Constructing market-adjusted stock trend scores

What the score isolates

A market-adjusted trend score can be built as the partial association between a stock and a trend variable after the concurrent market path is held constant. That leftover link is a partial correlation: the linear association between the stock series and the trend series after the shared linear effect of the market has been removed.

The point of the control is simple. A raw stock-to-trend reading can be a market ride. Holding the concurrent market path constant keeps only the name-specific remainder.

Assemble the residual from three pairwise correlations

The residual association can be assembled from the pairwise-correlation triplet. The three raw associations among the stock, the trend variable, and the market are sufficient to build the residual score.

The finished measure is bounded between -1 and +1. Values nearer those extremes indicate a stronger residual trend over the chosen window.

What market control can change

Once the market effect is removed through that linear control, the residual stock-trend link can shrink or change sign relative to the raw stock-market association. A name that looked aligned with trend on an unadjusted reading may look weaker, stronger, or reversed after the market path is held constant.

Compare nested lookbacks

A nested lookback is a set of sampling windows that all end on the same date and lengthen backward. Repeating the construction from the last five sessions through the last ten and out to the last thirty shows whether the residual trend is continuous or breaking down.

The shared end date is what makes the comparison fair. Each window answers the same question on a longer or shorter stretch of the same history.

Test the residual link

A trend-significance test applies a t-test to the residual measure. The question is whether the market-adjusted trend is statistically distinguishable from no association over the chosen window.

The test does not replace the score. It only asks whether the leftover stock-to-trend link differs from no relationship on that sample.

When two names diverge

Two names observed over the same calendar windows can diverge. One remains tightly tied to the market, while the other shows little market association in its price change. The residual score is what makes that split visible after the common path is controlled for.

The same residual score can feed a diversification screen by preferring names whose residual trend is not merely a copy of the market path. In that construction use, the screen flags names whose path is largely a copy of the market rather than stock-specific.