Construct a pairs-trading worksheet from residuals and quantile ranks

One worksheet, one procedure

Pairs-trading is a two-leg procedure that turns a constructed spread into entry, exit, and no-trade rules. The archive workflow builds that spread by fitting a linear-regression baseline on each leg, isolating residuals, ranking the series, and holding a constant mid-rank line as the decision threshold.

Editorial note: TradersWeek reads these steps as one testable procedure so entry, exit, and abstention can be specified together. That reading is editorial and is not attributed to the archive.

Index the lookback before you fit

A sequential index column is required before intercept and slope can be estimated for the residual calculations. Intercept and slope are estimated once on the full lookback, separately for returns and for cumulative returns.

Linear-regression is used here as a fitted intercept-and-slope baseline that isolates residuals from returns and from cumulative returns.

Isolate residuals on the full-sample-range

Each residual is the observed series value minus the fitted intercept-plus-slope line at that observation. Residuals are computed separately for returns and for cumulative returns.

Regression and residual formulas must span the entire entered data range or the worksheet does not function as specified. The full-sample-range is the complete lookback window that intercept, slope, residual, and rank formulas must cover together.

Rank returns, residuals, and the spread-ratio

Return series are converted to chart inputs by ranking each observation as the share of the sample that is less than or equal to it. Quantile-analysis is that rank transform.

The same less-than-or-equal rank transform is applied to residuals of returns and to residuals of cumulative returns.

The spread-ratio is the period return of one series divided by the period return of the other. The spread series is the ratio of one leg's returns to the other leg's returns. The spread plot uses the same full-sample rank transform applied to that return ratio.

Hold the mid-rank spread-signal-line

The spread-signal-line is a constant mid-rank reference used as the decision threshold on the ranked spread. The required formula set is completed by copying a constant 0.5 through the sample.

Editorial note: TradersWeek treats that mid-rank line as the explicit abstention threshold. That interpretation is editorial and is not attributed to the archive.

What this installment leaves out

Chart construction and extra quality checks for whether a pair is tradable are deferred to a later installment.