Model Uncertainty, Complexity and Rank in Finance
AbstractThere are three crucial mathematical system concepts in Finance, which are either being confused or misapplied - uncertainty, complexity and rank. First, the concept of epistemic uncertainty is sufficient for modeling and the concept of probability is unnecessary. This is illustrated by 'Galton's Error,' and the under-repesentation of systematic risk by American mutual funds. These funds use simple unidirectional projection ('regression') to compute Sharpe's beta for fund selection. There are at least five equivalent ways of representing the measured model uncertainty and a new and an improved risk categorization for mutual funds is presented. Second, the concept of (linear) system complexity is usually dealt with by presuming a model rank, as the Cowles Foundation erroneously prescribed in the early 1950s, and superimposing that model rank on the data, when a model is estimated. But the model rank does not have to be presumed: it can be identified from the data and all corresponding (Grassmanian) coefficients can be computed by CLS Projections. This is illustrated by the identification of the model rank of simple financial risk systems in six Asian countries, in particular in Taiwan. Third, often it is thought that Markowitz' portfolio optimization and exact and complete cash flow accounting are incompatible because of the non-existence, or empirical instability, of the information matrix. The problem is caused by the rank constraints imposed by the portfolio accounting identities. But these rank constraints also provide the solution, since they form exact selectors of the portfolio allocations, which are found by simple tensor algebra. This will be illustrated by the optimization of an Asian multi- currency stock investment portfolio.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0411013.
Length: 45 pages
Date of creation: 16 Nov 2004
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Note: Type of Document - pdf; pages: 45
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financial modeling; cash accounting; portfolio optimization; uncertainty; complexity; rank;
Find related papers by JEL classification:
- B40 - Schools of Economic Thought and Methodology - - Economic Methodology - - - General
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
- C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-11-22 (All new papers)
- NEP-IFN-2004-11-22 (International Finance)
- NEP-MIC-2004-11-22 (Microeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cornelis A. Los, 2004.
"Galton's Error and the Under-Representation of Systematic Risk,"
- Los, Cornelis A., 1999. "Galton's Error and the under-representation of systematic risk," Journal of Banking & Finance, Elsevier, vol. 23(12), pages 1793-1829, December.
- Cornelis A. Los, 2004. "Optimal Asian Multi-Currency Strategy Portfolios with Exact Risk Attribution," Finance 0409038, EconWPA.
- Cornelis A. Los, 1987. "Identification of a linear system from inexact data: a three variable example," Research Paper 8703, Federal Reserve Bank of New York.
- Los, Cornelis A., 1998.
"Optimal multi-currency investment strategies with exact attribution in three Asian countries,"
Journal of Multinational Financial Management,
Elsevier, vol. 8(2-3), pages 169-198, September.
- Cornelis A. Los, 2004. "Optimal Multi-Currency Investment Strategies with Exact Attribution in Three Asian Countries," Finance 0409047, EconWPA.
- R.E. Kalman & C.A. Los, 1987. "The prejudices of least squares, principal components and common factor schemes," Research Paper 8701, Federal Reserve Bank of New York.
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