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Equity Risk Factor Models 369 TABLE 20.5 A Comparison of Methods Methodology Pros Cons  


Global equity risk model Accounts for correlation (among factor returns) when estimating factor returns Combined SRM   Directly incorporates factor returns from SRMs   Handles portfolios with high concentrations Block diagonal model Risk estimates consistent with SRMs Handles portfolios with high concentrations Enhanced block Addresses con in the block diagonal model diagonal approach Handles portfolios with high concentrations Problems with portfolios that have highly concentrated exposures Large number of factors Assumes zero correlation among SRM factor returns Computationally intensive Global Equity Factor Model In this approach, we define a set of global factors- which may simply be the entire set of single country factors-and estimate the co-variance matrix of these factors and the respective specific volatilities. One specification of a global equity factor model can be written as R(t) = R^t) + Eft) + xc(t) R*(t) = G(t) + S(t-l)Fs(t) + I{t-l)Fft) + C(t-l)Fc(t) + u(t) (20.43) where R{t) = N X 1 vector of local excess returns from time t-ltot. That is, the return expressed in local terms over the local risk-free rate. R?n{t) is the return on the "th asset. G(t) = Constant term (across all assets) at time t. In certain situations- see Heston and Rouwenhorst (1994)-G(t) represents a "global factor return"-that is, a return on a globally diversified portfolio of returns contained in Re(t). S(t - 1) = N X M matrix of investment style exposures at time t-1. SJt - 1) is a vector of M investment styles for the wth asset. I{t -1) =N X / matrix of industry exposures at time t-1. I ft - 1) is a vector of/ industry exposures for the nth asset. C(t- 1) =NxK matrix of country exposures at time t-1. C (? - 1) is a vector of K country exposures for the nth asset. Fs(t) = M X 1 vector of returns on investment styles (factor returns) from time t-ltot. FSm(t) is the return on the mth investment style. Fs(t) = } X 1 vector of industry returns (factor returns) from time t - 1 to t. F} (t) is the return on the /th industry. Fc(t) = K X 1 vector of country returns (factor returns) from t-1 to t. Fc k(t) is the return on the &th country. u(t) = N X 1 vector of specific returns (on local equity) from time t-1 tot.