Abstract: Models that are based on mean-variance analysis seek portfolio weights to minimise the variance of the portfolio for a given level of return. The portfolio variance is measured using a covariance matrix that represents the volatility and correlation of asset returns. However these matrices are notoriously difficult to estimate and ad hoc methods often need to be applied to limit or smooth the mean-variance efficient allocations that are recommended by the model. Moreover the mean-variance criterion has nothing to ensure that tracking errors are stationary. Although the portfolios will be efficient, the tracking errors will in all probability be random walks. Therefore the replicating portfolio can drift very far from the benchmark unless it is frequently re-balanced.