If the Fama-French factor model is absolutely correct, which of the following is not true?

Question

BlackTom AI · Accepted Answer

Question restatement:
If the Fama-French factor model is absolutely correct, which of the following is not true?

Answer options:
1) Investors can outperform the market index by investing into the stocks without shorting.
2) The alphas of the regression of excess stock returns on the constant and three factors should be identically zeros.
3) The three factors must be on the mean-variance efficient frontier.
4) One’s optimal portfolio is a portfolio of the riskfree asset and the three factors.

Option-by-option analysis:
Option 1: Investors can outperform the market index by investing into the stocks without shorting.
- Why this is unlikely to be true under a correct Fama-French specification: If the model is perfectly correct, all assets’ expected excess returns are fully captured by the three factors, and the intercept (alpha) is zero for all assets or portfolios. Outperforming the market would imply earning abnormal returns after adjusting for factor risk, i.e., a nonzero alpha. Since alpha is expected to be zero in a correctly specified model, achieving persistent outperformance solely with long-only stock positions (no shorting) contradicts the model’s implication of no free lunch after factoring risk premia. Therefore this statement is not true under the absolute correctness of the model.
- Common misconceptions that this option tries to trigger: Some students might think long-only portfolios can beat the index by stock picking, but the FF model attributes expected returns to factor exposures, not idiosyncratic stock picking that yields persistent abnormal returns after adjustment.

Option 2: The alphas of the regression of excess stock returns on the constant and three factors should be identically zeros.
- Why this is true: In a correctly specified FF model, the expected intercept (alpha) from the regression of excess returns on the constant and the three factors is zero. The model asserts that all systematic risk is captured by the three factors, leaving no abnormal, stock-specific return component after accounting for the factor exposures. Hence, alphas being identically zero aligns with the theoretical implications of a true FF specification.

Option 3: The three factors must be on the mean-variance efficient frontier.
- Why this is problematic as a universal truth: The mean-variance efficient frontier is defined for portfolios achievable from the available set of assets. The three factor portfolios (often constructed as long-short portfolios like SMB and HML, plus the market factor) themselves are not guaranteed to be themselves on the efficiency frontier of the entire asset universe in every market condition. The FF model describes pricing of assets via factor loadings, not that the factor portfolios themselves must lie on the mean-variance efficient frontier. Therefore, this statement is not a necessary consequence of the FF model being correct, and it is not guaranteed to be true in all realizations.

Option 4: One’s optimal portfolio is a portfolio of the riskfree asset and the three factors.
- Why this is true: In a multi-factor asset-pricing framework like FF, the optimal (in a mean-variance sense) risky asset combination can be represented as a portfolio that combines the risk-free asset with the factor-mimicking portfolios (the market, SMB, and HML factors). This reflects the idea that all optimal exposures arise through the available factor portfolios plus the risk-free asset, consistent with the model’s structure. Thus, this statement aligns with the FF framework’s depiction of optimal portfolios.

Summary of reasoning across options:
- Option 1 is presented as not true under the assumption that the FF model is absolutely correct, because persistent outperformance after adjusting for the factor risks implies a nonzero alpha, which contradicts the model’s zero-alpha pricing result.
- Option 2 is true, since a correctly specified FF model yields identically zero alphas for assets when regressed on the constant and the three factors.
- Option 3 is not a guaranteed necessity of the FF framework; the factors being on the mean-variance frontier is not a required implication of the model, making this option questionable as a universally true statement.
- Option 4 is true, as the FF setup supports constructing optimal portfolios from the risk-free asset and the three factor portfolios.

Fall 2025.FIN.5321.02 Final Exam

If the Fama-French factor model is absolutely correct, which of the following is not true?

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