Select all of the below statements that are true.

Question

BlackTom AI · Accepted Answer

Question restatement: You must select all statements that are true about CAPM and related concepts.

Option 1: 'In the context of the CAPM, the market portfolio coincides with the tangent portfolio for all investors.' This is not universally true. In the CAPM framework, the market portfolio is the aggregate of all investable assets weighted by market value, representing the efficient frontier when combined with a risk-free asset. The tangent (or capital market) line originates from the risk-free rate and is tangent to the efficient frontier of risky assets. While for a mean-variance efficient market portfolio the tangent portfolio is the market portfolio, the statement claiming coincidence for all investors ignores heterogeneity in investor preferences, borrowing/lending constraints, and potential deviations from MMC on which individual choices may differ. In short, the assertion overgeneralizes beyond the CAPM’s standard assumptions about all investors and their feasible portfolios.

Option 2: 'The market beta of a stock is equal to the covariance of the stock’s return with the market return.' This is a common misconception. The market beta (β) is defined as the covariance of the stock’s return with the market return, divided by the variance of the market return: β = Cov(R_i, R_m) / Var(R_m). So the market beta is not merely the covariance; it must be standardized by how volatile the market is. If the statement had claimed beta equals covariance in the absence of normalization, it would be incorrect. Remember that beta measures sensitivity to market movements and is scaled by market risk relative to its own variance.

Option 3: 'The CAPM market portfolio is the price-weighted index of all risky assets.' This is incorrect. The CAPM market portfolio is not defined as a price-weighted index. It is the value-weighted (capitalization-weighted) portfolio of all investable risky assets, representing the total market value of those assets. A price-weighted index (like the Dow Jones Industrial Average) weights assets by price, not by market value, and is not the CAPM market portfolio.

Option 4: 'In the context of the CAPM, negative beta assets have negative risk premia.' This statement aligns with CAPM intuition: assets with negative beta tend to move opposite to the market, and their expected excess return (risk premium) should be proportional to beta. If beta is negative, the CAPM-implied risk premium is negative, meaning such assets would be expected to earn a negative excess return over the risk-free rate to compensate for their negative exposure to market risk. While in practice risk premia can deviate due to mispricing or non CAPM factors, the theoretical CAPM relationship ties expected return to beta with positive market premia, so negative beta implies a negative (or very small) risk premium in the standard model.

Summary of reasoning across options:
- Option 1 involves investor-specific portfolio choices and potential deviations from the theoretical market/tangent relationship; it is not universally true under standard CAPM assumptions.
- Option 2 confuses beta with covariance by omitting the variance normalization; the precise definition includes division by Var(R_m).
- Option 3 mischaracterizes the market portfolio as price-weighted rather than value-weighted (capitalization-weighted); this is a common factual inaccuracy.
- Option 4 is consistent with the CAPM’s linear relation between expected excess return and beta, yielding negative premia for negative beta assets, subject to market equilibrium and no arbitrage constraints.

Each option has been evaluated for consistency with CAPM concepts and common portfolio theory definitions, highlighting the precise mechanics or typical misunderstandings associated with each statement.

Select all of the below statements that are true.

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