Explain whether you agree or disagree with the following statement: "In the

mean-variance framework, the variance is lower the higher the correlation between the assets in the portfolio."

What will be an ideal response?

Consider the below equation representing a simple portfolio of two assets (asset 1 and asset 2):
var(Rp) = w12var(R1) + w22 var(R2) + 2 w1 w2cor(R1,R2) SD(R1) SD(R2).
From this equation, a higher positive correlation is associated with a higher portfolio variance. However, suppose the correlation is negative. Then a greater negative correlation is associated with a lower portfolio variance. Thus, the statement is only true if by "higher" we mean greater negative correlation. Because higher implies a greater positive number, one can arguably disagree with the statement.