Here are the results of perhaps the first major study in this area:

Starting the school day 50 minutes later has a significant positive effect on student achievement, which is roughly equivalent to raising teacher quality by one standard deviation. [Source]

Basically the finding is this:

Our results show that starting the school day later in the morning has a significant positive effect on student academic achievement. We find that when a student is randomly assigned to a first period course starting prior to 8 am, they perform significantly worse in all their courses taken on that day compared to students who are not assigned to a first period course. Importantly, we find that this negative effect diminishes the later the school day begins.

We verify that the negative start time effect is not solely driven by worse performance in the first period class. Hence, our results show that student achievement suffers from earlier start times in not only courses taken during the early morning hours, but also throughout the entire day.

Study

Carrell, Scott E., Teny Maghakian, and James E. West. 2011. "A's from Zzzz's? The Causal Effect of School Start Time on the Academic Achievement of Adolescents." American Economic Journal: Economic Policy, 3(3): 62–81.

DOI:10.1257/pol.3.3.62

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