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雷雷12322 · 2022年12月11日

麻烦老师详细解释下这道题目的含义吧,而且答案计算的逻辑也没看明白

NO.PZ2022071202000030

问题如下:

Question
  • P(FCF exceeded consensus) = 0.50

  • P(FCF met consensus) = 0.35

  • P(FCF fell short of consensus) = 0.15

While waiting for Abco to release last quarter’s FCF data, the investor learns that Abco will acquire a competitor. Believing that the upcoming acquisition makes it more likely that last quarter’s FCF will exceed the consensus, the investor generates a list of FCF events that may have influenced the acquisition:

  • P(Acquisition | FCF exceeded consensus) = 0.40

  • P(Acquisition | FCF met consensus) = 0.25

  • P(Acquisition | FCF fell short of consensus) = 0.35

Using Bayes’ Formula, calculate the probability that Abco is likely to exceed consensus FCF expectations for last quarter given the acquisition. P(FCF exceeded consensus | Acquisition) is closest to:

An investor in Abco stock forecasts the probability that Abco exceeded, met, or fell short of consensus expectations for free cash flow (FCF) during the prior quarter:

选项:

A.34%. B.59%. C.27%.

解释:

Solution

B is correct. The updated probability P(FCF exceeded consensus | Acquisition) is 59%.

  1. Calculate the unconditional probability that Abco will acquire the competitor firm:P(Acquisition) = (0.50 × 0.40) + (0.35 × 0.25) + (0.15 × 0.35) = 0.34, or 34%.

  2. Calculate the updated probability that Abco exceeded consensus expectations for FCF given that they acquire the competitor firm: P(FCF exceeded consensus | Acquisition) = [P(Acquisition | FCF exceeded consensus)/P(Acquisition)] × P(FCF exceeded consensus) = (0.40/0.34) × (0.50) = 0.59 or 59%.

A is incorrect because 34% is the unconditional probability that Abco acquires the competitor firm: P(Abco acquires) = (0.50 × 0.40) + (0.35 × 0.25) + (0.15 × 0.35) = 0.34, or 34%.

C is incorrect because the updated probability was calculated in error:

[P(Acquisition | FCF exceeded consensus) × P(Acquisition)]/P(FCF exceeded consensus) = (0.40 × 0.34)/(0.50) = 0.27 or 27%

  • QuestionP(FCF exceeded consensus) = 0.50

  • P(FCF met consensus) = 0.35

  • P(FCF fell short of consensus) = 0.15

While waiting for Abco to release last quarter’s FCF data, the investor learns that Abco will acquire a competitor. Believing that the upcoming acquisition makes it more likely that last quarter’s FCF will exceed the consensus, the investor generates a list of FCF events that may have influenced the acquisition:

  • P(Acquisition | FCF exceeded consensus) = 0.40

  • P(Acquisition | FCF met consensus) = 0.25

  • P(Acquisition | FCF fell short of consensus) = 0.35

Using Bayes’ Formula, calculate the probability that Abco is likely to exceed consensus FCF expectations for last quarter given the acquisition. P(FCF exceeded consensus | Acquisition) is closest to:

An investor in Abco stock forecasts the probability that Abco exceeded, met, or fell short of consensus expectations for free cash flow (FCF) during the prior quarter:

1 个答案

星星_品职助教 · 2022年12月12日

同学你好,

本题题干中说明“Using Bayes’ Formula”,所以是考察贝叶斯公式计算的题目。

贝叶斯题目的公式和乘法法则的形式是一样的。乘法法则公式为(AB)=P(A|B)×P(B)=P(B|A)×P(A),把上述连等式的后两项重新组合一下,就可以得到贝叶斯公式的形式:P(A|B)=P(B|A) / P(B) × P(A)。

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本题要计算的是P(FCF exceeded consensus | Acquisition) ,所以可以按照上述原则写出:

P(FCF exceeded consensus | Acquisition) = P(Acquisition | FCF exceeded consensus ) / P(Acquisition) × P (FCF exceeded consensus)

题干条件已知P(Acquisition | FCF exceeded consensus) = 0.40和P(FCF exceeded consensus) = 0.50,

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P(Acquisition)未知,但通过题干可以看出,acquisition由三种情况组成,分别为:

P(Acquisition | FCF exceeded consensus) = 0.40

P(Acquisition | FCF met consensus) = 0.25

P(Acquisition | FCF fell short of consensus) = 0.35

所以根据全概率公式可以求得P(Acquisition)= P(Acquisition | FCF exceeded consensus)×P(FCF exceeded consensus) + P(Acquisition | FCF met consensus)×P(FCF met consensus) + P(Acquisition | FCF fell short of consensus) ×P(FCF fell short of consensus) 

代入P(FCF exceeded consensus) = 0.50、P(FCF met consensus) = 0.35、P(FCF fell short of consensus) = 0.15,可得P(Acquisition)=0.4×0.5+0.25×0.35+0.35×0.15=0.34.

--------

结合P(Acquisition | FCF exceeded consensus) = 0.40和P(FCF exceeded consensus) = 0.50,求得最终的P(FCF exceeded consensus | Acquisition)=0.4/0.34×0.5=0.5882.

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