Financial Risk Manager Part 1
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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%?
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TTanishq
Explanation:
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%
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%
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.
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