One can estimate the Jensen's Alpha of a portfolio returns by regression portfolio returns on risk-free rates and market returns.[Fill in the blank]判断题
A
True
B
False

Question

One can estimate the Jensen's Alpha of a portfolio returns by regression portfolio returns on risk-free rates and market returns.[Fill in the blank]

BlackTom AI · Accepted Answer

Jensen's alpha is the intercept from the regression of portfolio excess returns on market excess returns: (Rp − Rf) = α + β (Rm − Rf) + ε.

1) Relevant knowledge points and concepts
- Jensen's alpha measures average abnormal return after adjusting for market risk.
- The standard model is in excess returns: dependent variable Rp − Rf and independent variable Rm − Rf.
- Using raw returns instead of excess returns changes the specification and interpretation unless the equivalent algebraic form is recognized.

2) Step-by-step reasoning
- Start with the canonical Jensen equation: (Rp − Rf) = α + β (Rm − Rf) + ε.
- Expand the right-hand side: Rp − Rf = α + β Rm − β Rf + ε.
- Rearranging gives: Rp = α + β Rm + (1 − β) Rf + ε.

3) Intermediate calculation steps shown
- (Rp − Rf) = α + β(Rm − Rf) + ε
- Rp − Rf = α + β Rm − β Rf + ε
- Rp = α + β Rm + (1 − β) Rf + ε

4) Why the correct answer is correct
- The conventional and clear way to estimate Jensen’s alpha is to regress excess portfolio returns on excess market returns; α is the intercept in that regression.
- The question states “regression portfolio returns on risk-free rates and market returns” which is ambiguous and not the standard formulation. While algebra shows an equivalent representation (Rp regressed on Rm and Rf with particular coefficient restrictions), that is not the usual estimation approach and can lead to mis-specification or multicollinearity issues. Therefore the statement as worded is incorrect.

5) Why the other option (True) is incorrect
- Marking True would accept the imprecise form “regress portfolio returns on risk-free rates and market returns” as equivalent to the standard excess-returns regression. Because Jensen’s alpha is defined from the excess-return regression, the unqualified statement is misleading and thus incorrect.

6) Conclusion
- Jensen’s alpha comes from regressing (Rp − Rf) on (Rm − Rf), so the statement as given is false. Final answer: False.

One can estimate the Jensen's Alpha of a portfolio returns by regression portfolio returns on risk-free rates and market returns.[Fill in the blank]判断题

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