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沪上小王子 · 2024年01月07日

这种题目的计算为什么不用expected return进行折现？

  1. CFA III
  2. Asset Allocation

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NO.PZ202212280100004702

问题如下：

B. 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. （原版书）

选项：

解释：

• The module that should be selected for each goal is the one that offers 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:

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 = $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.

我记得老师在讲强化课程时，特别提到minimum expected return不同于expected return，在计算整个portfolio的return时，要用各个subportfolio的expected return进行计算，那在本题计算要往每个sub portfolio分配多少资金时，不也应该用E（r）吗？

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lynn_品职助教 · 2024年01月07日

嗨，爱思考的PZer你好：


我记得老师在讲强化课程时，特别提到minimum expected return不同于expected return，在计算整个portfolio的return时，要用各个subportfolio的expected return进行计算，那在本题计算要往每个sub portfolio分配多少资金时，不也应该用E（r）吗？


同学理解的是对的呀。


先用minimum expected return算subportfolio,\


我们要投入的资金是通过未来现金流折现求和计算出来的，现金流已知，所以折现率越高，现在投入的资金越少，所以叫lowest funding cost最低资金成本，或者叫做minimum expected return。


只有在计算整个组合的预期收益率时才会用到 expected return，但这个时候也不涉及折现。


因此选出所有subportfolio使用的asset后，再来计算总portfolio的expected return，即用各个asset的 expected return加权平均这里是A, B, C, 和D。


这道题只让算了ABCD占总投资的比例，没有算E（r)。我们不用expected return来折现哈。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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