Numerical modelling apparatus

A method of performing numerical modeling of investment risk relating to financial assets using computer apparatus, the method comprising:

• receiving signals at an input unit of the computer apparatus, the signals containing data having information relating to set of financial assets;
• providing, by processor unit of the computer apparatus, matrix V, wherein the matrix V comprises plurality of elements, wherein each of the elements represents relationship of risk related to respective pair of the financial assets, and wherein each element is given by scalar product of two risk vectors, such that each of the financial assets has an associated risk vector according to the elements of the risk relation matrix;
• automatically decomposing, by the processor unit of the computer apparatus, the matrix V into eigenvectors and eigenvalues according to:
• V=E·Λ·E′
• wherein E is set of eigenvectors of the matrix V in columns, Λ is the corresponding diagonal eigenvalue matrix, and E′ is the transpose of E;
• providing, by the processor unit of the computer apparatus, dataset of portfolio weights w for each of the assets according to:
• w∝E·Λ−1/2·1
• where E is set of eigenvectors of the matrix V in columns Λ is the diagonal eigenvalue matrix and 1 is column vector all of whose elements are equal to one, wherein the portfolio weightings w are provided as column vector from:
• D
• =
• w
• ′
• ·
• E
• ·
• Λ
• 1
• /
• 2
• ·
• 1
• w
• ′
• ·
• V
• ·
• w
• where w represents column vector containing portfolio weights, E is the eigenvector matrix and Λ is corresponding diagonal eigenvalue matrix of the matrix V for the set of assets, and D is an Objective Function relating to the set of assets;
• and
• deriving, by the processor unit of the computer apparatus, components of each of the risk vectors in the basis of unit independent risks by the corresponding row of the matrix product E·Λ1/2 relating to each of the financial assets;
• and
• outputting, by the computer apparatus, the components of each of the risk vectors as a risk vector data set corresponding to investment risks relating to respective financial assets onto a tangible computer-readable recording medium or display device configured for use by user to evaluate portfolio of at least portion of the financial assets.

non-transitory tangible computer-readable recording medium having recorded thereon instructions to cause a computer apparatus to perform operations comprising:

• receiving signals at an input unit of the computer apparatus, the signals containing data having information relating to set of assets;
• providing, by a processor unit of the computer apparatus, matrix V, wherein the matrix V comprises plurality of elements, wherein each of the elements represents relationship of risk related to respective pair of the assets, and wherein each element is given by scalar product of two risk vectors, such that each of the assets has an associated risk vector according to the elements of the matrix;
• decomposing, by the processor unit of the computer apparatus, the matrix V into eigenvectors and eigenvalues according to:
• V=E·Λ·E′
• wherein E is set of eigenvectors of the risk matrix V in columns, Λ is the corresponding diagonal eigenvalue matrix, and E′ is the transpose of E;
• providing, by the processor unit of the computer apparatus, dataset of portfolio weights w for each of the assets according to:
• w∝E·Λ−1/2·1
• where E is set of eigenvectors of the matrix V in columns and Λ is the diagonal eigenvalue matrix and 1 is column vector all of whose elements are equal to one, wherein the portfolio weightings w are provided as column vector from:
• D
• =
• w
• ′
• ·
• E
• ·
• Λ
• 1
• /
• 2
• ·
• 1
• w
• ′
• ·
• V
• ·
• w
• where w represents column vector containing portfolio weights, E is the eigenvector matrix and Λ is corresponding diagonal eigenvalue matrix of the matrix V for the set of assets, and D is an Objective Function relating to the set of assets;
• and
• deriving by the processor unit of the computer apparatus, components of each of the risk vectors in the basis of unit independent risks by the corresponding row of the matrix product E·Λ1/2 relating to each of the assets;
• and
• outputting, by the computer apparatus, the components of each of the risk vectors as a risk vector dataset onto tangible computer-readable recording medium or display device.