Its total variance includes both components. Beta or covariance with the market measures systematic exposure; residual variance measures idiosyncratic risk in the market model.

For a fixed market benchmark, beta is the covariance rescaled by the same positive market variance. They have the same ranking but different units.

Investors can diversify it away. Equilibrium compensation depends on the risk that remains in the market portfolio, measured by beta.

No. General diversification reduces asset-specific risk, not systematic market risk. Special exact hedges are exceptions, not a general result. Two risky assets with perfect negative correlation can form a zero-variance long-only mixture; with perfect positive correlation, differing volatilities and permitted short sales, an exact hedge can also be possible.

It is undefined because the risk-free return has zero standard deviation, making the correlation denominator zero. Their covariance is zero.

For a nonzero-volatility portfolio, the marginal derivative with respect to an unconstrained weight is Cov(Rᵢ,Rₚ)/σₚ. The weighted Euler contribution is shown above; it reflects co-movement with the entire portfolio.

No. It offers too little expected return for its beta, so its price is too high under CAPM. A security above the SML offers more than the required return and is undervalued, assuming the estimated cash flows and risk are correct.

Under reliable expected cash-flow and risk estimates, it is a positive-NPV opportunity. The position size still depends on its contribution to portfolio risk and applicable constraints.

False. Unlever the equity betas of comparable listed businesses and relever at the target financing mix; explain comparability and estimation uncertainty.

False. Leverage increases equity beta and the required equity return; CAPM and MM II are consistent under common assumptions.

True. Beta equals correlation with the market multiplied by security volatility divided by market volatility. Different correlations produce different betas.

False. Portfolio beta is exactly the weighted average. Diversification reduces residual variance, not this identity.

False. Different operating risks can outweigh the leverage effect. Compare the same business risk before making that inference.

False. Zero systematic covariance can coexist with idiosyncratic variance.

False. Correlations with the market can differ.

The direction is reversed for broadly spread weights: individual variance terms diminish while common covariance terms remain. Concentrated portfolios require a weight-specific analysis.

That average is operating asset beta. Equity also reflects financing risk; with risk-free debt the standard tax-adjusted relevering formula adds the leverage effect.

At fixed positive operating beta and fixed positive D/E under the standard risk-free-debt formula, lower Tc raises betaE. “Always” is too strong: unlevered firms and changing asset risk, leverage or debt risk need separate treatment.

False. beta = rho × sigma_i/sigma_M; beta one can coexist with a higher volatility and correlation below one.

False. Beta remains the weighted average; imperfect correlations reduce total portfolio variance.

Under unchanged investments, positive asset risk and standard debt assumptions, yes. Financing reallocates risk rather than changing the operating assets.

False. Its forecast return exceeds the required return: positive alpha indicates underpricing in the CAPM framework.

False. Market weight is 5/3 and risk-free weight −2/3. Expected excess return and volatility both increase by 5/3 relative to the unlevered market position.

False. Leverage, operating exposures and operating leverage differ; even asset betas are only approximately comparable.

False. Different volatility ratios can offset different correlations.

False. An unlevered investor can buy high-beta shares or portfolios with weighted beta above one.

False. Portfolio beta equals that weighted average exactly.

False if weights differ and component betas differ. betaP = wA betaA + (1−wA) betaB.