Academic performance
If by cognitive function you mean IQ, then that's most of the focus of the intelligence research, as in the main motivation to study IQ. In one large UK study of children the correlation was 0.81.
But there are personality factors influencing academic performance as well. Even with respect to IQ [as measured in pracice], it is suspected that it is influenced in part by motivation, which itself may be an interaction between personality and the context/environment. And to the extent that self-discipline is different than [short-term] motivation, some research suggest it may matter even more for academic performance.