Asset Beta

The asset beta of a firm equals its equity beta if: a. the company has no debt b. the company has no equity c. the company’s debt equals its equity The correct answer was A). The formula for the asset beta is: Asset Beta = Equity Beta (1/(1+((D/E)(1-t))) Therefore, the two betas are identical only if the company has no debt in its capital structure (D = 0). If the company has no debt, then the asset beta must equal the equity beta. I don’t understand why the answer cannot also be B (E=0)? Thanks!

Logically, If the firm has no equity, what is equity beta?

Zero?

Well - to think about it, that would still make asset beta equal to equity beta :slight_smile: didn’t think about it but got the answer correct

Any other thoughts? I’m still confused.

the assumption is that the denominator (E) cannot be zero

If you try lim(E->0), B(asset)->0. Similarly, as you said, B(eqty x)=cov(x,m)/(sigma(m)^2)->0 as E->0. Thus, it looks to me that (b) should be accepted, too.

0/ any number = 0, any number/ 0 is undefined, not 0.

Uh, debt magnifies (levers) equity beta as a multiple of asset beta, so lim(E->0) EquityBeta -> infinity. So b doesn’t work.