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In this paper, I study a number of statistical issues that arise in the formulation of stress scenarios for market risk in financial instruments. The possibility of reducing the number of scenarios through the use of data-based, statistical dimension reduction methods is explored. Using data on returns to spot exchange, stock market and interest rate products for a number of countries, I show that principal components analysis may be used to reduce the effective dimensionality of the scenario specification problem in several cases. Given the data dimensionality uncovered by PCA for the datasets considered, various methods for specifying stress scenarios are discussed.