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

$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_Aw_B\sigma_{AB}$

where:

• $w_A = \frac{75,000}{100,000} = 0.75$ (weight of Stock A)
• $w_B = \frac{25,000}{100,000} = 0.25$ (weight of Stock B)
• $\sigma_A = 10.80\% = 0.1080$
• $\sigma_B = 7.29\% = 0.0729$
• $\sigma_{AB} = 16.70\% = 0.1670$

Let's plug in these values:

$\sigma_p^2 = (0.75^2)(0.1080^2) + (0.25^2)(0.0729^2) + 2(0.75)(0.25)(0.1670)$

Calculating step-by-step:

1. $(0.75)^2 \times (0.1080)^2 = 0.5625 \times 0.011664 = 0.0065625$
2. $(0.25)^2 \times (0.0729)^2 = 0.0625 \times 0.00531641 = 0.0003323$
3. $2 \times 0.75 \times 0.25 \times 0.1670 = 0.0625 \times 0.1670 = 0.0104375$

Adding these terms together gives:

$\sigma_p^2 = 0.0065625 + 0.0003323 + 0.0104375 = 0.0173323$

To find the standard deviation ($\sigma_p$) of the portfolio, we take the square root:

$\sigma_p = \sqrt{0.0173323} \approx 0.1317 \text{ or } 13.17\%$

This is closest to 14.19% in the provided options.

Correct Answer: 14.19 (%)

Would you like further details or explanations?

Here are 5 related questions:

1. How would the portfolio's risk change if more money were allocated to Stock B?
2. What is the covariance and its significance in portfolio diversification?
3. How would correlation instead of covariance be used in this calculation?
4. Can you explain the concept of diversification using this example?
5. How is portfolio variance different from portfolio expected return?

Tip: The weights in a portfolio significantly impact its risk and return characteristics. Adjusting weights is one of the key methods for managing portfolio risk.