We propose a multi-stage stochastic trading cost model in optimal portfolio selection. This strategy captures uncertainty in implicit transaction costs incurred by an investor during initial trading and in subsequent rebalancing of the portfolio. We assume that implicit costs are stochastic as are asset returns. We use mean absolute deviation as our risk and apply the model to securities on the Johannesburg Stock Market. The model generates optimal portfolios by minimizing total implicit transaction costs incurred. It provides least-cost optimal portfolios whose net wealths are better than those gener- ated by the mean-variance, minimax and mean absolute deviation models.