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rych · 2021年09月19日

什么时候该加权平均？

  1. CFA I
  2. Quantitative

NO.PZ2015120601000008

问题如下：

An analyst developed two scenarios with respect to the recovery of $100,000 principal from defaulted loans:

The amount of the expected recovery is closest to:

选项：

A.

$36,400.

B.

$55,600.

C.

$63,600.

解释：

C is correct.

If Scenario 1 occurs, the expected recovery is 60% ($50,000) + 40% ($30,000) = $42,000, and if Scenario 2 occurs, the expected recovery is 90% ($80,000) + 10%($60,000) = $78,000.

Weighting by the probability of each scenario, the expected recovery is 40%($42,000) + 60%($78,000) = $63,600.

Alternatively, first calculating the probability of each amount occurring, the expected recovery is (40%)(60%)($50,000) + (40%)(40%)($30,000) + (60%)(90%)($80,000) + (60%)(10%)($60,000) = $63,600.

这道题考察加权平均计算均值（expected recovery），权重为概率。

①首先算出scenario 1中的加权平均值为50,000×60%+30,000×40%=42,000；

同理scenario 2中加权平均值为80,000×90%+60,000×10%=78,000.

②然后再将scenario1 &2做加权平均，

42,000×40%+78,000×60%=63,600，选择B选项。


这里搞不太清prob of amount (%)是不是乘以scenario后还是乘以scenario前的数字，如果这里是乘以scenario前的数字。那为什么视频中关于eps 那道题求E(EPS)直接乘以EPS?而没有再乘以probability of recession 25%? 所以视频中there is 25% of probabilty that EPS is $2 and there is 75% of probabilty that EPS is $4 中的25% and 75%代表的是已经乘以recession probability 0.25后的数字吗？还是仅仅代表乘recession probability以前的数字？如果同样如这道题是代表乘以scenario前的数字，为什么 E(EPS)不等于25%*2*25%+75%*4*25%？

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1 个答案

星星_品职助教 · 2021年09月19日

同学你好，

由于没提到具体是哪个视频，默认是截图中的这道题。以后记得截图或者标明视频具体位置。

这道例题和本题区别在于例题中标明了此时就是recession的情况，相当于100%的概率都是recession，不存在prosperity的可能。

所以直接再recession的框架下进行就算就可以。这就是不需要“乘以scenario前的数字”的原因。

但如果没有例题中的这个限定，“scenario前的概率”就是要考虑的，如本题。

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