Predicting Bankruptcy: An Academic Model

by: Ivan Kitov

Predicting bankruptcy

Kitov (Modeling share prices of banks and bankruptcies) has modeled the evolution of share prices of several financial companies from the S&P 500 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 prospects, 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 have filed for bankruptcy since then.

Several banks were bailed out, with American International Group (NYSE:AIG) 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 (FNM) and Freddie Mac (FRE). All three companies had a sharp share price fall in the second half of 2008.

CIT Group Inc. (NYSE:CIT) got $2.3 billion of bailout money in December 2008 and a $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 not 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 (NYSE:C), 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.

click to enlarge

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).

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.
A 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).
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Disclosure: No positions