Freddie Mac and Fannie Mae: predicting bankruptcy

Original paper: Kitov, 2010. "Modeling share prices of banks and bankrupts," Quantitative Finance Papers 1003.2692, arXiv.org

(continued)

Predicting bankruptcy
Kitov (Modeling share prices of banks and bankrupts) has modeled the evolution of share prices of several financial companies from the S&P 500 list between May 2008 and December 2009. It was found that some predicted share prices sank below the zero line. Under our framework, the presence of a negative stock price may be considered as an equivalent to a net debt. When long enough and without any positive prospective, such a debt would likely result in a bankruptcy.

In reality, some companies with negative predicted share prices declared bankruptcy, some were bailed out and some have been suffering tremendous difficulties since 2008. The first group is represented by Lehman Brothers who filed for Chapter 11 bankruptcy protection on September 15, 2008. The net bank debt was estimated at the level of $600 billion. More than 100 banks filed for bankruptcy since then.

Several banks were bailed out, with American International Group the first to obtain a $150 billion government bailout. The AIG bailout was presented as a major move to save the collapsing US financial system. The biggest examples of bailout are also Fannie May and Freddie Mac. All three companies had a sharp share price fall in the second half of 2008.

CIT Group Inc. (CIT) got $2.3 billion of bailout money in December 2008 and $3 billion bond holder bailout in July 2009. However, it did not help and CIT declared bankruptcy in November 2009. These companies and many others have been struggling and likely will struggle in the future trying to restructure their debts and re-enter the stock market.

We seek to answer a number of questions:
Was it possible to predict the evolution of total debt of the bankrupts?
Was it possible to predict the dates of these bankruptcies?
Is it possible to predict the date of recovery?
It is possible to predict future bankruptcies?
Which company had to be bailed out and when?

All S&P 500 models with negative share prices were obtained together with other models for May 2008. In this regard we should not distinguish them. The reason for a separate investigation consists in the fact that negative share prices might result in bankruptcies. This is a phenomenon no described quantitatively by our models and thus deserving special attention. Otherwise, all models were equivalent and obtained according to the same procedures. It is worth noting that the models for the same companies obtained in October 2009 are highly biased by bailouts or do not exist together with bankrupt companies.

Table 4. Models for 10 companies: May, September and December 2008, and October 2009. (Tables are available in the original paper)
May 2008
September 2008
December 2008
October 2009

Table 4 lists 10 models with predicted negative or very close to negative prices as obtained in May, September and December 2008 as well as in October 2009. Figure 3 displays corresponding predicted and observed curves between July 2003 and December 2009. American International Group has a very stable model for the entire period as defined by the DIAR and SEFV. Theoretically, the company should suffer a rapid drop in share price from ~$1400 to the level of about -$300. In reality, this fall was stopped by a bailout with the share price hovering between $10 and $50 by the end of 2008 and through 2009. According to all four models the price should start growing in 2010. It will be an important test for our pricing concept.

For Citigroup, the models obtained in 2008 are similar and are based on the indices of food and rent of primary residence. Figure 3 demonstrate that negative prices were expected in the end of 2008. All three models predicted the bottom price at -$30. In October 2009, the defining CPI components are different as the model tries to describe the price near $2.

The history of CIT Group (CIT) includes two attempts of bailout and a bankruptcy in November 2009 with a total debt of $10 billion. In Figure 3, the May 2008 model predicts a very deep fall in the share price. Other two models in 2008 demonstrate just a modest fall below the zero line. The bailouts have likely biased the October 2009 model and it predicts the company to recover in 2010. It would be a good exercise similar to that for the AIG model. Unfortunately, the history of CIT Group has ended with a bankruptcy, as expected.

Fanny Mae and Freddie Mac were both bailed out in September 2008. As depicts Figure 3, the models between May and December 2008 are all different. However, all of them predicted negative prices. The models for FNM imply the bottom price level of -$50 to -$60 and the pivot point somewhere in 2009. The models for FRE do predict negative prices with the bottom at -$30, but only the September model has a pivot point.

Lehman Brothers was one of the first giant companies to file for bankruptcy protection in September 2008. The May 2009 model does predict negative prices in the beginning of 2009. The September and December 2009 models are likely biased by the bankruptcy but both indicate a deep fall in the price. It is important to stress that the bottom price for LEH was predicted at -$20 with a quick return into the positive zone. Therefore, the risk might be overestimated.

The models predicted for FITB, LM, MCO and MS are presented to emphasize the problem of resolution and selection of a valid model. For these four companies there is at least one model predicting negative or very close to zero prices. In reality, no one of them has touched the zero line. Moreover, they have not been falling since the end of 2008. So, in order to obtain an accurate prediction one should the best resolution, which might be guaranteed by the higher possible dynamic range. The 2008 crisis and the following recovery allowed the biggest change in the S&P share prices. Hence, the models obtained in 2010 have to be the most resolved and thus the most reliable. Good news is that these models will be valid in the future, but with different coefficients (Kitov, 2010).

Figure 3. Comparison of stock prices for several financial companies as predicted in May, September and December 2008, and October 2009

There are six companies, all with predicted negative prices but different fate. We have a question on relative merits of the previous bank bailouts - which bank did deserve a bailout and how much would it really cost? The models in Table 4, although they are only tentative ones and should be used with all necessary precautions, might provide a measure of debt size. One can estimate the debt as a product of the number of shares and relevant market price, which was negative for the bailed out and not bailed out companies. Table 5 lists the estimated debts. Lehman Brothers had a much smaller debt than that of Citigroup, CIT and AIG. So, it would have been much easier to bail out LEH from the mathematical point of view. Also, the joint debt of AIG, FRE and FNM is less than $200 billion.

So, we have answered all questions formulated in the beginning of this Section. When having valid pricing models for the companies under consideration, one could foresee all problems before they become serious and select appropriate measures including bailouts. Moreover, taking into account the deterministic evolution of the CPI and linear trends in the CPI differences (Kitov and Kitov, 2008), one could predict major problems long before they happen and avoid most of the 2008/2009 turmoil. For this, financial companies should learn the CPI components defining the evolution of their stocks.


Table 5. Total debt as calculated from negative share prices.

DiscussionA deterministic model has been developed for the prediction of stock prices at a horizon of several months. The model links the shares of traded companies to consumer price indices. In this paper, we presented empirical models for financial companies from the S&P 500 list. In May 2008, the model predicted negative share prices in the second half of 2008 for Lehman Brothers, American International Group, Freddie Mac. With known defining CPI components one could predict the approaching bankruptcies. This makes of crucial importance the estimation of correct empirical models, i.e. defining CPIs, for all shares. When reversed, the model also makes it is possible to predict the evolution of various CPI subcategories.

Despite its apparent opposition to the mainstream concepts, the pricing model is deeply rooted in economics: a higher pricing power achieved by a given company should be converted into a faster growth in corresponding consumer price index. This link works excellent for many S&P 500 companies. A further improvement in the model’s predictive power is likely possible using advanced methods of statistical and econometrical analysis. However, one should bear in mind that the model will work until its influence on the market is negligible. When a good portion of market participants uses the model it should fail because the market functioning will be disturbed.

Observed and predicted share prices are measured variables and the link between them is likely of a causal character during the studied period. Therefore, the mainstream stock pricing models are, in part, valid – when the evolution of the driving force is random the price is also random, but predictable.

An important possibility arises from our analysis. Using different subsets of the CPI, one can improve our tentative models for the studied companies, and easily obtain similar quantitative relationships for other companies. By extrapolating previously observed trends into the future, one may forecast share prices at various horizons. What likely is more important for a broader investor community, the proposed model also allows predicting the turning points between adjacent trends, when share prices are subject to a substantial decline.

The presented results are preliminary ones and do not pretend to provide an optimal price prediction. A comprehensive investigation with smaller components of the CPI will likely give superior results. So, we recommend refining the model in order to obtain accurate quantitative results for actual investment strategies. All in all, the lagged differences between two CPI components provide a good approximation for the evolution of many stock prices.

One may pose a question: Why did the researches in economics and finances fail to derive the model many years ago? The answer is a scientific one. There were no appropriate data. First, the partition of the headline CPI in hundreds of components is a very new development. Moreover, this process is ongoing and a researcher obtains a more adequate set of defining variables. This brings both higher resolution and reliability. Second, the reliability critically depends on the dynamic range of data. The crisis of 2008 and 2009 has resulted in a dramatic change in both share prices and CPI components. The increased resolution and dynamic range allowed deriving a sound quantitative model. There was no chance to find the link between the share prices and CPI before the data allow. This is a general consideration applicable to all economic and financial models – adequate data must come first (Kitov, 2009a).

References

Bureau of Labor Statistic. (2010). Consumer price index. Table, retrieved 01.02.2010 from http://www.bls.gov/data/.
Granger, C., Newbold, P. (1967). Spurious regression in econometrics. Journal of Econometrics, v. 2, pp. 111-120.
Hendry, D., Juselius, K. (2001). Explaining Cointegration Analysis: Part II. Energy Journal, v. 22, pp. 75-120
Johansen, S. (1988). Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control, v. 12, pp. 231-254.
Kitov, I., (2009a). Does economics need a scientific revolution?, MPRA Paper 14476, University Library of Munich, Germany.
Kitov, I. (2009b). Predicting ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finance, v., issue 2(2), Winter 2009, pp.129-134.
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany: LAP LAMBERT Academic Publishing.
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. III(2(4)_Summ), pp. 101-112.
Kitov, I., Kitov, O. (2009a). Sustainable trends in producer price indices, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(1(1)_ Summ), pp. 43-51.
Kitov, I., Kitov, O. (2009b). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany.

Deterministic mechanics of pricing

I've written a book on inflation and deterministic character of pricing of goods, services and stocks. It has been published by LAMBERT Academic Publishing. (I strongly recommend to publish monographs with LAP.)

The book is available via http://www.amazon.de/: "Determinisic mechanics of pricing" .

Abstract

The book presents a deterministic description of future prices of stocks, goods and services and commodities. Statistically, observed and predicted prices are cointegrated. The overall price inflation is a linear and lagged function of the growth rate of labor force, with projections foreseeing a deflationary period since 2012. There are long-term sustainable trends in the differences between various CPI and PPI subcategories. A deterministic link has been found between stock prices and CPI. To validate the link, empirical models for fifty four S&P 500 companies are presented, with statistically robust price predictions months ahead. One can compile a dynamic portfolio with a deterministic profit. In July 2008, the model would have accurately forecasted negative share prices of Lehman Brothers and AIG. The predictions are likely reliable until their influence on the stock market is negligible. Finally, we validate the link between the S&P 500 returns, real GDP per capita and the number of 9-year-olds in the United States.

The Feds must bail out Lehman Brothers

There is a fundamental question on relative merits of the previous bank bailouts - which bank did deserve a bailout and how much would it really cost? Our model of stock price, developed in articles and posts, provides an additional measure of the size of bank problems - total debt. One can estimate the debt as a product of the number of shares and their market price, which was negative for the bailed out and not bailed out banks. We base our estimate on relevant stock prices described in this blog. Table 1 lists the number of stocks, their peak negative price, and the debt:

Table 1.
....................vol............ price,$.......debt,$
LEH...... 689,000,000.......... -40...... -2.76E+10
C ..........11,000,000,000..... -10.......-1.10E+11
AIG....... 134,000,000........ -870 ......-1.17E+11
FRE...... 648,000,000......... -40 ........-2.59E+10
FNM...... 1,110,000,000...... -45 .......-5.00E+10
(see fictitious stock price estimates for Citigroup and AIG in Figures below)

The table shows that Lehman Brothers had smaller problems than Citigroup and AIG. So, it was was easier to bail out LEH from purely mathematical and financial point of view.

Also, the joint negative price of AIG, FRE and FNM is less than 200bn. It could be some (deliberate?) miscalculation of the >1000bn help package. The toxic debt might be bigger than the total debt associated with stock prices, but there should be unaccounted positive assets.

Beyond the bankruptcy – Fannie Mae, Freddie Mac, and Lehman Brothers

Introduction
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.

The full set includes 34 CPI components, which are tested as predictors for each share price. Among these components are major expenditure categories: 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), and other goods and services (O). All components used in the model are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.

Results
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.

Here I would like to illustrate the process on the example of isostatic compensation of ice floating in a water-filled tank. If you put some load on a piece of ice it will sink a bit deeper, but the level of water in the tank will also increase. Similarly, if some stock price increases it will affect prices of many goods and services, not only those related to the stock. There should be a component of the CPI which expresses the overall reaction the best. One can consider it as a reference component.

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.

All three empirical models just describe the evolution of corresponding prices using available CPI estimates. The models do not foresee stock the price evolution beyond current knowledge. However, since relevant CPI estimates are available for the last year, i.e. 11 months after the bankruptcy of Lehman Brothers, one can formally calculate the fictitious evolution of these share prices, as shown in Figures 1through 3. The LEH price demonstrates sustainable decrease between October 2008 and March 2009. Then the price regains some strength and approaches the zero line in August 2009. If bailed out in September 2008, the Lehman Brothers would start to grow in September 2009. One cannot say the same thing about AIG – it is still unstable.

The price of Fannie Mae lags behind both defining CPI components. Therefore, the prediction is possible only till April 2009. Unfortunately, the price continues its fall. There is no sign a turn. On the contrary, the price of Freddie Mac is well predictable into 2010. In March 2009, the price reached the bottom and then started to grow. It is still negative and will stay below the zero line in 2009.

Conclusion
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).

References
[1] 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
[2] 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
[3] 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.

Predicting bankruptcy : the case of Lehman Brothers

We continue testing our model againts bancruptcy cases. Lehman Brothers presents an old but crucial case. Before we start our quantitative analysis, we have to clarify the the term "predicting" has a narrow sense of quantitative description. In other words, we do not forecast the bankruptsy, but decompose relevant stock price, sp(t), into a sum of two CPI components, a linear and a free term:

sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t-2000) + D (1)

where CPI1 and CPI2 are defining CPI components; t is the calendar time; A, B, C, and D are empirically determined coefficients. Because prices for good and services 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 do not pretend that one could see the fall of LEH months before it had happened.

So, the empirical model describing the time history of LEH share price is as follows:

LEH(t) = -9.75*F(t-4) – 8.13*PC (t-2) + 94.9*(t-2000) + 2802 (2)

, where t is the calendar time, F(t) is the (not seasonally adjusted consumer price) index for food and beverages, leading the LEH(t) by four months, and PC(t-13) in the index of personal care leading the LEH(t) by 2 months. Or this model we used LEH prices between July 2003 and September 2008; the CPI components were taken till December 2008, i.e. three months ahead of the last LEH reading. Figure 1 demonstrates that the model predicted the fall below zero but three months later. Standard deviation of the residual is $4.7.

Once again, this model could not be obtained in August 2008.

Figure 1. Observed and predicted LEH share price.

Predicting bank bankruptcy – the case of AIG

Update 1. There is a post at MarketBeat devoted to AIG : AIG Shares: Still Not Worth Anything. In general it supports our model with a negative estimate of the share price. The case is getting more and more exiting ...

In the previous post on bankruptcy, we have described the evolution of share prices for the Colonial Bank (CNB) and the CIT Group (CIT). It was shown that CNB sank below the edge of bankruptcy. (All share prices are retrieved from YahooFinance.) Here we investigate the case of AIG. It has been bailed out. Not considering political, economic and financial aftermaths of such a bankruptcy we focus on the prediction by our 3-C model: 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 defining CPI components; t is the calendar time; A, B, C, and D are empirically determined coefficients. Because prices for good and services 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.

The full set includes 34 CPI components, which are tested as predictors for each share price. Among these components are major expenditure categories: 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), and other goods and services (O). All components used in the model are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.
When applied to AIG time series between July 2003 and August 2009, the 3-C model (1) for AIG is as follows:

AIG(t) = -89.29*F(t) – 08.31*FB (t-13) + 1031*(t-2000) + 32666 (2)

, where t is the calendar time, F(t) is the (not seasonally adjusted consumer price) index for food and beverages and FB(t-13) in the index of food without beverages leading AIG(t) by 13 months.
Figure 1 compares the stock price predicted according (2) with the observed one. There are two dives of the predicted price below zero – March and August 2009, the latter being of -$123. With standard deviation of $102, the predicted price in August likely hints at unresolved problems with AIG. However, the negative price might also result from the uncertainty in F and FB measurements.
We will continue tracking AIG stock price and reporting our predictions.


Figure 1. Comparison of the observed and predicted AIG’s share price. The latter is obtained using (2).