EDHEC-Risk Institute October 2016

Multi-Dimensional Risk and Performance Analysis for Equity Portfolios — October 2016

1. Literature and Practice Reviews

B i,t,c ( R ) in Equation (1.10) are predetermined exposures describing the relevant asset characteristics: local market, industry and risk index exposures. The Global Equity Model assigns assets to industry categories by mapping industry data to MSCI or FT classifications. GEM assigns each security to a single industry; hence industry factor exposures are 0 or 1 for each asset. Industry risk exposures indicate the percentage of total portfolio value in each industry classification. They use the same methodology for country factor exposures; GEM assigns each security to a single country, so that country exposures are also 0 or 1 for each asset. The risk indices used are the size index, the success (momentum) index, the value index and the variability in market index (volatility historical index). Risk index are defined as z-scores of companies within companies of the same country. For example, a firm whose size would be the average size of all companies would have a zero exposure to the size factor. The Global Equity Model allows to compare local country factor returns, local risk index returns, local industry returns across countries and to access the contribution of each factor relative to the others. For instance, Grinold, Rudd and Stefek (1989) examine the statistical significance of each factor’s return or the absolute level of volatility of each factor across countries. ( C ) , B i,t,s ( s ) and B i,t,r

If a stock is quoted in another currency than the dollar, the decomposition in Equation (1.10) is applied to the local currency returns, and the dollar return is expressed as the sum of the local return and a currency return. Figure 5 summarises the decomposition process. Menchero and Morozov (2011) investigate the relative importance of countries and industries across the entire world by constructing a global factor model containing one world factor, 48 country factors, 24 industry factors, and 8 risk index factors. Following the BARRA Global Equity Model (1998), they assign country exposures and industry exposures thanks to MSCI classification and every stock is assigned an exposure of 1 to the world factor. The 8 risk indexes factors are volatility (essentially representing market beta), size, momentum, value, growth, leverage, liquidity, and non-linear size. The authors use local excess returns in all regressions; this eliminates currency effects and allows them to have a common basis to compare countries and industries.

1.3.2 Extending a Set of Pricing Factors with Ad-Hoc Factors

While Barra model treats factor exposures as predetermined quantities, it is also possible to add new factors to a set of pricing factors and to estimate the

Figure 5: Excess Return Decomposition with the Global Equity Model

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