Computing Var with Covariance Matrix

[omerozd]

Hi,
When computing Value at risk with covariance matrix, horizontal and vertical Beta vectors of investment amounts were used in Meisser's book. And, in his example, there are asset A (with 8 million $ and 1.5% std. dev.) and Asset B (with 4 million $ and 2% std. dev) the correlation is 0.6, also. At the end, by putting the amounts into the equation, the portfolio std. dev. is found as 0.1798.

How does the std. dev. of the portfolio can be 0.1798 whereas the std devs. of the assets are 0.015 and 0.02.
Why do we use the amounts instead of the weights?

 

[emilioalzamora1]

Dont know where you have these figures (page in Meissner's book!) but the standard portfolio variance formula (for 2 assets) with your given data yields:

weights: 8 mil + 4 mil = 12 mil

Asset A = 8/12 = 0,66
Asset B = 4/12 = 0,33

sigma^2 (portfolio) = 0,66^2* 0,015^2 + 0,33^2*0,02 + 2*0,66*0,33*0,015*0,02*0,6 = 0,000224 >> which then yields a portfolio std dev. sqrt(0,000224) = 1,4981%

By the way: a good source for this topic is the book 'Managing Investment Portfolios' (Chapter 9) by the CFA Institute.

 

[Matthew Graves]

Looks to me like he's giving the portfolio std. dev. in absolute terms (e.g. $mil). If you take the portfolio std. dev. in percent, which is 1.4981% then multiply by 12 (since there is $12million in total) you get $0.1798m.

 

[emilioalzamora1]

I see, thanks @Matthew Graves!

As he was not pointing towards this and I have not had the Meissner book at hand the explanation makes sense. Apparently he then has standard deviation in dollar terms. Quite unusual actually but if the the computation is water-proof then I am happy with this.

Would be great to go on here having a discussion whether portfolio variance (std. dev.) is usually expressed rather in %-terms or in $-terms. @David Harper CFA FRM, what is your take on this?

 

[Matthew Graves]

Reporting portfolio std. dev. in absolute terms is unusual, definitely. I've never really seen this with any regularity except when reporting Value-At-Risk. Even then I wouldn't say it's the "standard" approach. I'd be interested in hearing the experiences of others as well though.