On the use of the Moore–Penrose generalized inverse in the portfolio optimization problem

Miyoung Lee and Daehwan Kim

Finance Research Letters, 2017, vol. 22, issue C, 259-267

Abstract: When the number of assets (N) exceeds the number of time periods (T), the sample covariance matrix is singular, and the portfolio optimization problem cannot be solved via traditional mean-variance algebra. In such a case, the Moore–Penrose (MP) generalized inverse becomes handy: In this paper, we critically examine the MP solution of the portfolio optimization problem. Our findings include: i) the MP solution leads to a portfolio of “pseudo-riskfree composite assets”; ii) it is orthogonal to principal components, iii) most importantly, it is poorly diversified. We illustrate our findings using equity market data.

Keywords: Portfolio optimization with singular covariance matrix; Moore–Penrose generalized inverse; Minimum norm; Principal component; Diversification (search for similar items in EconPapers)
JEL-codes: C38 C60 G11 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:22:y:2017:i:c:p:259-267

DOI: 10.1016/j.frl.2016.12.017

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