of factor loadings once parameters for the full sample are estimated. To accomplish this, we begin generating T at observation 250 based on model parameters estimated through
observation 250. For 250 to 299 , T is generated based on the parameters estimated for the sample ending at t = 250. To capture any additional parameter instability, the parameters are estimated again for the sample ending at t = 300. 300 to 349 are then generated based on the parameters estimated for the sample ending at t = 300. This sequence of re-estimating the parameters every 50 periods is then repeated through t = 650. Ultimately a sample of T is
estimated for 250 to 678
Examples of the paths of the factor loadings are presented in Figure 2. In the Energy, Industrials, and Materials sectors, the change in the price of oil would be anticipated to be an important determinant of expected returns. Figure 2a shows the time path of the 'real time' sensitivity of the Energy sector’s expected return to the oil factor. The figure indicates that the energy sector does not always respond to lagged changes in the price of oil in the same fashion. There are three distinct regimes over the past eight years in its evolution. The loading was negative and almost constant until the fall of 1997, when it turned and remained on a positive trend until the start of 2000. A positive sensitivity, in terms of our forecasting model would imply that a positive change in the lagged price of oil would, ceteris paribus, signal a higher conditional expected return for the Energy sector. Since then, the loading has once again turned negative and its magnitude has increased.
The change in the dividend yield would be expected to play some role in forecasting 'cyclical' sectors, such as Consumer Discretionary, Financials, Industrials, and Materials. Figure 2b shows the time path of the sensitivity to the dividend yield factor for the Financials sector. The sector has had a consistently positive exposure to the factor, which increased in magnitude following the market breakdown in 2000. The positive return sensitivity to changes in the dividend yield with respect to the Financials sector ‘peaked’ in April 2002, and while the exposure to the factor has come down since, it is still higher than the level observed prior to 1999.