According to , the model for Procter and Gamble (PG) is defined by the index of food away from home (SEFV - CUUS0000SEFV) and that of rent of primary residency (RPR). The former CPI component leads the share price by 3 months and the latter one leads by 8 months. Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and June 2010. Relevant coefficients are negative and positive, respectively. The slope of time trend is also positive.
So, the best-fit 2-C model for PG(t) is as follows:
PG(t) = -5.88SEFV(t-3) + 3.43RPR(t-8) + 17.60(t-2000) + 174.08
where t is calendar time.
The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $2.08 for the period between July 2003 and June 2010. In other words, the price of a PG share is completely defined by the behaviour of the two CPI components.
The model does predict the share price in the past and foresees a period of modest growth in the near future. This contradicts the predicted overall fall in the S&P 500 in 2010. One might expect a slight growth in PG share price, but this deviation also can manifest the end of the period where the model is valid. This deviation may be induced by the change in the trend in both or one of the underlying CPIs: SEFVand RPR, as Figure 1 illustrates.
Figure 1. Evolution of the price of SEFV and RPR.
Figure 2. Observed and predicted PG share prices. The original prediction, i.e. the prediction three months before actual time, is shown by red line. Black diamonds present the original line shifted 3 months ahead to fit actual data.
Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.08. The largest errors were observed in 2007.
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.