So some studies show a positive correlation on cognitive performance and some negative correlation for "morningness" and "eveningness".
The obvious conclusion to me is that there is no strong effect. Or that at some portions of the year, or parts of the globe, certain chronotypes have advantages, this certainly matches my anecdotal experience.
To the contrary. It's possible that the correlation is caused solely by a culture that raises owls as larks, "dumbing down" the latter with individuals maladapted to the lark life style. The effect could be increased by smarter owls being able to resist the conversion therapy a little better than less smarter owls – resulting in a selection bias.
The obvious conclusion to me is that there is no strong effect. Or that at some portions of the year, or parts of the globe, certain chronotypes have advantages, this certainly matches my anecdotal experience.