# Why we are solving for (weight*covariance)^2 to calculate portfolio variance

Video - 1:10

Can anyone explain why we are solving for (weight*covariance)^2 to calculate portfolio variance?

isn't the portfolio variance (w1σ1 + w2σ2)^2

Hi Ryan!

Great to have you in the course and thanks for reaching out!

Can you please confirm that you are referring to the notation that appears in, for example, minute 1:22 of the video? If that's the one, then portfolio variance is exactly how you say it is; we are just using matrix notation to represent it. Please feel free to refer to an explanation/definition of matrix multiplication or reply to this message should you need a clarification on this subject matter. Thank you!

Looking forward to your answer.

Best,

Martin

Hi Martin,

I have been really enjoying your style of teaching in the python courses so far and thanks for taking the time to answer!

If i understand you correctly, you're saying:

(w·Cov)^2 = the minute 1:22 econometric matrix notation = single number = portfolio variance = (w1σ1 + w2σ2)^2

I understand the mechanics of it, that squaring (w·Cov)^2 in matrix form is represented by WT * (Covariance Matrix) * W and other online sources have confirmed that Expected portfolio variance = WT * (Covariance Matrix) * W

What I don't quite understand is why this equation, (w·Cov)^2, represents portfolio variance. What does using the weight multiplied by covariance and then squaring it have to do with portfolio variance?