How To Fix TE256 - Cholesky decomposition fails, despite adding &1 to diagonal elements

SAP Error Message - Details

• Message type: E = Error

• Message class: TE - Market Risk Management

• Message number: 256

• Message text: Cholesky decomposition fails, despite adding &1 to diagonal elements

What causes this issue?

Cholesky decomposition of the original covariance matrix could not be
performed successfully. Subsequently, the system automatically altered
the covariance matrix to achieve positive definiteness, but not in the
material sense. This was achieved by adding a small number (epsilon) to
all diagonal elements of the matrix. However, even when epsilon = &V1&
is added, Cholesky decomposition cannot be performed successfully.

System Response

Given that adding larger amounts to the diagonal elements of the
covariance matrix might have material effects, the system stopped
altering the covariance matrix and stopped further processing of the
risk calculation.

How to fix this error?

You can use the function <LS>Matrix Checks for Risk Analytics</>
(transaction
<DS:TRAN.RMCOV>RMCOV</>, which calls program <AB>RFTBB_MATRIX_CHECK</>)
to analyze erroneous correlation and covariance matrices. Furthermore,
you can analyze the volatilities and correlations used by checking the
calculation basis available in transactions
<DS:TRAN.RMV0>RMV0</> (VaR) or <DS:TRAN.RMC0>RMC0</> (CFaR).

Procedure for System Administrators

The system issues an error message and will not allow you to continue with this transaction until the error is resolved.

Error message extract from SAP system. Copyright SAP SE.

Smart SAP Assistant

• What is the cause and solution for SAP error message TE256 - Cholesky decomposition fails, despite adding &1 to diagonal elements ?

  The SAP error message TE256, which indicates that "Cholesky decomposition fails, despite adding &1 to diagonal elements," typically arises in the context of financial calculations, particularly in the area of risk management or portfolio optimization. This error is related to numerical stability issues when attempting to perform Cholesky decomposition on a matrix that is not positive definite.
  Cause:
  
  
  Matrix Not Positive Definite: The primary cause of this error is that the matrix you are trying to decompose is not positive definite. This can happen if:
  
  The matrix has negative eigenvalues.
  The matrix is singular or nearly singular.
  There are issues with the data used to construct the matrix, such as incorrect or inconsistent values.
  
  
  
  Data Quality Issues: If the input data used to create the covariance or correlation matrix is flawed (e.g., contains outliers, is not representative, or has missing values), it can lead to a non-positive definite matrix.
  
  
  Numerical Precision: In some cases, numerical precision issues can lead to a matrix being treated as non-positive definite when it is very close to being so.
  
  
  Solution:
  
  
  Check Matrix Properties: Ensure that the matrix you are trying to decompose is indeed positive definite. You can do this by checking the eigenvalues of the matrix. All eigenvalues should be positive for the matrix to be positive definite.
  
  
  Regularization: If the matrix is not positive definite, you can try to regularize it by adding a small value (e.g., a small constant like 0.01) to the diagonal elements of the matrix. This is often referred to as "shrinkage" and can help stabilize the decomposition.
  
  
  Data Validation: Review the input data for any inconsistencies or errors. Ensure that the data used to construct the matrix is accurate and complete. Look for outliers or extreme values that may be affecting the matrix.
  
  
  Alternative Decomposition Methods: If Cholesky decomposition continues to fail, consider using alternative methods for matrix decomposition, such as Singular Value Decomposition (SVD) or Eigenvalue Decomposition, which may be more stable in certain cases.
  
  
  Consult Documentation: Check SAP documentation or support resources for any specific recommendations related to the error message TE256. There may be patches or updates that address this issue.
  
  
  Related Information:
  
  Cholesky Decomposition: This is a method for decomposing a positive definite matrix into the product of a lower triangular matrix and its transpose. It is commonly used in numerical methods for solving systems of linear equations, optimization problems, and simulations.
  Positive Definite Matrix: A matrix is positive definite if all its eigenvalues are positive, which implies that it is invertible and has a unique Cholesky decomposition.
  SAP Modules: This error may be encountered in various SAP modules, particularly those related to financial analytics, risk management, or any module that involves matrix calculations.
  
  If the problem persists after trying the above solutions, it may be beneficial to reach out to SAP support for further assistance, providing them with details about the specific context in which the error occurs.