Optimal portfolio selection and dynamic benchmark tracking

This paper analyzes different approaches to portfolio selection when the requirement to portfolio performance is formulated relative to a given benchmark. For example, it may be desirable to track a market index as closely as possible. We develop several portfolio selection algorithms based on different perceptions of risk and different risk/target measures, ranging from the traditional variance to the more modern value-at-risk. In a dynamic setting we address the issue of optimal portfolio rebalancing. We develop an algorithm for determining whether or not to rebalance a given portfolio, based on transaction costs and new information about market conditions. Our approaches are tested on a set of stock data from the Oslo stock exchange.