Financial Risk Manager Part 1
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As an analyst, you are analyzing a number of stocks of German Tech companies trading on the TecDAX. You come across two stocks DESolars AG and GERTech Co., with expected returns of 4.9% and 5.1%, respectively. In order to assess if an arbitrage opportunity exists between two stocks, you compile the following data to be used in the two-factor model:
- Actual GDP Growth: 2%
- Expected GDP Growth: 2%
- Actual CPI: 1.7%
- Expected CPI: 1.5%
- DESolars (GDP) beta: 1.1
- DESolars (CPI) beta: 0.9
- GERTech (GDP) beta: 1.1
- GERTech (CPI) beta: 0.9
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TTanishq
A
There is an arbitrage opportunity because the expected returns are different
B
There is no arbitrage opportunity because the factor sensitivities are identical
C
There is an arbitrage opportunity due to unexpected inflation
D
There is no arbitrage opportunity because the expected returns are consistent with the factor model
Explanation:
Explanation
In a two-factor arbitrage pricing theory (APT) model, an arbitrage opportunity exists when two assets have identical factor sensitivities (betas) but different expected returns.
Key Analysis:
- Factor Sensitivities: Both stocks have identical betas:
- GDP beta: 1.1 for both DESolars and GERTech
- CPI beta: 0.9 for both DESolars and GERTech
- Factor Surprises:
- GDP surprise = Actual GDP (2%) - Expected GDP (2%) = 0%
- CPI surprise = Actual CPI (1.7%) - Expected CPI (1.5%) = 0.2%
Expected Return Calculation: Using the APT model: Expected Return = Risk-free rate + β₁ × Factor₁ + β₂ × Factor₂
Since both stocks have identical factor sensitivities and are exposed to the same factor surprises, their expected returns should be identical according to the APT model. The slight difference in stated expected returns (4.9% vs 5.1%) is likely due to measurement error or other firm-specific factors, but does not represent a true arbitrage opportunity because the factor structure is identical.
Conclusion: There is no arbitrage opportunity because the factor sensitivities are identical, meaning both stocks should have the same expected return in equilibrium according to the APT framework.
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