bad vs undesirability

bad and undesirability both are nouns.

Word	Noun	Adjective	Verb	Adverb
bad	Yes	Yes	No	Yes
undesirability	Yes	No	No	No

As nouns, undesirability is a hyponym of bad; that is, undesirability is a word with a more specific, narrower meaning than bad:

Other hyponyms of bad include unworthiness, evil, evilness, worse, unsoundness, liability, inadvisability.

bad (noun)	undesirability (noun)
that which is below standard or expectations as of ethics or decency	the quality possessed by something that should be avoided

bad (adjective)	undesirability (adjective)
having undesirable or negative qualities
feeling or expressing regret or sorrow or a sense of loss over something done or undone
reproduced fraudulently
characterized by wickedness or immorality
capable of harming
below average in quality or performance
serious or severe
not capable of being collected
not working properly
nonstandard
(of foodstuffs) not in an edible or usable condition
feeling physical discomfort or pain (`tough' is occasionally used colloquially for `bad')
physically unsound or diseased
not financially safe or secure

bad (adverb)	undesirability (adverb)
very much; strongly
with great intensity (`bad' is a nonstandard variant for `badly')