## 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.

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