Algebraic Analysis of Optimal Investment Portfolios

Manuel Tarrazo

《Advances in Investment Analysis and Portfolio Management》 4期 (2010/08) Pp. 113-152

https://doi.org/10.6291/AIAPM.2010.04.05

並列摘要

The motivation for this study was to unmask flaws in portfolios allowing for short sales. By inspecting determinants, eigenvalues, condition numbers, norms and convergence rates, we have found that short sales portfolios have worse structural stability and less reliable optimal weights, are harder to manage, and exact more costly implementation than their no-short sales counterparts. It is possible that some of the shortcomings of short sales portfolios are shared by certain hedged funds. We also show that algebraic indicators such as the condition numbers, although defined at the model level, also explain the variable-specific standard errors of optimal portfolio weights. Condition numbers can be used as a rule of thumb in portfolio construction-simply choose portfolios with low condition numbers-and as a formal ranking metric to select both nested and non-nested portfolio groupings. Similarity mappings and the special matrices used in portfolio optimizations (real, symmetric, and positive definite) endow condition numbers with economic, as well as numerical analysis, properties. In sum, it is contradictory to assume that investors care about risk and do not care about the safety of the container where they place their securities. Therefore, we recommend complementing indicators of portfolio mean-variance efficiency with algebraic indicators to determine their numerical quality, structural soundness, and stability, in addition to their financial desirability.

並列關鍵字

Short Sales ； Optimal Portfolios ； Hedged Portfolios ； Regressions ； Portfolio Optimizations ； Simultaneous Equations Systems ； Ill-Definition ； Similarity ； Congruence ； Equivalence ； Eigenvalues ； Eigenvectors ； Condition Number ； Convergence ； Iterations ； Singular Values

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