Balanced baskets: a new approach to trading and hedging risks

ABSTRACT A basket is a set of instruments that are held together because the set's statistical profile delivers a desired goal, such as hedging or trading, that cannot be achieved through the individual constituents, or even subsets of them. Multiple procedures have been proposed for computing hedging and trading baskets, among which balanced baskets have attracted significant attention in recent years. Unlike principal component analysis methods, balanced baskets spread risk or exposure across their constituents without requiring a change of basis. Practitioners typically prefer balanced baskets because their output can be understood in the same terms they have developed an intuition for. We review three methodologies for determining balanced baskets, analyze the features of their respective solutions and provide Python code for their calculation. We also introduce a new method for reducing the dimension of a covariance matrix, called covariance clustering, which addresses the problem of numerical ill-conditioning without requiring a change of basis.