industry factor returns is equal to zero, and (2) the sum of market capitalization weighted country factor returns is equal to zero. II The constant in this regression is equal to the value-weighted return on the portfolio of all stocks in the cross-sectional regression. One interpretation is that the constant is the "global" factor return. In the case of a local model, note that if we add a constant term to the regression model, this would be equivalent to assigning a beta of one to each asset. In this case, the return on the local market is the estimate of the coefficient on the constant. Combined SRM In the combined model, factor returns are first estimated for each single region model using the techniques outlined earlier in the chapter. The exact definition of the single region model, and in particular what geographical area it covers, is up to the developer. For developed markets, single region models are typically defined for Canada, United States, western continental Europe, United Kingdom, Japan, and Pacific Rim. The factor return covariance matrix used to estimate risk is generated from taking the union of all SRM factor returns. This approach directly accounts for correlation between all factors. Block Diagonal Model In the block diagonal approach, there is no formal model of asset returns as in (20.44). Instead, this approach works as follows: Assume there are M (m = 1, . . ., M) single region models (i.e., factor and specific return co-variance matrices). For each single region model, the security return covariance matrix is expressed by V"(t) = Bm£lm{t)BmT + Am(t) for m = 1, . . . , M (20.' where Vm(t) =N xN covariance matrix of security returns at time t for mth model. Bm = Nm X Km matrix of exposures to investment style, industry and local market for mth model. Q"(t) = K X,K covariance matrix of factor returns at time t for mth model. Am(t) = Nm X Nm diagonal matrix of variances of specific returns at time t for mth model. In order to compute the risk of global equity portfolios, we generate an N X N matrix of security returns as follows: First, construct the global covariance matrix contribution to the total covariance matrix. This term is given by QBD(t) =   tfn1^7 0 0 0   0 0 B2n2(t)B2T 0 0   0 0 0   0   0 0 0 0     0 0 0 0 0 B MnM(t)BMT (20.47) Note that Q?D(t) incorporates the factor exposures from the SRMs. Next construct the global matrix of specific variances. This term is given by