Partial correlation and the market-adjusted stock trend

A weak percent-change baseline

Comparing a stock's percent change with a market benchmark's percent change is treated as a weak baseline because many stocks share a strong linear association with the market. The comparison therefore does not show how a change in market direction would affect the stock.

Partial correlation after a control variable

Partial correlation measures the strength and direction of a linear relationship between two continuous series after controlling for one or more other continuous series. The held-fixed series is a control variable: a third continuous series whose linear influence is held fixed when the remaining two series are related.

Three series in the linear model

The worked setup uses three series: a sequential trend index, the stock price, and a market index. The trend index is a sequential integer assigned to each observation so calendar order can enter the linear model as a variable.

The market-adjusted trend is the partial correlation of that trend index with the stock price series after controlling for the market index. The partial association of trend and stock price given the market isolates the stock's own linear path.

IBM nested lookbacks

The IBM illustration records ordered stock and market-index prices with a trend count of 1 on 17 November 2016, when the stock was 159.80 and the index was 2187.12. Six nested lookback windows of 5, 10, 15, 20, 25, and 30 sessions were computed to that as-of date.

The market-adjusted trend reading was 0.224 over 10 sessions and -0.380 over 5 sessions. IBM's 20-session market-adjusted reading was 0.881 with a t-statistic of 3.656, while the 5-session t-statistic was -0.642. The t-statistic is a hypothesis-test summary for whether the market-adjusted linear association differs from zero inside a given lookback.

Monsanto nested lookbacks

In the Monsanto example, the market-adjusted reading was negative at 15, 20, 25, and 30 sessions and positive only at 5 and 10 sessions. Monsanto's 30-session market-adjusted reading was -0.904 with a t-statistic of -4.714, compared with 0.726 and a t-statistic of 1.142 at 5 sessions.

Editorial reading of the nested windows

Editorial reading: the same as-of date can produce a market-adjusted trend of different sign and a t-statistic of different size, depending on how many ordered observations enter the lookback window. The archive records those historical IBM and Monsanto readings. It does not rank the windows, treat a larger t-statistic as a trading signal, or establish a present-day result.