Index-tracking is a form of passive fund management. The index-tracking problem is the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index. This approach differs from the full replication strategy, where a fund purchases all the stocks that make up a particular market index. A passively managed fund whose objective is to reproduce the return on an index is known as an index fund, or a tracker fund. The classical index-tracking approach represents the problem in a least square framework with errors computed using a sample of historical data. A new approach described in N. C. P. Edirisinghe “Index-tracking optimal portfolio selection” Quantitative Finance Letters, Vol. 1, 16-20, (2013), which this report is based on, replaces the classical risk measure of portfolio variance by the variance of tracking errors between stochastic index return and the return on the portfolio selection. In this report we formulate the index-tracking portfolio optimization model and present an illustrative example where we compare the presented model with the classical Markowitz mean-variance portfolio optimization model.