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, it means they are perfectly positively correlated. In this case, the portfolio's standard deviation (risk) is simply the weighted average of the individual assets' standard deviations. ### Mathematical Proof: The formula for portfolio variance with two assets is: σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂ Where: - σ_p = portfolio standard deviation - w₁, w₂ = weights of assets 1 and 2 - σ₁, σ₂ = standard deviations of assets 1 and 2 - ρ₁₂ = correlation coefficient between assets 1 and 2 When ρ₁₂ = +1.0: σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂(1) σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ This can be factored as: σ_p² = (w₁σ₁ + w₂σ₂)² Taking the square root: σ_p = w₁σ₁ + w₂σ₂ This shows that the portfolio standard deviation is exactly equal to the weighted average of the individual asset standard deviations. ### Key Points: 1. **Perfect positive correlation (ρ = +1.0)** means the assets move in perfect unison. 2. **No diversification benefits** - the portfolio risk cannot be reduced below the weighted average. 3. **Portfolio risk is linear** - it's simply the weighted sum of individual risks. ### Comparison with other correlation values: - **ρ < +1.0**: Portfolio risk is less than weighted average (diversification benefit) - **ρ = +1.0**: Portfolio risk equals weighted average (no diversification) - **ρ = -1.0**: Portfolio risk can be reduced to zero with proper weights (perfect diversification) Therefore, for a correlation coefficient of +1.0, portfolio risk is **equal to** the weighted average of the risk of the two assets in the portfolio.

Author: LeetQuiz .