Asset/Equity Beta

[Submariner]

An answer to a question reads as follows:
“Asset risk does not change with a higher D/E ratio. Equity risk rises with greater debt”
If I am not mistaken, asset risk = asset beta.
Therefore, the formula to derive asset beta has me a bit confused:
(B)asset = (B)equity * [1 / (1+ (1-t)) * D/E]
It seems that a change in D/E would change asset beta. Even using the formula for beta of comparables:
[(B)unlevered, comparable] = [(B)levered, comparable] / [1 + (1-t(comparable)) * D/E]
Where D/E is the D/E for the comparable, and [(B)unlevered, comparable] = (B)asset
What am I missing here?
Thanks!

 

[S2000magician]

Think about the pure-play method:

• You start with the equity beta of the pure-play (comparable) company
• You unlever it (with the pure-play company’s D/E ratio) to get the asset beta of the pure-play company
• The asset beta of your company is the same as the asset beta of the pure-play company
• You lever it (with your D/E ratio) to get your equity beta

The highlighted step is your answer: asset risk does not change with a higher debt/equity ratio. (Your assets don’t know how you financed them: assets are pretty stupid that way.)
What you’re missing is that you’re making an incorrect assumption; i.e., you don’t realize that you’re making it. You’re assuming that the pure-play company’s equity beta − the starting point − is the immutable number.
It’s not.
The pure-play company’s asset beta is the immutable number: if the pure-play company had had a different D/E ratio, it would also have a different equity beta, but when you unlever it you would get to the same asset beta.
There you go.