VIPSolutionsAnalysis of past monthly movements in IBM's stock price produces the following estimates: α = 2.30 percent and β = 1.56. If the market index subsequently rises by 12 percent in one month and IBM's stock price increases by 19.40 percent, what is the abnormal change in IBM's stock price? Multiple Choice +7.80 percent +1.62 percent −1.62 percent +2.30 percent
Question:
Analysis of past monthly movements in IBM's stock price produces the following estimates: α = 2.30 percent and β = 1.56. If the market index subsequently rises by 12 percent in one month and IBM's stock price increases by 19.40 percent, what is the abnormal change in IBM's stock price? Multiple Choice +7.80 percent +1.62 percent −1.62 percent +2.30 percent
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Asked by: Veera manikanta
Created at: 2025-10-06 05:40:03
Asked by: Veera manikanta
Created at: 2025-10-06 05:40:03
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# IBM Abnormal Return Calculation
Given:
- **Alpha (\(\alpha\))**: 2.30%
- **Beta (\(\beta\))**: 1.56
- **Market return (\(R_m\))**: 12%
- **IBM actual return (\(R_{\text{IBM}}\))**: 19.40%
## Step 1: Calculate Expected Return
The formula for expected return using the single-index model is:
\[
\text{Expected Return} = \alpha + \beta \times R_m
\]
Plug in the values:
\[
= 2.30\% + 1.56 \times 12\%
\]
\[
= 2.30\% + 18.72\%
\]
\[
= 21.02\%
\]
## Step 2: Calculate Abnormal Return
Abnormal return is the actual return minus the expected return:
\[
\text{Abnormal Return} = R_{\text{IBM}} - \text{Expected Return}
\]
\[
= 19.40\% - 21.02\%
\]
\[
= -1.62\%
\]
## Step 3: Select the Correct Choice
- **Correct answer: \(-1.62\%\)**
---
**Summary Table**:
| Choice | Value |
|--------------------|------------|
| **+7.80%** | |
| **+1.62%** | |
| **−1.62%** | ✅ Correct |
| **+2.30%** | |
---
**Final Answer:**
**−1.62 percent**
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