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Anne · 2024年01月24日

MCTR和ACTR分别是什么，需要掌握的公式有哪些？

  1. CFA III
  2. Asset Allocation

NO.PZ2022122801000008

问题如下：

A few months later, Carson receives a phone call from Hamidah. She’s now on the board of trustees of Artic Foundation for Medical Research (AFMR). AFMR was established to support various medical research initiatives. She is very excited and asks Carson to help identify the return objective of AFMR’s portfolio. Osaka notes the following:

• AFMR’s overall investment objective is to maintain its portfolio’s real purchasing power after distributions.

• The risk-free rate is 4.0%.

• An expected inflation rate is 3.5%.

• The portfolio’s standard deviation is 15.0%.

• The cost of earnings investment returns is 50 bp.

• AFMR targets a 5.5% annual distribution of assets.

AFMR’s return objective is closest to: (2020 mock PM)

选项：

A.

9.50%

B.

9.74%

C.

10.27%

解释：

The calculation is (1.055) (1.035) (1.005) – 1 = 9.74%.

AFMR’s assets should be invested with the objective of earning a nominal average annual return of 9.74%. This level reflects a spending rate of 5.5%, an expected inflation rate of 3.5% and a 50 bp cost of earning investment returns.

MCTR和ACTR分别是什么，需要掌握的公式有哪些？

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2 个答案

lynn_品职助教 · 2024年01月25日

嗨，从没放弃的小努力你好：


哦，那把总结的四个都放这里，同学说相等的是第四个吧


1、ACTRi=ACTRj，

 

2、Excess return to risk free asset/MCTRi=Excess return to risk free asset/MCTRj

 

3、wi*cov(Ri,RP)=σp2/n，如果组合中某个资产的收益与组合收益相关性较高，那么它的权重配置要少。

 

1、ACTRi=wi*MCTRi=wi*βi*σp


根据上一个回答中的定义来看，ACTR1是资产1对于总风险的贡献程度。既包括资产1的风险，又包括资产1的权重，所以ACTR1=w1*MCTR1


关于第四个公式


ACTR1=w1*MCTR1的理解，可以参考课上举的例子。多买一个苹果要多花2块钱，总共买10个苹果，那么买苹果对于水果消费的总的贡献就是2*10=20。所以MCTR1指的是多承担1单位的资产1的风险，对投资组合总风险的贡献度是多少。


公式推导以我个人的经验，在备考后期不用看了，只要把公式记住就可以，可以用上面的解释来辅助记忆。



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lynn_品职助教 · 2024年01月25日

嗨，努力学习的PZer你好：


MCTR和ACTR分别是什么，需要掌握的公式有哪些？


MCTR的全称是Marginal Contribution to Total Risk，中文翻译为对总风险的边际贡献，CFA教材的定义是当对其某一项资产的权重进行微小的改变，对组合整体风险变化产生的影响。简单的理解就是，当每多投一块钱的资产， 组合的标准差 会产生的变化。


与MCTR相关的另一个概念就是ACTR(Absolute Contribution to Total Risk), 也可以叫做绝对风险贡献，它是用来计算某一资产对组合风险的总贡献有多少。其计算方式就是在MCTR的基础上乘以权重，

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Anne · 2024年01月25日

我记得还有个公式是图中第一个和第二公式相等，这是为什么呢

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