Final answer:
The standard deviation of the portfolio, calculated using the formula for a two-asset portfolio with the given weights, standard deviations, and correlation coefficient, is approximately 39.01%.
Step-by-step explanation:
To calculate the standard deviation of this portfolio, we apply the formula for the standard deviation of a two-asset portfolio:
\( \sigma_p = \sqrt{w_1^2 \cdot \sigma_1^2 + w_2^2 \cdot \sigma_2^2 + 2 \cdot w_1 \cdot w_2 \cdot \sigma_1 \cdot \sigma_2 \cdot \rho} \)
Where:
- \( w_1 \) is the weight of stock 1, which is 0.30.
- \( \sigma_1 \) is the standard deviation of stock 1, which is 30.85%.
- \( w_2 \) is the weight of stock 2, which is 0.70.
- \( \sigma_2 \) is the standard deviation of stock 2, which is 42.51%.
- \( \rho \) is the correlation coefficient between the two stocks, which is 0.2.
Substituting the values into the formula, we get:
\( \sigma_p = \sqrt{0.30^2 \cdot 30.85^2 + 0.70^2 \cdot 42.51^2 + 2 \cdot 0.30 \cdot 0.70 \cdot 30.85 \cdot 42.51 \cdot 0.2} \)
After calculation, we find the portfolio standard deviation to be:
\( \sigma_p = \sqrt{0.09 \cdot 951.1225 + 0.49 \cdot 1807.2601 + 2 \cdot 0.21 \cdot 1310.9255} \)
\( \sigma_p = \sqrt{85.601025 + 885.557649 + 550.58841} \)
\( \sigma_p = \sqrt{1521.747084} \)
\( \sigma_p = 39.01% \) (rounded to two decimal places)