The Importance of Asset Allocation: A Mathematical Proof

Posted: 25 Nov 2014 Last revised: 4 Nov 2015

See all articles by Yongjae Lee

Yongjae Lee


Woo Chang Kim

Korea Advanced Institute of Science and Technology (KAIST)

Date Written: October 2015


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.

Keywords: Asset Allocation, Security Selection, Portfolio Performance Evaluation

JEL Classification: G10, C60

Suggested Citation

Lee, Yongjae and Kim, Woo Chang, The Importance of Asset Allocation: A Mathematical Proof (October 2015). Available at SSRN: or

Yongjae Lee

UNIST ( email )

gil 50
Ulsan, 689-798
Korea, Republic of (South Korea)

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Woo Chang Kim (Contact Author)

Korea Advanced Institute of Science and Technology (KAIST) ( email )

373-1 Kusong-dong
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

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