Explanation:

To calculate the standard deviation of a two-asset portfolio, we use the formula:

$\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \sigma_A \sigma_B \rho_{AB}}$

Where:

• $w_A = 0.30$ (weight of security A)
• $w_B = 0.70$ (weight of security B)
• $\sigma_A = 0.30$ (standard deviation of security A)
• $\sigma_B = 0.25$ (standard deviation of security B)
• $\rho_{AB} = 0.60$ (correlation between A and B)

Step-by-step calculation:

1. Calculate $w_A^2 \sigma_A^2 = (0.30)^2 \times (0.30)^2 = 0.09 \times 0.09 = 0.0081`$2. Calculate $w_B^2 \sigma_B^2 = (0.70)^2 \times (0.25)^2 = 0.49 \times 0.0625 = 0.030625$3`. Calculate `$2`w_A w_B \sigma_A \sigma_B \rho_{AB} = 2 \times 0.30 \times 0.70 \times 0.30 \times 0.25 \times 0.60$
   • First: $0.30 \times 0.70 = 0.21$
   • Then: $0.30 \times 0.25 = 0.075$
   • Then: $0.21 \times 0.075 = 0.01575$
   • Then: $0.01575 \times 0.60 = 0.00945$
   • Finally: $2 \times 0.00945 = 0.0189$4. Sum all components: $0.0081 + 0.030625 + 0.0189 = 0.057625$5. Take the square root: $\sqrt{0.057625} = 0.24005$ or 24.0%

Verification:

• Option A (16.8%) is too low - this would be the result if the correlation was negative or if we used a simple weighted average without considering correlation.
• Option C (26.5%) is too high - this would be closer to a simple weighted average of the standard deviations (0.30 × 30% + 0.70 × 25% = 26.5%), but this ignores the diversification benefit from less-than-perfect correlation.

Key Concept: The portfolio standard deviation is less than the weighted average of individual standard deviations when correlation is less than 1.0, demonstrating the diversification benefit.