This is a good question. It is probably good to start with a definition of what a Frontier Market is. Frontier markets are a subsection of Emerging Markets. You can think of the beginning stages of an Emerging Market. The word was coined probably around 1990.
The weakness of investing in such a market is that it has little money and for this reason what capital you put in can disappear if that economy does not get off the ground. This is a real risk. To get an economy or market going is not easy. Second, the country lacks financial experience. For this reason, there will be unforeseen hardships.
The strengths are twofold. First, you might be one of the first people investing in a market that can boom. The profits can be great. Second, by definition Frontier Markets have not emerged. This means there can be serious upside, because the markets are not overextended or saturated. In other words, there is room for growth.