Beta of individual positions

[shanlane]

Hello,

This may be a really dumb question, so I aplogize in advance if it is, but how can changing the size of a position change the Beta of an asset? I am referring to Ch 7 in Jorion where he states that at the golable minimum VaR, all positions have the same Beta. This seems completely illogical.

Does this have more to do with the performance of the portfolio than the performance of the asset? In other words, when the composition of the portfolio changes, the performance of the individual assets, in comparison to the portfolio will appear to have changed?

Also, is it a coincidence that in table 7-4 of Jorion that the Betas are both 1?

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Another insightful question (by which I mean, it took me three years to get through this chapter). As beta, like correlation, is unitless, normally you are correct: resizing the position won't impact beta directly (it may if it impacts covariance or variance)

One of the interesting things about Jorion's illustration is that in this two-asset portfolio, beta (like marginal VaR and correlation) are each of the position "with respect to the portfolio which includes the position itself."

He is showing beta (i, P) = beta (position, portfolio including position) = beta (CAD, CAD + EUR).
I itemized his calculations in http://www.bionicturtle.com/how-to/spreadsheet/2011.t8.b.2.-jorion-analytical-var
... it is instructive to work the solution to beta (CAD, CAD + EUR) as it requires covariance (C, C+E)

But you can probably intuit that in his Table 7-4 (seeking a global minimum variance) as he increases the weight of the CAD, CAD starts to dominate its portfolio, and the its beta with respect to a portfolio dominated by itself approaches 1.0. Just as the EUR, which starts with a 1.77 beta, tends down toward 1.0 as its weight diminishes. I hope that helps,

 

[shanlane]

That was extremely helpful.

Thanks!

Shannon