I think Himeno gave you the correct answer.
In case you really wan tto do a RTW in less than 10 days: there is a way around;
Instead of doing JFK-LHR-HKG-NRT-LAX-JFK (as an example) you can do
JFK-LHR-HKG-NRT-LAX-BOS, then later BOS-SFO-JFK. Buy a BOS-NYC as a seperate ticket. You have a second (almost free) trip and get around the 10 days minimum.