Modeling Bank of America's Share Price

One by one, we are modeling share prices of companies from the S&P 500 list. We have already presented quantitative models for companies in various subcategories: information and technology, energy, industrials, consumer staples, materials, and financials (Western Alliance Bancorporation). It is now Bank of America's (BAC) turn.

As before, our pricing model is based on the presence of a linear link between a share price and the difference between various components of CPI. (Share prices are retrieved from YahooFinance and CPI components are from BLS.gov.) The intuition behind the model is simple; a higher pricing power for a given subcategory of goods and services, and thus related companies, is expressed in a faster increase in corresponding stock prices.

In the first approximation, the deviation between relevant price indices is proportional to the ratio of the pricing powers. The presence of sustainable (linear or nonlinear) trends in the differences, as found in (Kitov, Kitov, 2008; Kitov, Kitov, 2009ab) allows predicting the evolution of the differences, and thus the deviation between prices for corresponding goods and services. The share prices have to follow up.

So, there exist sustainable trends in the differences between various subcategories of consumer (and also producer) price indices. We consider the sustainability as an equivalent to the possibility to describe such (linear of nonlinear) trends by simple functions of time. Figure 1 demonstrates that the difference between core CPI, cCPI, and the index for transportation, h, from 2002 to 2008 can be approximated by a simple time function:

dCPI(t) = cCPI(t) - h = a + bt (1)

where dCPI(t) is the difference, a and b are empirical constants, and t is the elapsed time. After 2008, a transition period to a new trend has been observed. It is worth noting that the core CPI includes the index for housing with a weight of ~50%. So, the difference depends on the pricing power of housing relative to other goods and services in the core CPI, which excludes food and energy.

In Figure 1, the regression line between 2000 (January) and 2008 (July) has slope -1.52, i.e. other goods and services in the core CPI had lower pricing power than that of the housing. The downward trend finished in August 2008 and the new trend is likely an upward one. This is also our working hypothesis that the new trend in the difference will be long-term and positive.

Figure 1. Upper panel: core CPI, cCPI, and the index for housing, h. Lower panel: the difference between the cCPI and h. The slope between 2000 and 2008 (July) is -1.52, i.e. other goods and services in the core CPI had lower pricing power than that of the housing.

After a short tentative investigation by trial-and-error method, we find that our best-fit pricing model for a share price, BAC(t), can be represented by a linear function of the lagged difference between the cCPI and h:

BAC(t-18) = -2.2*(cCPI(t) – h(t)) +43; 1999-2009 (2)

where t-18 is the eighteen month time lag between the share price and CPI change, i.e. the change in BAC's share is reflected in the core CPI only in 18 months.

Considering the dependence of financial institutions on credits, especially in housing subcategory, one can consider the time lag as a reasonable one. Obviously, the lag does not allow predicting the share price, but the lag allows predicting the change in the index for housing relative to other goods and services at a 18- month horizon. The share price will be potentially predicted with a high accuracy if the new trend could be approximated by a linear function, as the one between 2000 and 2008.

Figure 2 demonstrates the accuracy of the preliminary model. There are no large deviations between the predicted observed (adjusted for dividends and splits) prices in shape and amplitude. The 18-month lag between the BAC and dCPI is well observed, with the latter actually passed the peak in July 2008. Since August 2008, the predicted price has been declining in line with the decreasing pricing power of the index for housing.

Extrapolating the observed price with relationship (2), one can find that the housing index will continue its decline relative to the core CPI till September 2010. Correspondingly, the observed BAC price reached its bottom in February 2009.

The evolution of the predicted and observed price will be reported. New data are necessary to obtain the model for the next period with a sustainable trend.

Figure 2. Comparison of the observed and predicted BAC (adjusted for dividends and splits) share price.

References:

• Kitov, I., Kitov, O., (2008). Long-Term Linear Trends In Consumer Price Indices, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 3(2(4)_Summ), pp. 101-112.
• Kitov, I., Kitov, O., (2009a). A fair price for motor fuel in the United States, MPRA Paper
• 15039, University Library of Munich, Germany.
• Kitov, I., Kitov, O., (2009b). Sustainable trends in producer price indices, Journal of Applied Research in Finance, v. 1, issue 1.

Disclosure: no positions

Comments

[Warm_Paw:]

WTF?
Even after extrapolating, using intuition and trial and error, the reader hasn't a clue what this article just said.
Hey Ivan, spell it out for me.
Say what you mean and mean what you say.

Jul 02 09:45 AM

[Ivan Kitov:]

Warm_Paw,

I am sure you do not care about the index for housing, as many people do. So, I would say that the following excerpt has its value for those who are involved:

"Extrapolating the observed price with relationship (2), one can find that the housing index will continue its decline relative to the core CPI till September 2010. "

Jul 02 09:53 AM

[Bighorndon:]

I hope Ivan has a day job. This gig is an exercise in futility.

Jul 02 09:54 AM

[1 of 4:]

I guess management has nothing to do with it?

Jul 02 10:18 AM

[Gravity404:]

Take a look at Ivan's other articles.

I will summarize them for you:

8>9+^%#$X ^^<76$@! = ?

Jul 02 11:10 AM

[Ivan Kitov:]

Formally, you are doubt in the quality of articles checked and edited by Seeking Alpha staff at their web-site. Therefore, I would recommend to complain via seekingalpha.com/page/... .

Jul 02 11:27 AM

[jbonefish:]

I think I get it and I like the fact that you adjusted for time lag. Have you established any trigger points in the relationship where you will take a long/short position? Otherwise, it is just math in hindsight ... clever as it may appear.

Jul 09 11:19 PM

[Ivan Kitov:]

The index for housing will likely to grow faster than other goods and services in the core CPI. This is the message, not the model for BAC shares.
Also check this for more information:
seekingalpha.com/artic...

I would need some time to give any short-long answer. This type analysis is couple weeks long. Needs testing.


On Jul 09 11:19 PM jbonefish wrote:

> I think I get it and I like the fact that you adjusted for time lag.
> Have you established any trigger points in the relationship where
> you will take a long/short position? Otherwise, it is just math in
> hindsight ... clever as it may appear.

Jul 13 03:43 AM