Modeling share price: Aflac Incorporated

Here we revisit our stock price model for Aflac Incorporated (AFL). This model was first estimated in March 2011 and has been several times re-estimated with new data (last November 2012). Currently, we have the closing monthly price for March 2014 and the consumer price indices for February 2014. We decompose a share price into a weighted sum of two consumer price indices. This allows linking any share price with relative pricing power of goods and services associated with the company. Accordingly, our goal is to test the original model and to update time lags and coefficients. Overall, the model has demonstrated an excellent predictive power and stability over the whole period since 2011. It can predict at a one-month horizon and the current prediction foresees no significant changes in the AFL price in 2014.  

As in all previous models, the AFL share price is defined by the consumer price index of household furnishing and operations (HFO) and that transportation services (TS); both presented in Figure 1. In February 2012, the defining time lags were as follows: the HFO index led the share price by 1 month and the TS by 6 months, but in the current model the first lag is one month. All relevant best-fit models for AFL(t) are as follows:  

AFL(t) =  -5.02HFO(t-2) – 2.87TS(t-6)  + 20.42(t-1990) + 997.71,  March 2011

AFL(t) =  -4.63HFO(t-0) – 2.90TS(t-5)  + 20.41(t-1990) + 953.49, September 2011

AFL(t) =  -4.63HFO(t-1) – 2.87TS(t-6)  + 20.23(t-1990) + 948.72, December 2011

AFL(t) =  -4.65HFO(t-1) – 2.86TS(t-6)  + 20.20(t-1990) + 949.35, February 2012

AFL(t) =  -4.43HFO(t-2) – 2.71TS(t-6)  + 19.10(t-2000) + 1094.64, September 2012

AFL(t) =  -4.91HFO(t-1) – 2.59TS(t-6)  + 18.81(t-2000) + 1131.05, March 2014

 

where AFL(t) is the AFL share price in U.S. dollars,  t is calendar time.  

Figure 2 depicts the high and low monthly prices for an AFL share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The model residual error ($4.38 for the period between July 2003 and March 2014) is depicted in Figure 3.

Figure 1. Defining indices. 

Figure 2. Observed and predicted AFL share prices. 

Figure 3. The model residual error $4.38.

Share price modeling: Computer Science Corporation

Four years ago, we first presented a share price (monthly closing price adjusted for splits and dividends) model for Computer Science Corporation (NYCE: CSC). All predictions were based on our concept of share pricing as decomposition into a weighted sum of two CPI components.  The intuition behind our concept is simple; a faster growth in the CPI directly related to the share price (e.g. energy consumer price for energy companies) relative to some independent and dynamic reference (e.g. some goods and services which price does not depend on energy) should be manifested in a higher pricing power for the company. Our model selects (using the LSQ method) a defining CPI and the best reference index from a set of 92 CPI with estimates started before 2000. This set is fixed - it is important for model stability. Both CPIs for a given model must define the studied price for at least 8 months in a row, i.e. the model has to be the same for a relatively long time: the longer – the better.

 Approximately three years ago we revisited the original CSC model using all data available through March 2011.  The defining indices were estimated five years ago (in 2008): the consumer price index of motor vehicle parts (MVP) and the index of sporting goods (SPO). (All details are provided by the Bureau of Labor Statistics.) It is crucial for the model that the defining CPI components are leading by 0 and 5 months, respectively. Figure 1 depicts the evolution of both defining indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011:  

CSC(t) = -3.83MVP(t-0) + 3.16SPO(t-5) +16.31(t-1990) – 137.20, March 2011

      

where CSC(t) is the share price in US dollars, t is calendar time. In April 2011, we predicted the curve in the upper panel of Figure 2 which is synchronized with the observed one. The residual error was of $3.28 for the period between July 2003 and March 2011.  Since the MVP index has been growing since 2002 and the SPO index had a slight negative trend, we predicted that the share price would not be growing in 2011. We revisited the CSC pricing model in 2012 and obtained the same defining indices as in 2008: 

CSC(t) = -3.81MVP(t-1) + 3.35SPO(t-7) +15.97(t-1990) – 158.37, January 2012 

with slightly increased time delays of 1 month and 7 months, respectively. In the middle panel of Figure 2 the predicted and observed prices are depicted.  

Here, we revisit the original model with the data available on March 18, 2014. The best fit model is the same: 

CSC(t) = -3.13MVP(t-1) + 3.30SPO(t-7) +12.51(t-2000) – 51.97, March 2014

 

Slight drift in coefficients expresses the time trend in indices and observed for all pricing model from the very beginning. The functional dependence and time delays for both indices are the same. The lower panel of Figure 2 depicts the current model together with the high and low monthly prices expressing the intermonth price uncertainty. Thus, the pricing model for CSC is valid since 2008. The error term is presented in Figure 3. The standard deviation is $3.56 since July 2003.

One cannot excluded that the  MVP will suffer some further decrease  and the SPO will retain its long-term level. Then the positive price trend defined by the linear time term and negative MVP coefficient will result in further CSC share increase. 

Figure 1. Evolution of the price indices MVP and SPO.

 

Figure 2. Observed and predicted CSC share prices for three revisions: 2011 (upper panel), 2012 and 2014 (lower panel). 

Figure 3. The model error, i.e. the difference between the observed and predicted price; stdev = $3.56 for the period between July 2003 and March 2014.