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Answer: 5.349%
## Step-by-Step Explanation ### Step 1: Calculate Excess Returns for Each Factor First, we need to calculate the excess return for each factor by subtracting the risk-free rate from the expected return: - **Factor A**: 6.5% - 3.20% = 3.30% - **Factor B**: 7.7% - 3.20% = 4.50% - **Factor C**: 4.0% - 3.20% = 0.80% ### Step 2: Calculate Factor Exposure Contribution Multiply each factor beta by its corresponding excess return: ``` 0.88 × 3.30% + (-0.55) × 4.50% + 1.40 × 0.80% = 2.904% + (-2.475%) + 1.120% = 1.549% ``` ### Step 3: Calculate Total Expected Return Add the alpha and risk-free rate to the factor exposure contribution: ``` Total Return = Factor Exposure Contribution + Alpha + Risk-Free Rate = 1.549% + 0.60% + 3.20% = 5.349% ``` ### Final Answer The predicted yearly return on ABC Bank shares is **5.349%**, which corresponds to option B. This calculation follows the multi-factor model framework where the expected return equals the risk-free rate plus alpha plus the weighted sum of factor risk premiums.
Author: Tanishq Prabhu
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An equities analyst at an asset management business is evaluating a prospective investment in ABC Bank stock using an internal three-factor model. Each of the three factors is represented by an exchange-traded fund (ETF) with a factor beta of one and a factor beta of zero for the others. The analyst gathers the following data:
| Expected annual return of ETF factor | Factor A | Factor B | Factor C |
|---|---|---|---|
| 6.5% | 7.7% | 4.0% | |
| Factor beta for ABC Bank stock | 0.88 | -0.55 | 1.40 |
What is the predicted yearly return on ABC Bank shares using the internal model if the annualized risk-free interest rate is 3.20% and the alpha is 0.60%?
A
1.549%
B
5.349%
C
4.749%
D
2.149%