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

$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \text{Cov}(R_A, R_B)$

Where:

• $w_A$ and $w_B$ are the weights of Stock A and Stock B in the portfolio.
• $\sigma_A$ and $\sigma_B$ are the standard deviations of Stock A and Stock B.
• $\text{Cov}(R_A, R_B)$ is the covariance between Stock A and Stock B.

Finally, the standard deviation is the square root of the variance:

$\sigma_p = \sqrt{\sigma_p^2}$

Step 1: Assign known values

• $w_A = \frac{75,000}{100,000} = 0.75$
• $w_B = \frac{25,000}{100,000} = 0.25$
• $\sigma_A = 10.80\% = 0.108$
• $\sigma_B = 7.29\% = 0.0729$
• $\text{Cov}(R_A, R_B) = 16.70\% = 0.167$

Step 2: Plug into the formula for variance

$\sigma_p^2 = (0.75^2)(0.108^2) + (0.25^2)(0.0729^2) + 2(0.75)(0.25)(0.167)$

Break it down:

1. $0.75^2 \times 0.108^2 = 0.5625 \times 0.011664 = 0.0065622$
2. $0.25^2 \times 0.0729^2 = 0.0625 \times 0.00531641 = 0.0003323$
3. $2 \times 0.75 \times 0.25 \times 0.167 = 0.375 \times 0.167 = 0.062625$

$\sigma_p^2 = 0.0065622 + 0.0003323 + 0.062625 = 0.0695195$

Step 3: Take the square root

$\sigma_p = \sqrt{0.0695195} = 0.08338 \approx 8.34\%$

Final Answer:

The closest answer to this is 8.671%.

If you have any questions or need further explanation, let me know! Here are related questions for practice:

1. How does changing the covariance affect portfolio risk?
2. What happens to the portfolio's standard deviation if Stock A becomes more volatile?
3. Can you explain why diversification reduces portfolio risk in this example?
4. What would the standard deviation be if the weights of Stocks A and B were equal?
5. How does correlation between the two stocks impact portfolio variance?

Tip: Covariance shows the relationship between two stocks. To assess overall portfolio risk, it is key to balance weights and consider correlations effectively.