we computed the absolute and relative marginal contribution to the factor component of tracking error for a given change in the underlying asset position. Next, we compute the impact on tracking error from changing a portfolio's exposure to a factor. We begin by defining a 1 X K vector of active factor exposures b"(t - 1). ba(t-l) = wa(t-l?B(t-h) ^w:(t-i)Bn!l(t-b)^w:(t-i)Bn!2(t-b)-- ^K$-W^{t-h)---'Yu£{t-\WntK{t-h) n=\ "=1 (20.82) Absolute marginal factor contributions to tracking error (AFCTE) are computed with respect to each of the K elements in b"{t - 1). Specifically, the contribution to total tracking error from each of the K factors is given by the Kxl vector. AFCTE= doa(t) I,(t\t-l)b*(t-lj1 oa(t) l(t-l) (20.83; There are two things to note about the absolute marginal contributions to tracking error by factor: 1. AFCTE is a K X 1 vector whose kxh element is the marginal contribution to tracking error from the kxh factor. AFCTE- = d<5*(t) _1l(t\t-l)b£(t-lj1 oa(t) '(t-1) (20.S 2. AFCTE does not contain any specific risk terms because specific risk does not contain any factor exposures. AFCTE can also be written in relative terms, that is, as an RFCTE. The &th term of the relative marginal factor contribution to tracking error (RFCTE,) is RFCTE, = 3o'(*)/o'(*) Jtit-lfx db%(t-l)/b£{t-l) oa(t) (20.85; Note that the sum of the RFCTE^'s is equal to the proportion of factor risk in tracking error. That is, 5>FCTE,=X- S=l ;=1 :(t-iy Ga(t) x AFCTE k = <3*(tf (20.S