10 million (= US2.83 million / US10.00 million) shoulallocateto Mole C.Finally, the surplus of US2,566,549 (= US10,000,000 – US4,604,349 – US2,829,102), representing 25.7% (= US2.57 million / US10.00 million), shoulinvestein Mole A following Sarzi’s suggestion. 请问老师，这样回答够吗Rozeers shoulinvest in Mole B for go1, aninvest in Mole C for go2, sinthese two have the highest annualizeminimum expectereturn 5% an6.9% corresponngly. The assets will investein these two moles are US,604,349.40 anUS,829,102.15, hence, the percentage for these two shoul46% an28%, the percentage for investing in mole A shoul26%.

2024-01-02 20:56 1 · 回答