What is the formula for pure sector allocation return?

The formula for pure sector allocation return is indeed captured by the chosen answer, which reflects the difference in weights and returns between the portfolio and the benchmark sectors.

The rationale behind this formula emphasizes isolating the impact of sector allocation decisions from the effects of stock selection within those sectors. In this case, the term [w(port) - w(bench)] represents the active weight—how much the portfolio deviates from the benchmark weights in those sectors. The term [r(sector bench) - r(overall port bench)] captures the return differential between the sector benchmark and the overall portfolio benchmark. By multiplying these two components, you're able to quantify the return attributable specifically to the allocation effect of sectors.

This understanding aligns significantly with performance attribution analysis, where the goal is to determine how much of the portfolio's return can be attributed to the decision to be overweight or underweight in particular sectors compared to the benchmark. Hence, this formula effectively segregates the impact of allocation from that of stock selection, making it a core principle in performance evaluation and sector allocation analysis.