It sounds as though the quotation is talking about emerging market countries. An investor keeps a collection of diversified stock in his holdings. This is the asset allocation of his portfolio holding. He will usually keep some of his stocks in emerging market countries. A young emerging market country's economy is expected to grow rapidly. The stock holdings of the country should grow rapidly as the economy grows. However, as the country matures its economic growth should begin to slow. The investor should then take some of this emerging market investment and invest it in a young country with expected rapid economic growth. In this way, his emerging market investments should grow with the young country. In this way he hopes to achieve above average growth of his investment.

As the story of [a country name] matures, one’s [the country name] exposure should mature with it to include stocks listed in other countries in order to maintain exposure to above average growth.

I'm guessing it is related to investment. and I found that exposure means the proportion of asset which is exposed to the risk of fluctuatoin. But I have no idea what this whole sentence means.

English is not my first language. I would appriciate it, if you could make it very very very clear to understand.