acumen vs perspicacity

acumen and perspicacity both are nouns.

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

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

acumen: shrewdness shown by keen insight
perspicacity: intelligence manifested by being astute (as in business dealings)

Other hypernyms of acumen include astuteness, perspicaciousness, shrewdness.

acumen (noun)	perspicacity (noun)
shrewdness shown by keen insight	the capacity to assess situations or circumstances shrewdly and to draw sound conclusions
a tapering point	intelligence manifested by being astute (as in business dealings)