Half a year ago, we presented a share price model for Loews Corporation (NYSE: L) based on the decomposition into a weighted sum of two consumer price indices (selected from a larger number of CPIs), linear trend and constant, all coefficients and time lags to be estimated by a LSQ procedure. Here we test the previous model and make a regular update using new data. All in all, the original model is valid since October 2008 and does not show any sign of future changes. This is a reliable model valid during the past 47 months!
A preliminary model for Loews Corp. was obtained in September 2009 and covered the period from October 2008. This old model included the index of food without beverages (FB) and the index of transportation service (TS). The most recent model also used the monthly closing prices as of April 2011 and the CPI estimates published on April 14, 2011. The defining indices were almost the same: the index of food (F) and the TS index. Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between October 2009 and September 2011. The F index leads by 5 months and the TS index by 4 months. When new data through September 2011 are used, the model does not show any tangible change - only coefficients have been slightly drifting:
L(t) = -2.03F(t-5) – 2.12TS(t-4) +28.23(t-1990) + 448.98, March 2011
L(t) = -2.01F(t-5) – 2.09TS(t-4) +27.96(t-1990) +440.65, September 2011
where L(t) is the share price in US dollars, t is calendar time. The new model is depicted in Figure 2 together with high and low monthly prices as a proxy to the uncertainty bound of the share price. The predicted curve leads the observed one by 4 months. The residual error is of $2.38 for the period between July 2003 and September 2011. In the fourth quarter of 2011, the model foresees a very slight increase. The model obtained in March 2011, accurately predicted the fall observed in the second and third quarters.
Figure 1. Evolution of the price indices F and TS.
Figure 2. Observed and predicted share prices.