When Olympics are hosted every 4 years in a different country. It will lead to more problems than getting benefits to host country.
For example: once the games are done, all new stadiums and apartments build for Olympics are just used as tours for general public.
As we are witnessing for 2016 Rio Olympics, we are seeing lot of protest from local people. Even police protested: http://edition.cnn.com/2016/07/05/sport/rio-olympics-2016-security/
So the Proposed solution:
We can build a Olympic island, that is not part of any country. It is owned by IOC. Countries can invest money into it and they will get respective profits from their investment.
Every 4 years it can get upgrades and stuff like that.
IOC can build a plan how a country can invest a money into it.