levelheadedness vs perspicacity

levelheadedness and perspicacity both are nouns.

Word	Noun	Adjective	Verb	Adverb
levelheadedness	Yes	No	No	No
perspicacity	Yes	No	No	No

As nouns, perspicacity is a hypernym of levelheadedness; that is, perspicacity is a word with a broader meaning than levelheadedness:

levelheadedness: the property of having or showing sound judgment.
perspicacity: the capacity to assess situations or circumstances shrewdly and to draw sound conclusions

Other hypernyms of levelheadedness include judgement, judgment, sound judgement, sound judgment.

levelheadedness (noun)	perspicacity (noun)
the property of having or showing sound judgment.	the capacity to assess situations or circumstances shrewdly and to draw sound conclusions
	intelligence manifested by being astute (as in business dealings)