A series of recent studies in economic growth theory have considered a class of models of international borrowing where, in the absence of a perfect investment commitment, the borrowing constraint depends on the historical performances of the country. Thus, a better level of past economic activity gives a higher reputation, thereby increasing the possibility of accessing the international credit market. This note considers this problem in a stochastic setting based on the volatility of the internal net capital. We study how the optimal consumption level and the maximal expected welfare depend on the combined influence of the trajectory of past economic variables and the volatile environment. In particular, we show how the strength of the history effect and the relative weight of the historical performance depend on the degree of risk.