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 ] .

Abstract: A method for arithmetic and geometric performance attribution which accurately links single-period attribution effects over multiple periods. The arithmetic attribution method optimally distributes the residual to yield a minimum-distortion residual-free arithmetic attribution system. The geometric attribution method defines the attribution effects in terms of ratios. The arithmetic method determines portfolio performance over multiple time periods as a sum of terms of form (Rt? Rt)(A+?t), where the coefficients ?t are defined as ? t = [ R - R _ - A ? ? k = 1 T ? ( R k - R _ k ) ? k = 1 T ? ( R k - R _ k ) 2 ] ? ( R t - R _ t ) . The value of A is A = 1 T ? [ ( R - R _ ) ( 1 + R ) 1 / T - ( 1 + R _ ) 1 / T ] , where R? R, or, for the special case of R= R, A=(1+R)(T?1)/T, where T is the number of time periods.

Abstract: A method for arithmetic and geometric performance attribution which accurately links single-period attribution effects over multiple periods. The arithmetic attribution method optimally distributes the residual to yield a minimum-distortion residual-free arithmetic attribution system. The geometric attribution method defines the attribution effects in terms of ratios. The arithmetic method determines portfolio performance over multiple time periods as a sum of terms of form (Rt? Rt)(A+?t), where the coefficients ?t are defined as ? 1 = [ R - R _ - A ? ? k = 1 T ? ( R k - R _ k ) ? k = 1 T ? ( R k - R _ k ) 2 ] ? ( R t - R _ t ) . In preferred embodiments, the value of A is A = 1 T ? [ ( R - R _ ) ( 1 + R ) 1 / T - ( 1 + R _ ) 1 / T ] , where R? R, or, for the special case of R= R, A=(1+R)(T?1)/T, where T is the number of time periods.

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, . . .