In the CAPM regression:

𝑅
𝑖
−
𝑅
𝑓
=
𝛼
𝑖
+
𝛽
𝑖
×
(
𝑅
𝑚
−
𝑅
𝑓
)
+
𝜖
𝑖

which statement is the most accurate?

Question

In the CAPM regression:

𝑅
𝑖
−
𝑅
𝑓
=
𝛼
𝑖
+
𝛽
𝑖
×
(
𝑅
𝑚
−
𝑅
𝑓
)
+
𝜖
𝑖

which statement is the most accurate?

BlackTom AI · Accepted Answer

Question restatement: In the CAPM regression: Ri − Rf = αi + βi × (Rm − Rf) + εi, which statement is the most accurate?

Option 1: The term beta times the market risk premium captures the asset's systematic risk.
- This aligns with CAPM intuition: βi measures sensitivity to the market, and (Rm − Rf) is the market risk premium. Their product = systematic (non-diversifiable) risk contribution to expected excess return. This statement correctly identifies the core channel by which systematic risk enters the model.

Option 2: As long as the estimated alpha is not zero, you can always conclude with certainty that CAPM does not hold.
- This is too strong. A nonzero estimated alpha may arise from sampling error, model misspecification, or estimation noise. In finite samples, alpha deviation from zero does not definitively prove CAPM failure; it merely suggests discrepancy that warrants further testing, but it is not conclusive on its own.

Option 3: A highly volatile residual will be concerning for a well-diversified investor, as it implies a risky investment.
- In a well-diversified portfolio, idiosyncratic (residual) risk should be largely diversifiable, and residual volatility does not require compensation in a CAPM framework. This statement confuses idiosyncratic risk with systemic risk; for a diversified investor, high residual variance is less worrisome, making this claim misleading.

Option 4: Alpha represents a compensation for idiosyncratic risk.
- This misstates the interpretation of alpha. In CAPM, alpha is the abnormal return not explained by beta exposure to the market, i.e., it is not a reward for taking idiosyncratic risk but rather a potential mispricing or model residual. The idea that alpha compensates for idiosyncratic risk conflates abnormal return with diversifiable risk, which is incorrect in this framework.

Summary of reasoning across options:
- Option 1 correctly identifies the mechanism by which systematic risk enters CAPM: βi times the market risk premium captures the asset’s exposure to market movements.
- Options 2–4 contain common misconceptions about alpha, residual risk, and the interpretation of CAPM diagnostics, each with logical missteps or overstatements about what the model implies.

Line breaks are included to improve readability and separate the reasoning for each option, as requested.

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In the CAPM regression: 𝑅 𝑖 − 𝑅 𝑓 = 𝛼 𝑖 + 𝛽 𝑖 × ( 𝑅 𝑚 − 𝑅 𝑓 ) + 𝜖 𝑖 which statement is the most accurate?

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