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Compare original and shifted pairing
| Benchmark (%) | Correct asset (%) | Rotated asset (%) |
|---|---|---|
| -2 | -3 | -0.5 |
| -1 | -0.5 | 1 |
| 0 | 1 | 2.5 |
| 1 | 2.5 | 6 |
| 2 | 6 | -3 |
Keep the individual series summaries
The rotated asset list contains the same five numbers, so its mean and centered squared sum are unchanged. Benchmark values are also unchanged. The cross-products change because the period pairing changes.
Read the resulting slope
Correct pairing gives centered cross-product 21 and slope 2.1. The rotated cross-product is zero, giving slope zero and intercept still 1.2%. Marginal means alone cannot detect the mismatch.
Use actual period evidence
Retain matching dates or period identities. If one observation is missing, remove the complete pair or apply a documented treatment; do not independently shorten one list and shift subsequent observations. The example is hypothetical, not a recommendation to rearrange data to improve a fit.