In January 2012, we updated our share price model for Procter and Gamble (NYSE: PG) and showed that the original PG model had been working since September 2009 without any change. We presented the evolution of the model since 2009 in a series of figures. The original model does not show any sign of possible failure and here we re-estimate it using new data which are available in March 2012.
Our pricing concept is based on the decomposition of a share time history into a weighted sum of two consumer price indices, linear time trend and constant. The intuition is clear – there is a set of goods and services which any company produces and this set defines the share price evolution of a given company relative to other companies. These other companies are also driven by prices for some goods and services. Hence, for a given company one needs two defining sets of goods and services to estimate its relative pricing power – one related and one as an independent reference. Thus, the relevant stock price can be defined by two CPIs which include corresponding goods and services. It should also be taken into account that any change in the defining CPIs may lead the share price reaction by months. Apparently, demand and supply are separated in time.
A share price model for Procter and Gamble was originally published in July 2010. According to our concept, it was defined by the index of food away from home (SEFV - CUUS0000SEFV) and that of rent of primary residency (RPR); the evolution of these indices is presented in Figure 1. In the original model, the former CPI component led the share price by 3 months and the latter one led by 8 months:
PG(t) = -5.88SEFV(t-3) + 3.43RPR(t-8) + 17.60(t-1990) + 174.08, July 2010
In April 2011, we updated the original model using some new data (closing price for March 2011) and found that the same model was also applicable with a small change in the time lead for the SEFV – it was 4 months instead of 3 months in the original model. New coefficients were also slightly different, but very close to the original ones:
PG(t) = -5.40SEFV(t-4) + 2.93RPR(t-8) + 18.16(t-1990) + 187.47, March 2011
In September 2011, the updated model used the monthly closing price for September 2011 and CPIs for August 2011. It validated the model obtained for the previous period but is characterized by the same time lags and a small shift in the coefficients estimated by the LSQ technique.
PG(t) = -4.94SEFV(t-4) + 2.47RPR(t-8) + 18.15(t-1990) + 184.89, September 2011
In December 2011, the closing prices were estimated using the CPI data for December 2011 and thus both time shifts are one month longer. Accordingly, the best-fit models for PG(t) are as follows:
PG(t) = -4.76SEFV(t-5) + 2.27RPR(t-9) + 18.29(t-1990) + 187.61, December 2011
The current model is similar to all previously obtained models:
PG(t) = -4.42SEFV(t-4) + 2.00RPR(t-8) + 18.01(t-1990) + 185.91, February 2012
where PG(t) is the monthly closing price (dividend and split adjusted) in U.S. dollars, t is calendar time.
Figure 2 depicts the predicted curve which actually leads the observed price by 4 months with the residual error of $2.25 for the period between July 2003 and February 2012 (see Figure 3 for the model residuals). In other words, the price of a PG share is completely defined by the behaviour of these two CPI components.
The model does predict the share price in the past. There is a nonzero probability that the price will fall to $60-$62 by May 2012: the model error was $8 in February.
Figure 1. Evolution of the price of SEFV and RPR.
Figure 2. Observed and predicted PG share prices.
Figure 3. The model residual error.