Covariance

B is correct. The current portfolio has high positive covariance, meaning the stocks move together and provide limited diversification benefits. Adding assets with LOW or NEGATIVE covariance (Treasury bonds often move opposite to stocks during market stress, international stocks respond to different economic factors, real estate has different return drivers) would significantly reduce portfolio volatility through effective diversification while maintaining growth potential.

A is incorrect because adding more domestic large-cap stocks with similar positive covariance does not improve diversification; they will continue to move together during market downturns. C is incorrect because increasing concentration increases risk and high positive covariance is the problem, not the solution. D is incorrect because negative covariance is highly desirable for diversification; when one asset falls, the negatively covariant asset tends to rise, stabilizing portfolio returns.

C is correct. Positive covariance indicates that when one security rises, the other tends to rise as well, and when one falls, the other tends to fall. They move in the same direction, though not necessarily by the same magnitude.

A describes negative covariance, not positive covariance. B describes zero or near-zero covariance, indicating no linear relationship between the securities. D is incorrect because covariance (like correlation) measures association, not causation; positive covariance shows they move together but does not prove one causes the other to move (both might respond to common factors like economic conditions).

C is correct. Asset Y with negative covariance (-100) provides the greatest reduction in portfolio volatility. Negative covariance means when the existing portfolio declines, Asset Y tends to rise (or decline less), offsetting portfolio losses and reducing overall volatility. This inverse relationship maximizes the risk-reduction benefits of diversification.

A (covariance +400) provides minimal diversification because it moves strongly in the same direction as the portfolio, amplifying rather than offsetting volatility. B (covariance +50) provides some diversification since the positive covariance is relatively small, but negative covariance is superior. D (covariance 0) provides good diversification since the asset moves independently, but negative covariance actively offsets portfolio movements rather than just being independent.

B is correct (the EXCEPT answer). This statement is FALSE. Covariance is NOT standardized to a -1.0 to +1.0 scale. that describes CORRELATION, not covariance. Covariance can range from negative infinity to positive infinity, and its magnitude is difficult to interpret because it depends on the units and scale of the securities being measured. This is why correlation (standardized covariance) is preferred for interpretation.

A is accurate: positive covariance indicates same-direction movement between securities. C is accurate: negative covariance is highly desirable for diversification because securities move in opposite directions, offsetting each other and reducing portfolio volatility. D is accurate: covariance is a fundamental input in Modern Portfolio Theory (MPT), used in calculating portfolio variance and determining optimal portfolio weights along the efficient frontier.

B is correct. Statements 1, 2, and 4 are accurate.

Statement 1 is TRUE: Negative covariance reduces portfolio variance (total risk) because when one asset falls, the negatively covariant asset tends to rise, offsetting losses and stabilizing portfolio returns. This is the mathematical foundation of diversification benefits.

Statement 2 is TRUE: Zero covariance means securities move independently, providing good diversification. High positive covariance means securities move together, providing minimal diversification because they tend to fall together during downturns. Independent movement (zero covariance) is superior to coordinated movement (positive covariance) for risk reduction.

Statement 3 is FALSE: Covariance magnitude is HARDER to interpret than correlation magnitude, not easier. Covariance depends on the units and scale of the securities (a covariance of +200 between two volatile stocks is different from +200 between two bonds), making it difficult to assess strength. Correlation standardizes covariance to a -1.0 to +1.0 scale, making it interpretable across any securities.

Statement 4 is TRUE: Stocks and Treasury bonds historically have shown low or negative covariance. During market stress, investors often flee stocks and move to Treasury bonds for safety, causing stocks to fall while bonds rise (flight to quality). This inverse relationship makes them excellent diversification partners in multi-asset portfolios.