Quantitative Methods Q184
184An analyst has established the following prior probabilities regarding a company’s next quarter’s earnings per share (EPS) exceeding, equaling, or being below the consensus estimate.
Several days before releasing its earnings statement, the company announces an increase in its dividend. Given this information, the analyst revises his opinion regarding the likelihood that the company’s EPS will be below the consensus estimate. He estimates the likelihood of the company increasing the dividend given that EPS exceed/meet/fall below consensus as reported below:
| Prior Probabilities | |
| EPS exceed consensus | 15% |
| EPS equal consensus | 40% |
| EPS less than consensus |
Several days before releasing its earnings statement, the company announces an increase in its dividend. Given this information, the analyst revises his opinion regarding the likelihood that the company’s EPS will be below the consensus estimate. He estimates the likelihood of the company increasing the dividend given that EPS exceed/meet/fall below consensus as reported below:
| Probabilities the company increases dividends conditional on EPS exceeding/equaling/falling below consensus | |
| P(increase div│EPS exceed) | 75% |
| P(increase div │EPS equal) | 20% |
| P(increase div │EPS below) | 75% |
Using Bayes’ formula, the updated (posterior) probability that the company’s EPS will be below the consensus given that the dividend has increased is closest to:
- Option : A
- Explanation :
First, calculate the unconditional probability for an increase in dividends: P (Increase div) = P (Increase div | EPS exceed) * P (EPS exceed) + P (Increase div | EPS equal) * P (EPS equal) + P (Increase div | EPS below) * P (EPS below) = 0.75 * 0.15 + 0.20 * 0.40 + 0.05 * 0.45 = 0.215 Then update the probability of EPS falling below the consensus as: P (EPS below | Increase div) = [ P (Increase div | EPS below) / P (Increase div) ] * P (EPS below) = ( 0.05 / 0.215) * 0.45 = 0.1047
Accessibility
Oversized Widget
Saved in this browser. Nothing changes for anyone else.