objectivity vs perspicacity

objectivity and perspicacity both are nouns.

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

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

objectivity: judgment based on observable phenomena and uninfluenced by emotions or personal prejudices
perspicacity: the capacity to assess situations or circumstances shrewdly and to draw sound conclusions

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

objectivity (noun)	perspicacity (noun)
judgment based on observable phenomena and uninfluenced by emotions or personal prejudices	the capacity to assess situations or circumstances shrewdly and to draw sound conclusions
	intelligence manifested by being astute (as in business dealings)