This paper presents an optimal portfolio balancing strategy in discrete time for a crra investor, such as a pension fund, who invests only on one risk-free asset and one risky asset where both xed and (linear) proportional transaction costs exist. Based on our theoretical results, we provide a heuristic that can generate an approximate solution to this problem while considering periodic (negative or positive) changes in net contribution, which occurs often for pension funds. According to our computational results, our optimal asset allocation strategies match actual asset allocation schemes of some internationally renowned pension funds. Furthermore, we also learned that net contribution and liquidity have signicant impacts on an optimal asset allocation of a pension fund.