Predicting BofA's Share Price (An Advanced Model)

We continue predicting share prices of S&P 500 companies with Bank of America (BAC). This time, we use an advanced model (see previous model here). The first company studied with this model was Boeing (BA). The advanced model includes four components of the CPI in the USA instead of two at the preliminary stage. For Boeing, the accuracy of prediction has been significantly increased.

There are 18 CPI components tested for each share price: the headline CPI ((C)), the core CPI, i.e. the headline CPI less food and energy ((CC)), food and beverages ((F)), housing ((H)), apparel ((A)), transportation ((T)), medical care ((M)), recreation ((R)), education ((ED)), communication ((CO)), services ((SR)), other ((O)), energy ((E)), shelter ((SH)), the CPI less food ((FC)), the CPI less energy ((EC)), the CPI less medical care ((MC)), the CPI less shelter ((SHC)). All components are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.

We extended the set of indexes by introduction of several components represented by the CPI less some indexes or commodity, by inclusion of special index for energy, and by the split of the index of communication and education.

Because of time constraints associated the CO and ED series (no data before 1998), we limit our modeling to the period between 2000 and 2009. The model is as follows:

sp(t) = B₁*(CPI₁(t-t₁)-CPI₂(t-t₂))+B₂*(CPI₃(t-t₃)-CPI₄(t-t₄))+C (1)

where sp(t) is the share price at time t; CPI_i(t-t_i) is the i-th component of the CPI with possible time lag t_i; B₁, B₂ and C are coefficients of linear function obtained by regression, where both L¹- and L²-metrics are used.

The lags are expected because of time delay between the change in one price and the adjustment of other related prices. At this stage, we do not use these lags because of limited computer capacity. All share prices are retrieved from Yahoo Finance.

Now we apply the advanced four-component model to the Bank of America’s share price. For computational reasons, we first normalize all time series to their peak values between January 2000 and May 2009.

The peak value of the price is called PMAX, and the peak values of the first and second differences in (1) are called CMAX₁ and CMAX₂, respectively. Then we find coefficients B₁, B₂ and C minimizing the difference between the reported price, BAC(t), and that predicted by (1). Finally, the best fit empirical relationship is as follows:

BAC(t) = PMAX*[ (-2.208)*(F(t) - SH(t))/CMAX₁ – 1.96*(O(t) - SR(t))/CMAX₂ + 0.264] (2)

where

PMAX=$47.23; CMAX₁=38.534, CMAX₂=112.14

Figure 1 presents the observed time series and that obtained using (2). The overall fit between these curves is superior to that obtained with the two-component model [1], with standard deviation 3.96.

We would like to refrain from any detailed comments on the CPI components found by our search procedure, but all CPI components are likely to be related to Bank of America. In any case, the advanced model demonstrates a higher predicting power. If one would have relationship (2) in the early 2000s, s/he would be able to predict the BAC(t) using linear trends in corresponding CPI differences, shown in Figure 2.

Figure 1. Comparison of the observed and predicted BAC (adjusted for dividends and splits) share price. The latter is obtained using (2).

Figure 2. Red line - the difference between the indexes of other G&S (O) and services(SR). Black line - the difference between the indexes of food and beverages (F) and shelter (SH).

Disclosure: no positions

Comments

[skwestorange:]

From Figure 1 it is very difficult to see that this model predicts the price. There does not seem to be any lead-lag relationship between the black and red lines.

Jul 08 08:57 AM

[Ivan Kitov:]

you are right. I might miss correct words in this article and have to repeat this portion in every post - the essence of prediction is NOT in the description of the price evolution using past values of CPI components. The prediction is possible because the differences between various CPI components reveal sustainable trends. If one stays in the beginning of such a trend, as it happens now, one can see several years ahead along the trends. The share price just evolves in sync with the CPI components. So, one can foresee the share price since the CPI difference is predefined by the trend.
We have presented dozens of examples in articles and papers.



On Jul 08 08:57 AM skwestorange wrote:

> From Figure 1 it is very difficult to see that this model predicts
> the price. There does not seem to be any lead-lag relationship between
> the black and red lines.

Jul 08 10:11 AM