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- Title
Some New Results in Theory and Application on Positive Definiteness of Portfolio Covariance Matrix.
- Abstract
Covariance matrix carries a big weight in the domain of portfolio. Most researchers spend more time on model construction, risk measurement and algorithm analysis, but paid little attention to the deeper theory research and rigorous proof on the positive definiteness of the covariance matrix. This paper aims to obtain the equivalent condition about the positive definite of covariance matrix. In theory, some innovative and significant results are identified by matrix theory on risk value range of equal weight portfolio and optimal portfolio. These results obtained by using rigorous mathematical proof in this paper can explain some actual portfolio problems about risk. In practice, four numerical examples are shown to verify the validity of the proposed lemmas and theorems. Finally, the results of this paper show that the positive definiteness of the covariance matrix will no longer be an assumption, but a condition of the rigorous theoretical basis, which provides theoretical support for the research of portfolio theory.
- Subjects
MATHEMATICAL proofs; LIFTING &; carrying (Human mechanics)
- Publication
IAENG International Journal of Applied Mathematics, 2021, Vol 51, Issue 1, p25
- ISSN
1992-9978
- Publication type
Article