the SRM factor return correlations that are different from the histories used to estimate the off-block correlations. The steps required to produce the asset return covariance matrix based on the enhanced block diagonal methodology are: Step 1 Estimate the block diagonal covariance matrix of factor and specific returns. Step 2 Estimate the complete, full-information factor return covariance matrix using the combined SRM methodology. We generate this by first defining the union of all factor returns-across all SRMs-and then estimating the correlation among these factor returns. Step 3 Complete the block diagonal factor return covariance matrix by filling in the off-diagonal blocks (i.e., the zeros) with the correlation estimates from the combined SRM matrix. An algorithm has been developed that performs this operation and that satisfies the following properties: II The blocks of the original block diagonal matrix remain unchanged. This ensures that the individual SRMs are fully consistent with the enhanced block diagonal covariance matrix. II The condition number of the completed block diagonal covariance matrix-the enhanced factor return matrix-is bounded to be less than or equal to some predefined value.17 This ensures that the final covariance matrix has the proper statistical properties and that the resulting covariance matrix is fully consistent (i.e., pairwise correlations make sense) and positive definite. 11 The completed covariance matrix converges to a positive definite matrix. Step 4 Create the covariance matrix of asset returns by combining the enhanced factor return covariance matrix with the specific return covariance matrix. MEASURING AND IDENTIFYING SOURCES OF RISK In this section, we present various measures of predicted risk as defined in the linear factor model. These measures range from tracking error and portfolio volatility estimates to contributions to risk by asset. A portfolio's sources of risk are determined by: II Each asset's exposure to some factor, regardless of whether that factor be the asset itself, some fundamental factor, or something else. ill The distribution of the returns on assets. II The weight of each asset in the portfolio benchmark (if applicable). 17Stated another way, the smallest eigenvalue of the enhanced correlation matrix is set arbitrarily close to the smallest eigenvalue of the block diagonal matrix.