Reproduce a six-observation ranking table
These invented observations represent one instrument at six eligible signal times. Each return uses the same later holding horizon; the numbers are arithmetic inputs, not measured strategy performance. Rank from smallest to largest. The two signal values of 2 occupy positions 2 and 3, so each receives rank 2.5. The two returns of 3% occupy positions 4 and 5, so each receives rank 4.5.
- Both rank means are 3.5. The centered cross-product sum is 13.5; each centered squared-rank sum is 17. Spearman rho = 13.5 / sqrt(17 × 17) = 0.794118.
- The association is positive, but observation D has a larger return than E and F despite its lower signal. The coefficient summarizes such ordering disagreements across the sample.
- Pearson correlation on the original signal and return values is 0.855717. Changing returns from percentage points to decimal units leaves either coefficient unchanged.
| Observation | Signal x | Later return y | Rank x | Rank y |
|---|---|---|---|---|
| A | 1 | -2% | 1 | 1 |
| B | 2 | 1% | 2.5 | 3 |
| C | 2 | 0% | 2.5 | 2 |
| D | 4 | 4% | 4 | 6 |
| E | 5 | 3% | 5 | 4.5 |
| F | 6 | 3% | 6 | 4.5 |