0   0 A2(t) 0 0 0 ABD(t) = 0 0   0 0   0 0 0   0   0 0 0 0 AM(t) (20. Finally, the global covariance matrix of security returns, based on the block diagonal factor return covariance matrix, is V(t) = aBD{t) + ABD(t) (20.' Currencies (and risk associated with currency exposures) can enter the block diagonal covariance matrix as a separate block. That is, it is assumed that currencies are uncorrelated with noncurrency factor returns so that the covariance matrix of asset returns can now be written as rBD V*u(t) =   V(t) 0 0 0 0 0 V2BD(t) 0 0 0 0 0   0 0 0 0 0 yfPit) o 0 0 0 o v{t) (20.50) where VBD(t) isaCxC covariance matrix of currency returns. The main problem with the block diagonal covariance matrix is that it ignores potentially important correlations. For example, if one block represents the United States and another Canada, it clearly would not seem credible to assume zero correlation among these equity markets. A natural next step would be to improve upon the block diagonal approach so that we are completely consistent with the single region models while, at the same time, estimating important correlations among factor returns. This leads to the enhanced block diagonal methodology, which is discussed next. Enhanced Block Diagonal Model In the enhanced block diagonal model, we attempt to provide the consistency that the SRMs offer while, at the same time, enabling us to estimate correlations between the SRM factor returns. In addition, we seek a methodology that is flexible enough to allow for situations where the blocks of the covariance matrix are estimated differently than the off-block elements. There are three situations where we may be required to use different estimation techniques for the block and off-block elements of the factor return covariance matrices. First, there may be too many factors when we consider the union of all SRM factor returns. This can lead to problems when estimating the combined SRM. Second, there may be situations where the SRM covariance matrices are available but not their underlying factor returns. In this case, we may need to use proxy factor re-