the subscript n refers to the nth asset and there are K (k = 1, . . . , K) countries, / (;' = 1, . . . , /) industries, and M (m = 1, . . . , M) investment styles. The model represented in equation (20.44) states that the local return on the nth asset is the sum of: Global factor return, G(t) Contribution from investment styles, SJt- l)Fs(t) Contribution from industries, In(t - l)Fs{t) Contribution from countries, CJt - l)Fc(t) According to this specification we can write the return on the ?zth stock that belongs to the ;th industry and kth country as R%t) = G(t) + SJt-l)Fs(t) + FJt) + FcJt) + ujt) (20.45) Equation (20.45) provides a rather restricted representation of reality even when viewed against the backdrop that models are supposed to simplify reality so that we can better understand and interpret complex phenomena. There are two major assumptions supporting (20.45): 1.    Industry effects are global. Alternatively expressed, each stock is allocated to one industry that represents a global industry (e.g., global automotive). This assumption ignores potentially strong regional effects that could result from differences in capital-labor ratios across countries. 2.    Securities in the same country have similar exposures to domestic and global factors. For example, Citigroup and JDS Uniphase are affected by the U.S. factor and the global factor in the same fashion. This is clearly unrealistic given the different exposure of each company to non-U. S. factors as reflected, for instance, in each company's proportion of foreign sales to total sales. Equation (20.44) may be estimated using least squares regression. While it is beyond the scope of this chapter to explain the estimation process in detail, we review some important issues related to estimating (20.44). II Since industry and country exposures sum to one across all stocks, we have two sources of perfect collinearity (including the constant vector). Therefore, we need to drop one industry and one country when estimating factor returns. In practice, one can get quite different estimates of factor returns depending on which variables are dropped from the regression. II Rather than arbitrarily choosing an industry (country) to interpret the industry (country) factor returns, we may measure the industry (country) factor returns relative to a value-weighted portfolio. In practice, this means that to estimate equation (20.44) using weighted least squares, where the weights are the market