Returns Measured for Managed, Benchmark, and Active Portfolios         In Single Source Contribution To Return Country Model? Country Total and local return Total and local Possibly Currency Total return Currency No Investment style Total return and local return Total Yes Industry and       sector Total and local return Total and local Yes Asset Total and local return Total and local Yes Cross product Total return Total No The managed portfolio's total return, rAt), is written as (from 19.56): ,(t) = YwUt-l)K(t) n=\ N N N ^wUt-l^i^ + ^wUt-lW^+^wUt-lWifit^it) 72=1 72=1 72=1 = £t(t) + et(t) + xcp(t) (19.57) From equation (19.57), we see that the managed portfolio's total return is the sum of: 11 Its local return, £p(t). 11 The portfolio's exchange rate return, &p(t). 11 A cross term, which is the product of the exchange rate return and local returns, xcp{t). The Global Factor Model A global factor model expresses the cross section of total asset returns in terms of local factors, exchange rate returns, and cross terms. Mathematically, the model is R(t) = Bt{t- 1)F (t) + u* (t) + £ (t) + xc(t) (19.5! Let wm{t- 1) represent market portfolio weights. The portfolio return wm{t- l)TR(t) may be decomposed into the following sources: country, currency, investment style, industry, sector, and specific contribution. The specific return contribution to total return is based on the term wm{t - l)Tu (t). Similarly, the currency contribution is given by wm(t - 1)TE: (t). This contribution can be decomposed into two parts-the forward premium and a surprise currency change.11 "References include: G. P. Brinson and N. Fachler, 1985, "Measuring Non-U.S. Equity Portfolio Performance," Journal of Portfolio Management, Spring; and E. M. Ankrim and C. H. Hensel, 1994, "Multicurrency Performance Attribution," Financial Analysts Journal, March-April, 29-35.