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