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borabora
Topic Author
Posts: 46
Joined: June 4th, 2014, 8:55 am

### Portfolio variance

Hi All,could someone take me through why the portfolio variance can be written like this $x'Mx$ in matrix form? where $M$ is the cov matrix and $x$ the assets weights. Is there any mathematical rule behind that?$Var(x'R)$= $x'Mx$, where $R$ are the assets returnsAlso a similar thing, the cov of 2 portfolio returns as $x'My$ , where $y$ are the weights of the other portfolio. Thanks
Last edited by borabora on July 10th, 2015, 10:00 pm, edited 1 time in total.

Jhammer
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Portfolio variance

borabora
Topic Author
Posts: 46
Joined: June 4th, 2014, 8:55 am

### Portfolio variance

Jhammer on google many mention the formulae to compute the variance but I could not find a singer author explaining in detail the maths behind why Var(x'R) = x'Mx.
Last edited by borabora on July 8th, 2015, 10:00 pm, edited 1 time in total.

kermittfrog
Posts: 63
Joined: September 9th, 2010, 10:25 am
Location: Frankfurt

### Portfolio variance

At the risk of feeding trollshttp://faculty.washington.edu/ezivot/econ424/portfolioTheoryMatrix.pdf

ExSan
Posts: 4597
Joined: April 12th, 2003, 10:40 am

### Portfolio variance

QuoteOriginally posted by: boraboraHi All,could someone take me thorough why the portfolio variance can be written like this $x'Mx$ in matrix form? where $M$ is the cov matrix and $x$ the assets weights. Is there any mathematical rule behind that?$Var(x'R)$= $x'Mx$, where $R$ are the assets returnsAlso a similar thing, the cov of 2 portfolio returns as $x'My$ , where $y$ are the weights of the other portfolio. ThanksCoursera: Financial Engineering + others, explain this equation, check them up

borabora
Topic Author
Posts: 46
Joined: June 4th, 2014, 8:55 am

### Portfolio variance

I will have a look...
Last edited by borabora on July 10th, 2015, 10:00 pm, edited 1 time in total.
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