# Beta and unsystematic risk

Hi all,

I’m having a hard time understanding the concept behind beta not taking into account unsystematic risk. For instance, imagine that tomorrow Apple suffers a terrorist attack, next month Tim Cook dies, in two months iOS is under a cyber attack, and in six months there’s a leak about a sex scandal among Apple’s top executives. Apple’s stock price will certainly be extremely volatile over the next year and consequently, its beta will soar. Therefore, Apple’s beta is surely reflecting the company’s unsystematic risk…

Thanks!!

Not necessarily. At the same time the volatility of its returns increases, the correlation of its returns with the market may decrease. Its beta could increase, remain unchanged, or decrease.

Can you elaborate? Why would the beta remain unchanged or decrease? If the systematic risk is already incorporated, this higher unsystematic risk and thus higher volatility should be translated into a higher beta IMO… can you give me an example of a case where the beta decreases?

I think I’m completely missing the point because at the moment I would even say that the only reason all companies within the same industry do not have the same beta is only because of their unsystematic risk and their capital structure - If company A and B operate in the same industry and both have the same capital structure, shouldn’t their betas be the same, as beta does not reflect company-specific risk?

I know you are right, but I just don’t understand why! Thanks mate.

\beta = \frac{Cov\left(returns_{AAPL},returns_{market}\right)}{\sigma_{returns_{market}}^2}=\rho\left(returns_{AAPL},returns_{market}\right)\left(\frac{\sigma_{returns_{AAPL}}}{\sigma_{returns_{market}}}\right)

If \left(\dfrac{\sigma_{returns_{AAPL}}}{\sigma_{returns_{market}}}\right) doubles and \rho\left(returns_{AAPL},returns_{market}\right) drops by 50%, then \beta is unchanged.

If \left(\dfrac{\sigma_{returns_{AAPL}}}{\sigma_{returns_{market}}}\right) doubles and \rho\left(returns_{AAPL},returns_{market}\right) drops by 60%, then \beta decreases.

When all of these weird things happen to AAPL, they’re not happening to the market as a whole, so you should expect that the correlation between AAPL’s returns and the market’s returns will decrease. The question, of course, is: by how much?

Of course man I was blinded. Thank you very much!

My pleasure.

Magician when you have time, and if you don’t mind, could you please have a look at the below post?

Many thanks!