between the rth group's weight in the managed [iupt{t - 1)] and benchmark [wbt(t - 1)] portfolios. For example, if [wp(t - 1) - wb(t - 1)] is positive, then the managed portfolio is overweight relative to the benchmark portfolio. Difference between the return of the zth group in the benchmark portfolio and the benchmark portfolio's total return. Interaction effect. This term has no intuitive content. Its only purpose is to make the right-hand side of equation (19.13) add up to the total active return. The interaction effect of the z'th group is defined as I /(*) = £/,.(*) (19.17) where 1^) = ^ (t-l)-w^(t-l)\rKp{t)-r^b{t)\ To summarize the results, the stock selection and allocation effects are measures of specific levels of return attribution. The allocation effect measures a portfolio manager's ability to select different groups of stock. Stock selection, on the other hand, measures how well a portfolio manager selects stocks within a particular group. In this calculation, more weight is given to groups that have a higher weight in the benchmark portfolio. Why introduce the interaction effect? In order to get meaningful results it is important that the stock selection and allocation effects sum to the total active return. Unfortunately, stock selection plus allocation do not equal the total active return. To address this issue, the new term-the interaction effect-is created so that stock selection, allocation, and interaction sum to the total active return. In effect, the interaction term is a residual measure of performance. It captures what's left over after we account for stock selection and allocation. Is there any way to get rid of the interaction effect? There is. But we have to forfeit some intuition in terms of how we define stock selection. In some commercial attribution systems, stock selection is defined using the managed portfolio weight in place of the benchmark portfolio weight; that is, Si(t) = w*(t-l)[%p{t)-rub{t)\ (19.18) Given this definition, the sum of the stock selection and allocation (or group weight) effects is now equal to the active portfolio return. rs(t) =S(t)+A(t) (19.19) Which definition of stock selection is more appropriate? For managers who actively manage a portfolio against a benchmark, the stock selection measure that uses the benchmark weight is clearly a more relevant measure. That is to say, more importance should be given to groups of stocks that make up a larger part of the