returns. To compute multiperiod attribution, we begin with percent returns and convert these to log returns. Sources of return are defined in terms of log returns. The sources of return and the total portfolio return are then converted back to percent returns. Specifically, the approach works as follows. Step 1: Define portfolio returns in terms of percent returns and estimate the one-period sources of return. This allows us to write the portfolio percent return as the sum of K + 1 sources of returns. rp(t) = Ysk(t) (19-37) 6=0 Step 2: Convert each one-period portfolio percent return into a continuous portfolio return by multiplying equation (19.37) by the ratio of the portfolio log return to the percent return. This is done in two steps. First, create the adjustment factor: ^^)=pPof1liolgretum =H^ '=>""T <i9-38> Portfolio percent return rp (t +;) Second, multiply each source of return by the adjustment factor so as to convert the portfolio percent return into a portfolio log return. Multiply equation (19.37) by K(t + /') to get w('+>')=XK<'+>>s*<'+>> (19-39) 6=0 Equation (19.39) is the continuous time counterpart to the discrete portfolio return (19.37). The element k(? + j)Sk{t + ;') is the continuously compounded form of the source Sk(t + /). From our eariier discussion, we know that one-period log returns sum to multiperiod returns, that is, 00 = XW (f+;) <19"40> ;=0 Substituting (19.39) into (19.40) we have T K nl£(0 = XXK(f + ;)St(f + ;>S^ (19.41) ;'=0£=0