Residual risk factors, portfolio composition and risk measurement

When risk managers develop firm-wide measures of risk, the efforts can impose substantial costs both of developing information systems and, on an ongoing basis, of computation and aggregation. These costs can lead risk managers to base risk measures on a set of risk factors (including asset prices) of lower dimension than the dimension of underlying sources of risk. Such truncation of the set of risk factors, however, could cause risk measures to systematically underestimate a portfolio's risk. This paper presents examples where risk aversion leads a firm to hedge risk factors that have high explanatory power for many asset returns; however, the firm may remain exposed to other, less-important risk factors if their market price of risk is sufficiently high. Statistical techniques for identifying sources of risk that choose risk factors based on the variability of asset prices without taking account of the market price of risk could systematically underestimate portfolio risks. * We thank Henri Pages for helpful comments and suggestions. The views expressed in this paper are the authors' and do not necessarily reflect positions of the Federal Reserve Bank of New York, the Federal Reserve System, the Euro-Currency Standing Committee, or the Bank for International Settlements.