It will be examined what the optimal trading strategy is for an investor when trading costs are present. This will be done for different portfolios. The trading costs are assumed to be proportional to the amount of each asset traded. Amongst other findings, it was found that for periodic rebalancing the yearly interval and for no-trade region rebalancing the 1% interval provide the investor, with risk aversion A = 10, with the highest utility as well as the highest absolute return. When the different scenarios were compared to the benchmark scenario, which is a scenario without rebalancing, it was seen that the returns of the benchmark cases are most of the time higher. However, due to the fact that the standard deviation of these scenarios is also higher, the higher return is offset and there are scenarios with rebalancing which still provide the investor with a higher utility.

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