3/31/14

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.

No comments:

Post a Comment