Anyone else think about this when you learned about portfolio variance? Making the simple substitution (in a 2 asset portfolio): x = (weight of asset 1)(st dev of asset 1), y = (weight of assest 2)(st dev of asset 2) in the equation essentially yields you the law of cosines, with the correlation coeffiecent acting as the cosine. Correct logic here? I wonder if this is how they initially deduced the equation. The relationship between the two seems pretty clear and it makes sense to me. Anyone have any interesting mathematical relationships? I’m sure there are others.
I’ve used this in a teaching context. Basically you can use vector addition on your assets to give a visual representation of how each contributes to the risk of your portfolio. If (portfolio weight)*(SD) represents the risk contributed by each asset, respectively, and ArcCosine(correlation) represents the angle between them, then the magnitude of the vector sum represents the SD of the final portfolio portfolio.
It works as a diagram, and you can use it to show how correlation works to reduce the volatility of the portfolio.
What do I know about co-signing? It’s generally a bad idea, unless you want to get stuck holding the bag for somebody else’s loan.
And that is all I know about co-signs.
you sir are a scholar and a gentleman
Haha, I’ll agree.
I find your posts to be quite tangent to the original conversation… 
Great, thank you. This is exactly what I was looking for. I wonder now, if you can treat them as vectors, then how far does this go? Can you put them together into matrices and find eigenvectors? And do they mean anything?
The eigenvectors of a covariance matrix form a basis that amount to pointing out directions of unique variance. The large ones can be thought of as representing independent risk factors that affect the portfolio. The small ones are most likely noise.
Hmm, ok. I’m starting to get way ahead of myself now, but it seems like this would be the way that you would go about minimizing risk in a large portfolio. Correct? Also, where did you learn about this stuff? Is this in the famed Level IV exam?
This is Study Session 19. One of those LOS’s that most people just glance over.
Chad, you had made mention of being a prof before. Exactly how mathematically inclined are you?
Of the Level 1 exam? It’s been awhile since I’ve looked at it -.-. I remember them talking about the covariance matrix, but don’t remember them getting into anything beyond it, which is what I was interested in.
I’m not super mathematical. I did physics as an undergrad, and so I can follow a fair amount of the quant work. And I like to use mathematics as a tool to help me make decisions. But I’m not going to be inventing new mathematics to solve investment problems, and I think that there’s plenty of danger in applying too much mathematical sophistication to data which is inherrently noisy and possibly biased.
The danger is that you start having to make additional assumptions the deeper you go, and you can easily lose track of what assumptions you are making, so you end up with a beautiful idea that flops when you apply it.
why did you stop doing physics? if i had any mathematical aptitude i think i would like physics…maybe in a parallel universe another alladin is doing smth nice.
I think anybody who can define and use angiovector cotangencies (or whatever he called it) is pretty doggone mathematical.
I think anybody who can define and use angiovector cotangencies (or whatever he called it) is pretty doggone mathematical.