# covariance

• Jul 31st 2013, 06:39 AM
parex
covariance
Hi,

I'm having problems sorting out whether a segment of a youtube video on portfolio theory is correct. The issue relates to calculating the variance of a two-asset portfolio. Since there is no linearity the addition of a second asset cannot be assumed to simply add its variance to the variance of the first asset, due to the fact that the two assets, treated as random variables, are not necessarily uncorrelated. Therefore, the formula would be something like:

Var (p) = [Weighting (Asset 1)2 * Var (Asset 1)] + [W(Asset 2)2 * Var (Asst 2)] + [ 2 * W1* W2* cov (Ass1, Ass2) ]

However, the equation in the youtube video is:

Var (p) = [Weighting (Asset 1)2 * Var (Asset 1)] + [W(Asset 2)2 * Var (Asst 2)] + [ 2 * W1* W2* SD (Ass1) * SD (Ass2) ]

Further, the author of the video claims that [ 2 * W1* W2* SD (Ass1) * SD (Ass2) ] is the covariance.

What am I missing?

Investments - Portfolio Theory 04 - YouTube

min 1:08:19

Disclaimer: I also posted this topic under Math Business.
• Jul 31st 2013, 07:03 AM
ANDS!
Re: covariance
In a video over an hour. . .might help to indicate where in the video you are talking about (or let YouTube embedding do it for you).
• Jul 31st 2013, 07:24 AM
DerWundermann
Re: covariance
The video provides wrong information.

If both assets are uncorrelated, the covariance is zero, then:

Var (p) = [Weighting (Asset 1)2 * Var (Asset 1)] + [W(Asset 2)2 * Var (Asst 2)]

However, if both assets are correlated, then

Var (p) = [Weighting (Asset 1)2 * Var (Asset 1)] + [W(Asset 2)2 * Var (Asst 2)] + [ 2 * W1* W2* cov (Ass1, Ass2) ]

or, alternatively:

Var (p) = [Weighting (Asset 1)2 * Var (Asset 1)] + [W(Asset 2)2 * Var (Asst 2)] + [ 2 * W1* W2* rho*SD (Ass1) * SD (Ass2) ]

where rho is the correlation between them.

Cheers!
• Jul 31st 2013, 09:39 AM
parex
Re: covariance
ANDS!,

I thought I did:

"min 1:08:19"

If it didn't work, or there's a better way, send me some instructions, or hyperlink.