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%.
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%.
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: