This paper investigates the adequacy of various principal components (p.c.) approaches as data reduction schemes for processing contingent claim valuations on baskets of equities. As a general proposition we are interested in discovering possible features and rules-of-thumb for the applicability of p.c. techniques. In particular, what accuracy does one lose in valuation-hedging schemes as the dimensionality of the p.c. space is reduced? We also have an interest in validating the posted “stylized” facts of implied volatility as they apply to our data sets.