The Importance of Asset Allocation : A Mathematical Proof

This paper aims to provide a mathematical justification for asset allocation. Asset allocation is widely employed in practice, yet the question of its efficiency remains open. Asset allocation allows portfolio managers to concentrate on a relatively small number of assets, while security selection offers a bigger opportunity set for those who are capable of managing a large number of securities. In this paper, we study the trade-off between the ease of managing a portfolio and the size of opportunity sets depending on the number of securities under management. We derive and compare analytical expressions for the portfolio performances of asset allocation and security selection, and find that a majority of portfolio managers can actually benefit from employing asset allocation. Furthermore, the results are demonstrated empirically