one estimation universe, and one (complete) set of global factors is used to explain the cross-sectional variation in local stock returns. The term "global" is derived from the fact that returns to stocks issued in more than two countries around the globe are used in the cross-sectional regression to estimate factor returns. A primary advantage of this model is that it may not require a large number of factors. That is, the number of global factors is typically less than combining the factors from various single regions (such as the United States, Europe, and Japan). A potential drawback of this approach is the loss of power to explain the cross section of stock returns. 2.   Combined SRM global model (full-information methodology). This model starts out with factor returns from each of the SRMs. For example, we may have a total of four SRMs, one each for the United States, (Western) Europe, Japan, and Asia except Japan. We estimate the factor return covariance matrix by combining factor returns across all SRMs. This covariance matrix is then combined with the specific variances from the SRMs to form the total covariance matrix. 3.   Block diagonal model. Unlike the combined SRM model, we assume that the factor returns among different SRMs are uncorrelated and we estimate the factor return covariance matrix for each SRM separately. In fact, this is not a model of returns. Instead, it is a compilation of the various single region (local) covariance matrices. According to this approach, we start with the single region covariance matrices estimated using the techniques described earlier in the chapter. For example, we may estimate factor covariance matrices for the single regions: United States, Canada, continental Europe, United Kingdom, Japan, and Asia except Japan. Each region's factor covariance matrix represents a block. We then assume zero correlation among the blocks. So, for example, we assume that the U.S. equity market factors (and specific returns) are uncorrelated with the factors that explain the Canadian equity market. Specific risk is treated in an analogous manner to factor risk. A primary practical advantage of the block diagonal approach is that it provides managers with the same risk estimates as the single region models. So, for example, a U.S. equity portfolio's risk that is generated from a U.S. single region model is the same as that from the block diagonal model. An important disadvantage of the block diagonal approach is that it assumes zero correlation between major equity markets (such as the U.S. and Canadian markets). 4. Enhanced block diagonal model. According to this methodology, SRMs are used to estimate factor return risk similar to the way they were applied in the block diagonal model. However, it is no longer assumed that the factor returns across SRMs are uncorrelated. Rather, we estimate the correlations among fac tor returns of different SRMs and incorporate them into the block diagonal model. An algorithm has been developed and applied to ensure that the result ing factor return covariance matrix is fully consistent. A primary advantage of this approach is that it takes into account potentially important correlations among SRM factor returns. However, unlike the other methods discussed, this approach can be more computationally intensive. Table 20.5 provides a brief comparison of these four methodologies.