In several previous posts on bankruptcy, we have described the evolution of share prices for banks just before their bankruptcy or on their approach to negative prices: Colonial Bank (CNB), the CIT Group (CIT), American International Group (AIG), and Lehman Brothers (LEH). It was shown that the CNB sank below the edge of bankruptcy and CIT is on the brink with unclear future. AIG has been fluctuating around the waterline for a while, and LEH was definitely ready for a bankruptcy.
On the other hand, the CIT Group and AIG are bailed out, and thus, our model predicting share prices should fail to predict the artificially supported prices. Therefore, it would be instructive to estimate the fictitious evolution of share prices after the bankruptcies or alternative evolution after the bailouts. In this post we compare Lehman Brothers, Fannie Mae (FNM) and Freddie Mac (FRE). All three had a sharp fall in the second half of 2008.
Model and data
To predict share prices we use the 3-C model [1-3]: a share price, sp(t), is described with the following empirical function:
sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t-2000) + D (1)
, where CPI1 and CPI2 are empirically determined CPI components; t is the calendar time; A, B, C, and D are empirical coefficients. Because the prices for goods and services (in the headline CPI) can lag or lead relevant share prices the time lags t1 and t2 are introduced. Both time lags can be positive or negative. In our model, we test all possible lags between 0 and +13 months. So, we chose the best from 34*33*14*14 ~ 200,000 possible models, with two extra degrees of freedom introduced by linear and free terms.
When applied to the LEH time series between July 2003 and September 2008, the 3-C model (1) gives the following empirical relationship:
LEH(t) = -10.40*FB(t-4) + 5.84*DUR (t+2) + 67.96*(t-2000) + 952; STDEV=$4.73 (2)
, where t is the calendar time, FB(t) is the (not seasonally adjusted consumer price) index for food leading the LEH by four months, and DUR(t+2) in the index of durable goods lagging two months behind the LEH. Figure 1 compares the stock price predicted according (2) with the observed one. This model differs from that in the previous post in two aspects. First, it uses DUR instead of the personal care index (PC). This is not a fundamental change, however. Each empirical model based on two components of the CPI includes one index, which is sensitive to the change in a given share price, and one index, which expresses the overall reaction of prices for goods and services induced by the change in the share price.
Then the difference between these two components maps the change in the price. Since there are many components of the CPI, which might represent the overall reaction of the CPI on the given price change, their exchange does not influence the model much. In the case of LEH, the defining component is the index for food (or food and beverages), and the reference component is the PC or DUR.
The empirical models for FNM and FER are as follows:
FNM(t) = -7.38*FB(t-8) – 8.47*R (t+3) + 42.57*(t-2000) + 2119; STDEV=$4.42 (3)
FRE(t) = -6.07*FB(t-4) - 3.42*O (t-9) + 57.96*(t-2000) + 1917.8; STDEV=$4.16 (4)
, where R is the index of recreation and O is the index for other goods and services in the CPI. Figures 2 and 3 compare the observed and predicted prices for FNM and FER, respectively.
We have predicted fictitious share prices of three companies. This prediction might be helpful for the assessment of future policy on Freddie Mac and Fannie Mae.
Figure 1. Comparison of the observed and predicted LHE’s share price. The latter is obtained using (2).
Figure 2. Comparison of the observed and predicted FNM’s share price. The latter is obtained using (3).
Figure 3. Comparison of the observed and predicted FRE’s share price. The latter is obtained using (4).
 Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: June-September 2009, MPRA Paper 15863, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15863/01/MPRA_paper_15863.pdf
 Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15862/01/MPRA_paper_15862.pdf
 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.