Answer: equal to the weighted average of the risk of the two assets in the portfolio.

## Explanation When two assets have a correlation coefficient of +1.0, they are perfectly positively correlated. This means they move in exactly the same direction and proportion. In this case, there is **no diversification benefit**. ### Key Concepts: 1. **Portfolio Risk Formula**: For a two-asset portfolio, the standard deviation (risk) is calculated as: $$\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho_{12}}$$ Where: - $\sigma_p$ = portfolio standard deviation - $w_1$, $w_2$ = weights of assets 1 and 2 - $\sigma_1$, $\sigma_2$ = standard deviations of assets 1 and 2 - $\rho_{12}$ = correlation coefficient between assets 1 and 2 2. **When $\rho = +1$**: The formula simplifies to: $$\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2}$$ $$\sigma_p = \sqrt{(w_1\sigma_1 + w_2\sigma_2)^2}$$ $$\sigma_p = w_1\sigma_1 + w_2\sigma_2$$ 3. **Interpretation**: The portfolio risk equals the **weighted average** of the individual asset risks. There is no reduction in risk through diversification. ### Why Other Options are Incorrect: - **Option A (less than)**: This would occur when correlation is less than +1.0, allowing for diversification benefits. - **Option C (greater than)**: This would occur in certain cases with negative correlation or when considering other risk measures, but not for standard deviation with perfect positive correlation. ### Real-World Implication: When assets are perfectly positively correlated, combining them doesn't reduce overall portfolio risk. Investors need assets with less than perfect positive correlation to achieve diversification benefits.

Author: LeetQuiz .