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linyuze · 2024年01月21日

irr是不是应该用每个portfolio 的expected return，而不是在特定年限和概率下的return

  1. CFA III
  2. Asset Allocation

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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.

解释：

Guideline Answer:
■ 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:


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.

如题

irr是不是应该用每个portfolio 的expected return，而不是在特定年限和概率下的return

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1 个答案

lynn_品职助教 · 2024年01月21日

嗨，爱思考的PZer你好：


irr是不是应该用每个portfolio 的expected return，而不是在特定年限和概率下的return


不是哈，我们这里用的是 minimum expected return，也就是lowest funding cost。


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（图2）。


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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！

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