Here we model the evolution of Prudential Financial (NYSE: PRU) stock price. Prudential is a company from financial sector which provides provides various financial products and services. The model has been obtained using our concept of share pricing as a decomposition of a share price into a weighted sum of two consumer price indices. 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.
Originally, we addressed the PRU model in 2009 and found two CPIs explaining the monthly closing prices of PRU since 2003. They were the consumer price index of food and beverages (F) and the index of transportation services (TS). The defining time lags were as follows: the food index led the share price by 5 months and the TS index led by 4 months:
PRU(t) = -6.09F(t-5) – 3.15TS(t-4) + 59.76(t-1990) + 930.50, September 2009
In 2010, we revisited the original model and estimated new coefficients and lags. These estimates were close to the original ones:
PRU(t) = -5.45F(t-5) – 3.98TS(t-3) + 59.66(t-1990) + 1055.38, September 2010
Here we revise the model and re-estimate all coefficients and lags. We have borrowed the time series of monthly closing prices of PRU from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. The best-fit model for PRU(t) is as follows:
PRU(t) = -5.14F(t-5) – 3.80TS(t-4) + 56.20(t-1990) + 1005.63, February 2012
where PRU(t) is the PRU share price in U.S. dollars, t is calendar time. One can conclude that the model has not been changing since January 2009 and thus provides a good estimate of the price at a four month horizon.
Figure 1 displays the evolution of both defining indices since 2002. Figure 2 depicts the high and low monthly prices for a share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the bounds of the share price uncertainty and lead by 4 months.
The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $5.58. The share price is expected to grow in the first half of 2012, but the current price level already corresponds to that expected in June. Therefore, a negative correction in March-April is not excluded. Otherwise, Prudential Financial has a good short-term (months) perspective.
Figure 1. The evolution of F and TS indices
Figure 2. Observed and predicted PRU share prices.
Figure 3. The model residual error: stdev=$5.58.