Modeling share price: a negative correction for Lincoln National Corporation is not excluded

Here we model the evolution of Lincoln National Corporation (NYSE: LNC) stock price. LNC is a company from financial sector which «is engaged in multiple insurance and retirement businesses in the United States». Lately, we presented similar models for the following financial companies: Franklin Resources (BEN), Morgan Stanley (MS), and Goldman Sachs (GS). 

 

The model has been obtained using our concept of stock pricing as a decomposition of a share price into a weighted sum of two consumer price indices (CPIs). The background idea is a simplistic one: there is a potential trade-off between a given share price and goods and services the company produces and/or provides. For example, the energy consumer price does influence the price of energy companies. It should be taken into account that one defining consumer price (or relevant CPI) has to be related to the share and the other CPI should be an independent one as representing a dynamic reference. We expect a higher relative growth of the defining CPI to manifest itself in a higher pricing power for the company.  Both defining CPIs may lead the price of lag behind by a few months. 

We have borrowed the time series of monthly closing prices of LNC from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through February 2014 are published by the BLS.  It is instructive that the evolution of LNC share price is defined by the same consumer price indices as for Morgan Stanley: the index of food away from home (SEFV) and the index of owner’s equivalent rent of residence (ORPR). Both defining time lags are one month, i.e. one has a one month prediction for LNC using contemporary CPIs. The relevant best-fit model for LNC(t) is as follows:  

LNC(t) =  -9.39SEFV(t-1) + 4.38ORPR(t-1)  + 35.65(t-2000) + 647.76,  February 2014 

where LNC(t) is the LNC share price in U.S. dollars,  t is calendar time. Figure 1 displays the evolution of both defining indices since 2002.  Figure 2 depicts the high and low monthly prices for LNC share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). 

The model is stable over time. Table 1 lists the best fit models, i.e. coefficients, b1 and b2, defining CPIs, time lags, the slope of time trend, c, and the free term, d, for 7 months. In 2012, the same model was obtained, as listed in Table 2. Therefore, the estimated LNC model is reliable since May 2012.  The model residual is shown in Figure 3. The standard deviation between July 2003 and February 2014 is $4.12.  

The model for MS is very similar to LNC: 

MS(t) = -7.57SEFV(t-0) + 4.26ORPR(t-2) + 23.66(t-2000) + 398.90; February 2014 

One could expect a similar price evolution. This was true before 2012, but as Figure 4 demonstrates, the increase in LNC price since 2012 was much larger than that for MS.   This is the effect of a larger absolute value of coefficient b1 and the change in SEFV slope around 2012. (Notice that coefficients b2 are very close for LNC and MS.) With the expected return of food price to its long term trend, LNC will likely suffer a negative correction in the first half of 2014.

 

Table 1. The best fit models for the period between August 2013 and February 2014

Month	b1	CPI1	lag1	b2	CPI2	lag2	c	d	sterr, $
February 2014	-9.3913	SEFV	1	4.3797	ORPR	1	35.6511	647.7617	4.1205
January 2014	-9.4788	SEFV	1	4.414	ORPR	1	36.0393	654.6229	4.1348
December 2013	-9.4851	SEFV	1	4.4173	ORPR	1	36.0607	654.9437	4.1513
November 2013	-9.7695	SEFV	1	4.4984	ORPR	1	37.3449	686.3328	4.11
October 2013	-9.6895	SEFV	1	4.4759	ORPR	1	36.9113	678.5064	4.0554
September 2012	-9.6671	SEFV	1	4.4742	ORPR	1	36.7518	675.4866	4.0411
August 2013	-9.6214	SEFV	1	4.4657	ORPR	1	36.4715	670.2025	4.0105

 

Table 2. The best fit models for 2012

Month	b1	CPI1	lag1	b2	CPI2	lag2	c	d	sterr, $
December	-9.574	SEFV	1	4.538	ORPR	2	35.589	650.855	3.899
November	-9.572	SEFV	1	4.545	ORPR	2	35.529	649.277	3.894
October	-9.612	SEFV	1	4.571	ORPR	2	35.614	650.524	3.847
September	-9.609	SEFV	1	4.599	ORPR	2	35.412	644.772	3.786
August	-9.709	SEFV	1	4.659	ORPR	2	35.716	648.572	3.762
July	-9.659	SEFV	1	4.641	ORPR	2	35.472	644.183	3.758
June	-9.663	SEFV	1	4.651	ORPR	2	35.435	642.850	3.755
May	-9.715	SEFV	1	4.677	ORPR	2	35.638	645.902	3.758

 

Figure 1. The evolution of SEFV and ORPR indices

Figure 2. Observed and predicted LNC share prices.

Figure 3. The model residual error: stdev=$4.12.

Figure 4. Comparison of MS and LNC.