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 tradeoff 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 bestfit model for LNC(t) is as follows:
LNC(t) = 9.39SEFV(t1) +
4.38ORPR(t1) + 35.65(t2000) + 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(t0) +
4.26ORPR(t2) + 23.66(t2000) + 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.