Method and system for multi-period performance attribution with metric-preserving coefficients

Abstract

A method for arithmetic performance attribution which accurately links single-period attribution effects over multiple periods. In preferred embodiments, the method determines portfolio relative performance over multiple time periods (t=1, 2, . . . , T) as a sum of terms of form R - R _ = ∑ i ⁢ ⁢ t ⁢ ⌊ c 1 ⁢ a i ⁢ ⁢ t + c 2 ⁢ a i ⁢ ⁢ t 2 ⌋ , where ait is a component of active return for period t, the summation over index i is a summation over all components ait for period t, R ⁢ ⁢ is ⁢ ⁢ R = [ ∏ t = 1 T ⁢ ( 1 + R t ) ] - 1 , ⁢ R _ ⁢ ⁢ is ⁢ ⁢ R _ = [ ∏ t = 1 T ⁢ ( 1 + R _ t ) ] - 1 , Rt is a portfolio return for period t, Rt is a benchmark return for period t, and the coefficients c1 and c2 are c1=A, and c 2 = [ R - R _ - A ⁢ ∑ j ⁢ ⁢ t ⁢ a j ⁢ ⁢ t ∑ j ⁢ ⁢ t ⁢ a j ⁢ ⁢ t 2 ] . More generally, the invention is an arithmetic method for determining portfolio relative performance over multiple time periods (t=1, 2, . . . , T) as a sum of terms of form: R - R _ = ∑ i ⁢ ⁢ t ⁢ ∑ k = 1 ∞ ⁢ c k ⁢ a i ⁢ ⁢ t k , where ait is a component of active return for period t. In preferred quadratic implementations (in which the only nonzero coefficients ck are those for which k=1 or k=2), the coefficients c1 and c2 are defined as in the above-mentioned preferred embodiments. In all embodiments, the method of the invention is metric preserving at the component portfolio level. Other aspects of the invention are a computer system programmed to perform any embodiment of the inventive method, and a computer readable medium which stores code for implementing any embodiment of the inventive method.

Dependencies are inferred from the claim text.