Asked • 05/16/19

Prove that variance of a portfolio cannot exceed variance of individual assets?

When reading on Markowitz's portfolio theory, I stumbled across the fact that in a market with two risky assets, if no short selling is not allowed, the variance of a portfolio consisting of the two assets cannot exceed the variances of the risky assets individually. That is:$${\\sigma _p}^2 \\le \\max \\{ {\\sigma _A}^2,{\\sigma _B}^2\\} $$Where A and B are two different assets.Could you kindly prove this statement, and possible provide some intuition for why this is the case?

1 Expert Answer

By:

Jason P. answered • 05/17/19

Tutor
5 (4)

Data scientist, 20-years of experience, Graduate degree, FRM PRM CBE

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