True or False?
The statement is false. While the individuals referred to in the statement are obviously behaving sensibly in their own interests, when all individuals try to do this they will bid asset prices up in the higher interest rate countries and bid those higher interest rates back down to their equilibrium levels. While a single individual can gain from acting on her own, all individuals acting together cannot gain---the statement involves a fallacy of composition.
World asset prices will adjust relative to each other to their equilibrium levels where world investors are just willing to hold the existing stocks. It thus follows that for an increase in the interest rates in a particular small open economy to occur, world asset holders must have changed their opinion regarding the risk from holding the country's assets---those assets have come to be regarded as more risky, so their market prices fell and interest rates on them increased.