The objective of this thesis is to investigate performance for dierent investment alternatives for an investor wanting to track a multidimensional stock index. Performance is measured in terms of transaction cost, active return against the index and tracking error. The problem is approached by comparing performance for a full replication strategy against a strategy in which the traded portfolio is a dimension reduction of the index as well as against a strategy, trading the dimension reduced portfolio, aiming to predict and in turn minimize transaction costs. The full replication case and the dimension reduction case trade with a volume-weighted strategy, whilst the last strategy trades at times historically being least expensive to trade at. The dimension reduction is done based on results from a principal component analysis together with empiric results on transaction costs associated with trading a certain stock. The transaction cost prediction model implemented is the PAR-model, presented by Rashkovich and Verma (2012). The results show that when reducing the dimension of the index, meaning that stocks with undesired characteristics can be excluded, performance is improved. The transaction cost minimizing strategy show some improvement against the full replication strategy, but its performance is inferior to trading a dimension reduced portfolio with a volume-weighted strategy. This highlights the diculties in predicting stock market behavior. Hence, the strategy recommended for an investor wanting to track a multidimensional index is to conduct a dimension reduction according to preferences and use a volume-weighted trading strategy
