The correct answer is A (2.7%). The correlation (ρ) between the returns of the two securities is given by the formula:

$ρ = \frac{Cov(R_i, R_j)}{σ_i σ_j}$

Given that the two securities have equal standard deviations (σ_i = σ_j = σ), the formula simplifies to:

$0.75 = \frac{5.5\%^2}{σ^2}$

Solving for σ:

$σ = \sqrt{\frac{5.5\%^2}{0.75}} ≈ 2.7\%$

• B (3.7%) is incorrect as it miscalculates the standard deviation by assuming σ_i = 2σ_j.
• C (7.3%) is incorrect as it represents an intermediate step in the calculation rather than the final result.