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Equity Risk Factor Models 367 Academics and industry professionals have conducted a wide array of research


into measuring and identifying so-called global factor returns. The broad thrust of this research has focused on understanding better the relative importance of industry, country, and global factors. We summarize this literature in terms of five key points: 1.    Holding all other things equal, the standard deviation of factor returns is a measure of the relative importance of a factor in explaining risk. The rationale is that if a factor is going to explain variability in returns it has to have some variability itself. 2.    Improving industry classifications from "broad" to "narrow" appears to increase the relative importance of industries. 3.    Over the past two years, industries appear to play a more significant role within Europe than they do worldwide. 4.    Within Europe, the relative importance of industries has been increasing over time. 5.    It is misleading to analyze the correlations of country and industry indexes over time because they do not provide hard evidence about the relative importance of industry and common factors. In short, it is difficult to disentangle industry and country effects from the returns on observed indexes. A factor model, which we explain later, allows one to separate country from industry effects. Ultimately, the scope for active strategies along the industry dimension will be determined by the relative importance of industry factors in explaining security returns, by managers' ability to predict the future evolution of these factors, and by the degree of liquidity in industry indexes. CountPy and Currency Effects Country and currency exposures depend on the geographical distribution of a firm's activities. For example, a company with a headquarters in the United States but with most of its costs and sales in Germany and Japan would have country exposures to Germany and Japan, and currency exposures to the euro and yen (vs. the U.S. dollar). In order to properly account for these exposures, a global equity factor model needs to incorporate both country and currency factors. Typically, and as shown below, country factors explain the cross-sectional variation in local returns. Currency factors, on the other hand, explain the total (currency plus local) returns. Modeling Global Equities In a global equity model, risk is derived from estimating the covariance matrix of total returns, R(t). This involves volatilities and correlations among a variety of factor returns, including industries, investment styles, countries, and currencies. In practice, there is a trade-off between the number of factors that need to be estimated in a properly specified global equity model and the number of historical data points (returns) required to estimate a covariance matrix. We present four different methods of modeling global equities, which are variations of the linear cross-sectional factor model discussed earlier. These models are: (1) global equity (cross-sectional) factor model, (2) combined single region model (SRM), (3) block diagonal model, and (4) an enhanced block diagonal model.