Suppose we train on M individuals consisting of T observations (i.e. TxM design matrix). The dependent variable is one-year return for each security (H = horizon of one year). In a factor model specification, we align security characteristics and economic factor exposures observed at time T with the dependent variable observed at T+H. Therefore any operational forecasting factor model must use information that is stale by at least one-year.
This can have traumatic consequences especially as market conditions are continuously changing. For example, such a forecasting model would not “recognize” a bear market until at least one full year into the bear market (maybe when the bear market ended as in the illustration below). Likewise, a full one year after the end of the bear market on March 2009 such a forecasting model would continue to predict substantial negative returns thru March 2010 and then some. Or consider today -- a 1 year forecasting model’s most recent training data is an observation from August 2010 – changes in factor premia are lagged by construction.
Check out this slide from an Axioma Risk Model presentation:
Notice the lagged "echo" volatility spike that takes place months after October 2008 -- several months after the realized volatility spike. Perversely, as realized risk (gray line) is declining the predicted risk (red/blue line) is increasing! This is because the realized volatility enters the training data with some lag. There is no "instantaneous" adjustment to current conditions.
What creative work-arounds or modeling approaches can be used to dealing with this problem endemic to forecasting models? Are there statistical methods to cope with this?