definition of a compounded return, the answer is [1 + 51(t)][l + St(t + 1)]. According to (19.28), however, the answer is not straightforward due to the cross terms between the first and other sources. All the terms in (19.28) containing the first source are: 1 + SJt) + SJt + 1) + S^SJt + 1) + S^Sft +1) + s^sjt +1) + sjtpjt + i) + s^s^t +1) {^-iy) which does not equal [1 + 51(t)][l + St(t + 1)]. Quickly, one can see that the problem of isolating sources of return becomes unwieldy as the compounding period (T) increases along with the number of factors (K). Developers of commercially available software that generates performance attribution reports appreciate the problems associated with computing multiperiod attribution and employ methods for handling this issue. Most vendors have their own proprietary methods for computing multiperiod return attribution (i.e., linking sources of return over time). Next, we present two methodologies to link sources of return. The first methodology presented was proposed by the Frank Russell Company. An advantage of the methodology that we present is that it is relatively simple and, therefore, it facilitates the explanation of the numerous issues associated with linking returns. Methodology for Linking Sources Of Return There are quite a few different methods for combining attribution effects over time. A recent summary of these methods can be found in Mirabelli (2000/2001). Among them is a simple yet effective methodology proposed by the Frank Russell Company.10 This methodology is based on the differences between so-called continuously compounded (log) returns and discretely compounded (percent) returns. Before we explain this methodology we review the differences between percent and continuous returns. Earlier, we defined the one-period local return for the Kth asset as pt,t)=PUt) + d"(t-h>t)-P£(t-l) (1930) and its total return (including currency) as Rn(t) = Ri(t) + E!j(t) + Ri(t)xEij(t) (19.31) where Et(t) is the exchange rate return. The returns in (19.30) and (19.31) are in percent format. The continuous-time counterpart of (19.30) is the one-period log return, which is given by 10For details, see David R. Carino, of Frank Russell Company, Inc., 1999, "Combining Attribution Effects over Time," Journal ofPerformance Measurement, Summer, 5-14.