Delta Skew Measure as volatility changes

Question

I'm reading Trading Volatility (Colin Bennett) and there's a phrase regarding delta skew measure on p. 208 that I don't quite understand:

An example of skew measured by delta is [25 delta put - 25 delta call] / 50 delta. As this measure WIDENS the strikes examined as vol rises, in addition to normalizing (i.e., dividing) by the level of Volatility, it is a "pure" measure of skew.

I have a problem with the word "widens". As I understand for OTM options if you increase the implied vol the absolute delta will rise. So if vol has rised as written above, then wouldn't a 25 call/put has a tighter strike range? (Lower strike for the call and higher strike for the put). Because for the same delta 25, since vol is higher, the strike does not need to work as much in our favor so to speak. Therefore, wouldn't it be that when vol rises, the strike range of the skew is tighter and when vol decreases, the strike range will be wider?

I feel like my reasoning is in reverse somehow but I just can't put a finger on it.

Thanks for any help.

Answer 1

The important thing here is that delta gets smaller as you get further out of the money.

You are correct that the delta of the option will increase if vol increases. So to find the new 25 delta strikes, you will need to go further out of the money, i.e. wider strike range.