The correct answer is A (-0.5). The correlation coefficient measures the degree to which two assets move in relation to each other. A correlation of -0.5 indicates a negative relationship, which is the most effective among the given options for reducing portfolio risk. This is because diversification benefits are maximized when assets are not perfectly correlated. Specifically:

• Perfect positive correlation (ρ = +1): Portfolio risk is unaffected, as the standard deviation of the portfolio is a weighted average of the individual asset risks.
• Imperfect correlation (ρ < +1): Portfolio risk decreases as the correlation coefficient moves away from +1. Lower values of ρ (closer to -1) further reduce risk.
• Perfect negative correlation (ρ = -1): Under certain conditions, the portfolio can be made risk-free.

The standard deviation of a two-asset portfolio is given by:

$\sigma_p = \sqrt{w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2}$

Since the standard deviation is a strictly increasing function of ρ, the smallest correlation coefficient (-0.5) results in the lowest portfolio risk.