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.