Price Delay Measures

A price delay measure asks: how much of a stock's price reaction to market-wide news happens immediately, versus trickling in over the following days? Some stocks — heavily traded, widely followed — absorb market moves almost instantly. Others, especially small, illiquid, or thinly analyzed names, only fully reflect a market move over several subsequent trading days, because fewer people are watching and trading them in real time.

The standard construction, due to Hou and Moskowitz, regresses a stock's return on the contemporaneous market return alone, then re-runs it adding several lags of the market return. If including the lags meaningfully improves the fit (raises the $R^2$), that means a chunk of the stock's reaction to market news was actually delayed rather than instantaneous — the "delay" score is built from the ratio of these two $R^2$ values.

Suppose a stock's contemporaneous-only regression gives an $R^2$ of 0.10, and adding four days of lagged market returns raises it to 0.16. The delay measure attributes $(0.16-0.10)/0.16 \approx 38\%$ of the stock's explained variance to lagged, delayed price adjustment rather than instantaneous incorporation — a high-delay stock compared to a large liquid name where lags would add almost nothing.

Researchers use price delay this way as a proxy for how much attention a stock gets: it tends to be higher for smaller, less analyst-covered names, and stocks with high measured delay have historically shown a modest but persistent extra return, consistent with investors demanding compensation for holding names that are slower and costlier to research and trade.