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Finance

FIGURE 1 9.3 Breakdown of Contributions from Finance

More detail is of course available. Figure 19.3 shows the breakdown at the stock level of the contributions from finance, providing for each stock the return and average active weight over the period that contributed to the overall performance versus benchmark.

Next, we explain the issue of linking daily returns in multiperiod return attribution.

Multiperiod Attribution

Return attribution begins with calculating sources of return over a single time period (e.g., one day). Single period sources are then compounded, or linked, so that returns are computed over multiple periods (e.g., one month). Multiperiod attribution requires that we compound each group's (or factor's) contributions so that the sum of the compounded group contributions is equal to the compounded total return. In the following section, we use the linear factor model to describe linking. Note, however, that all results directly carry over to the case where the asset grouping methodology is applied.

Linking Returns Consider the one-period portfolio return written in terms of the linear factor model. We know from our earlier discussion that the return on the managed portfolio is given by:s

rp{t)=bP(t-l)F(t) + up(t) (19.24)

:In order to avoid cluttering notation, we drop the local superscript when writing returns.