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3/30/10

Sure - disinflation continues ...

Mark Thoma at "Economists'view" informs us that inflation has been falling for a while and is not going to stop the descend despite many worries. Well. we predicted this outcome 5 years ago [1, 2]. Moreover, the next stage is a deflationary period, also predicted and confirmed many times [3].

Below is the most recent figure with the 1.1% GDP deflator reading in 2009 from my monograph "Deterministic mechanics of pricing". It is only 2 years before the overall price (GDP deflator) will sink below the zero line. ( The original prediction was obtained in 2005 and has been showing an excellent predictive power since.)

S&P 500 returns revisited

working paper has been published by MPRA:
Ivan O. Kitov, Oleg I. Kitov
Abstract
The predictions of the S&P 500 returns made in 2007 have been tested and the underlying models amended. The period between 2003 and 2008 should be described by the dependence of the S&P 500 stock market index on real GDP because the population pyramid was highly inaccurate. The 2008 trough and 2009 rally are well predicted by the original model, however. The rally will end in March/April 2010 and the S&P 500 level will be decreasing into 2011. This prediction should validate the model.
Key words: S&P 500, returns, prediction, population pyramid, GDP
JEL Classification: G1, D4, J1

3/28/10

Modeling share prices of financial companies: American International Group

American International Group was the first company bailed out by the US financial authorities in September 2008. This action introduced a bias into the link between AIG share price and defining CPIs, which existed before September 2008. The model listed in Table 1 (see original paper) is likely to be inappropriate as related to the link and not a robust one. The defining CPIs for the December 2009 model are as follows: the index for food away from home (SEFV) leading by 1 month and the index of prescribed drugs (PDRUG) leading by 13 months. In another post, we investigated the evolution of the bet-fit model for AIG from May 2008 to December 2009.

So, the best-fit 2-C model for AIG(t) is as follows:

AIG(t)= -187.7 SEFV(t-1) + 40.9PDRUG(t-13) + 673(t-2000) + 19957

The predicted curve should lead the observed price by 1 month with the residual error of $96. In other words, the price of an AIG share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted one month back for synchronization.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In February 2010, the price had to be at $270. In March 2010, the price is expected at $452. On 26th of March, the price was at $34. Apparently, the model is highly biased by the bailout and can hardly give an accurate prediction. One should wait before the price will really go up to get an appropriate model.

Figure 1. Observed and predicted AIG share prices.

References
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

Modeling share prices of financial companies: BAC

The model for Bank of America (BAC) is defined by the index of food without beverages (FB) and that of food away from home (SEFV). The latter CPI component leads by 13 months. From our past experience, the larger is the lag the more unreliable is the model. However, both defining components provide the best fit model in the second half of 2009. Both coefficients in the BAC model are negative. This means that increasing food price forces the share price down. The growth in the indices of food and food away from home has been compensated by linear time trend in the share price

So, the best-fit 2-C model for BAC(t) is as follows:

BAC(t)= -2.88FB(t-3) – 3.09SEFV(t-13) + 35.69(t-2000) + 964.6

The predicted curve should lead the observed price by 3 months with the residual error of $2.52 for the period between July 2003 and February 2010. In other words, the price of an BAC share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted three months back for synchronization.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In March, April and May 2010, the price is expected at $18.5, $17.1 and $18.3, respectively. On 26th of March, the price was at $17.90.

Figure 1. Observed and predicted BAC share prices.

References
Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

Modeling share prices of financial companies: AIV

The model for Apartment Investment and Management Company (AIV) has both defining CPIs leading the share price: the index of other food at home (OFH) and the index of prescribed drugs (PDRUG) are both five months ahead of the price. At first glance, this set of defining CPIs does not look convincing. This might be an effect of the changing trend in the CPI. Before November 2009, the best-fit model included the index of food and beverages (F) and the PDRUG, both leading by 8 months. This set determined the best-fit model during the 12 months previous to November 2009 (Kitov, 2010).

In a smaller set of 34 CPI components used by Kitov (2010), the index of food and beverages and that of medical care (M) were the driving ones between November 2008 and October 2009 and provided the standard error of $2.058, but for a shorter period. With the PDRUG, the standard error for the same period between July 2003 and October 2009 is $2.055, i.e. only marginally better. This fact demonstrates how sensitive the model is to the defining CPIs. When more components are included, one could expect changes in the previously obtained models and lower standard errors.

So, the best-fit 2-C model for AIV(t) is as follows:

AIV(t)= -1.25OFH(t-4) + 1.23PDRUG(t-4) - 7.83(t-2000) – 151.7

The predicted curve should lead the observed price by 4 months with the residual error of $2.19. In other words, the price of an AIV share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted four months back for synchronization. The residual error is also shown.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In March, April and May 2010, the price is expected at $19.5, $18.9 and $21.8, respectively. On 26th of March, the price was at $18.66.

Figure 1. Observed and predicted AIV share prices, and the residual error.

ReferencesKitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

The probability to get rich

Another monograph has been published and is available on amazon.com
Mechanics of personal income distribution. The probability to get rich






The processes behind distribution of personal incomes and related measures of inequality have always been in the center of political and economic discussions. We have developed a microeconomic model which accurately describes the shape of personal income distribution (PID), as estimated in the Current Population Surveys. The model predicts the age-dependent PIDs as a function of real economic growth and demography. The underlying physical concept was borrowed from geo-mechanics. Our approach serves as a firm basis for definitions of income inequality. Officials, both government and financial, might be interested in the projections of poverty levels and mean incomes. For economists, the model provides a new tool of quantitative research. For the broader scientific community, the model links economics to hard sciences. All readers may estimate the probability to get rich depending on age and current income.

3/27/10

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.

The S&P 500 returns will drop to -0.05 in 2011

Believe you or not, we predicted the fall in the S&P 500 returns in March 2009. In February 2009, there was no indication of the following linear growth in the returns. Below we present our model and predictions for 2010 and 2011. The model in best described in (Kitov, 2010).

The returns will drop again to -0.5!


S&P 500 returns and real GDP
As discussed in (Kitov, Kitov and Dolinskaya, 2009), there exists a trade-off between the growth rate of real GDP pre capita and the change rate of the number of 9-year-olds. Corresponding relationship should work in both directions and the number of 9-year-olds can be estimated from GDP measurements. So, one can replace N9(t) with GDPpc(t), taking into account that second term in the relationship between real GDP per capita and population is constant.
Figure 1 displays the observed S&P 500 returns and those obtained using real GDP, as presented by the US Bureau of Economic Analysis (http://www.bea.gov/). The observed returns are presented by MA(12) of the monthly returns. The predicted returns, Rp(t), are obtained from the following relationship:

Rp(t) = 0.6*dln(GDPpc(t)) - 0.0092,

where GDPpc(t) is represented by MA(6) of the (annualized) growth rate during or six previous months or two quarters as only quarterly readings of real GDP are available.
The period after 1996 is relatively well predicted including the increase in 2003. Therefore, it is reasonable to assume that the 9-year-old population was not well estimated by the US Census Bureau after 2003. This conclusion is supported by the cointegration test conducted for real GDP per capita and the charge rate of the number of 9-year-olds, which proves the existence of a long-term equilibrium linear relation between these two variables since the early 1960s (Kitov, Kitov and Dolinskaya, 2009). As a result, one can use either N9(t) or GDPpc(t) for modeling of the S&P 500 returns, where appropriate. Obviously, the GDPpc(t) is consistent with the S&P 500 returns after 2003.


Figure 1. The observed and predicted S&P 500 returns. The latter are obtained using quarterly readings of the growth rate of real GDP. One may expect rapid economic growth in 2010.

There is a concern related to the accuracy of population and real GDP measurement in 2006. In Figure 1, the predicted curve fell to -0.075 in the third quarter of 2006. There was no significant decrease in the S&P 500 returns during the same period. A possible reason for the discrepancy is that the real GDP was underestimated. This issue should be resolved in the next comprehensive revision to the GDP.
A striking feature in Figure 1 is the agreement between the annual curves in 2008 and 2009. The GDP readings predict the S&P 500 returns in time and amplitude. Moreover, the S&P index leads the GDP curve and predicts a rapid real economic growth in 2010. This is a good prediction to validate the link. All in all, real GDP per capita is a good predictor of the S&P 500 returns, especially during periods of big changes.

Using the number of 3-year-olds and the model linking it to the S&P 500 returns we have predicted the evolution between 2008 and 2014. The graph shown in Figure 2 is borrowed from (Kitov, 2010) with the amendments related to 2010.

If the level of S&P 500 will not reach 1200 by the end of March 2010, it will manifest the start of the fall. In any case, April 2010 will be the last months with growth, if any. Since May 2010, the fall is inevitable. It will be fast and deep – down to -0.5 (cumulative over the previous 12 months) by August 2011. One should bear in mind, that all predictions for 2009 and the beginning of 2010 have been realized.

Figure 2. Observed and predicted S&P 500 returns. By August 2011, the 12-month cumulative return will drop to -0.5. The period between March 2009 and March 2010 was predicted with high accuracy, taking into account the change in calibration.



Figure 3. The S&P 500 returns are currently reaching the peak with the following fall down to -0.04 (in average over the previous 12 months) by August 2011, as Figure 2 shows.

KITOV, I. KITOV, O., DOLINSKAYA, S. (2009). Modelling Real Gdp Per Capita In The Usa:Cointegration Tests, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 4(1(7)_ Spr)

Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.



TPREF: Call for papers

The Editor in Chief would like to invite submissions for the 1stVolume, Issue 1, Summer 2010 of the Theoretical and Practical Research in Economic Fields (TPREF).

Modeling share prices of financial companies: LM

(continued)

The model for Legg Mason (LM) is based on the index of food and beverages (F) and the index of appliances (APL) from the housing index, leading by 4 and 13 months, respectively Overall, the predicted time series is very close to the observed one with standard deviation of $7.03 between July 2003 and February 2010. The largest input to the standard deviation comes from a short period in 2006. Otherwise, both curves are very close even during the dramatic fall from $80 per share in the end of 2007 to $10 per share in February 2009 and during the fast recovery in 2009.

So, the best-fit 2-C model for AXP(t) is as follows:

LM(t)= -5.77F(t-4) – 8.44APL(t-13) + 31.25(t-2000) + 1743.5

The predicted curve should lead the observed price by 4 months. In other words, the price of a LM share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted four months back for synchronization.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In March and April 2010, the price is expected at $30 and $33, respectively. On 26th of March, the price was at $29.5. However, the predicted curve shows a sudden fall to the level of $22 in May/June 2010.

Figure 1. Observed and predicted LM share prices.

Modeling share prices of financial companies: AXP

Original paper:

Introduction
Recently, we have developed and tested statistically and econometrically a deterministic model predicting share prices of selected S&P 500 companies (Kitov, 2010). We have found that there exists a linear link between various subcategories of consumer price index (CPI) and some share prices, with the latter lagging by several months. In order to build a reliable quantitative model from this link one needs to use standard and simple statistical procedures.

Following the general concept and principal results of the previous study, here we are predicting stock prices of financial companies from the S&P 500 list. In several cases, robust predictions are obtained at a time horizon of several months. In close relation to these financial companies we have also investigated several cases of bankruptcy and bailout. These cases include Lehman Brothers (LH), American International Group (AIG), Fannie Mae (FNM) and Freddie Mac (FRE). Regarding these bankruptcies, we have tested our model against its predictive power in May and September 2008. The main question was: Could the bankruptcies be foreseen? If yes, which companies should or should not be bailed out as related to the size of their debt?

In the mainstream economics and finances stock prices are treated as not predictable beyond their stochastic properties. The existence of a deterministic model would undermine the fundamental assumption of the stock market. If the prices are predictable, the participants would have not been actively defining new prices in myriads of tries, but blindly followed the driving force behind the market. It is more comfortable to presume that all available information is already counted in. However, our study has demonstrated that the stochastic market does not mean an unpredictable one.

In this paper, we analyze sixty six financial companies from the S&P 500 lists as of January 2010 as well as a few bankrupts from the financials. Some of the companies have been accurately described by models including two CPI subcategories leading relevant share prices by several months. Other companies are characterized by models with at least one of defining CPI components lagging behind related stock prices. We have intentionally constrained our investigation to S&P 500 - we expect other companies to be described by similar models.
Our deterministic model for the evolution of stock prices is based on a “mechanical” dependence on the CPI. Under our framework, the term “mechanical” has multiple meanings. Firstly, it expresses mechanistic character of the link when any change in the CPI is one-to-one converted into the change in related stock prices, as one would expect with blocks or leverages. Secondly, the link does not depend on human beings in sense of their rational or irrational behavior or expectations. In its ultimate form, the macroeconomic concept behind the stock price model relates the market prices to populations or the numbers of people in various age groups irrelevant to their skills. Accordingly, the populations consist of the simplest possible objects; only their numbers matter. Thirdly, the link is a linear one, i.e. the one often met in classical mechanics. In all these regards, we consider the model as a mechanical one and thus a physical one rather than an economic or financial one. Essentially, we work with measured numbers not with the piles of information behind any stock.

For the selected stocks, the model quantitatively foresees at a several month horizon. Therefore, there exist two or more CPI components unambiguously defining share prices several months ahead. It is worth noting that the evolution of all CPI components is likely to be defined, in part, by stochastic forces. According to the mechanical dependence between the share prices and the CPI, all stochastic features are one-to-one converted into stochastic behavior of share prices. Since the prices lag behind the CPI, this stochastic behavior is fully predetermined. The predictability of a measured variable using independent measured variables, as described by mathematical relationships, is one of the principal requirements for a science to join the club of hard sciences. Therefore, our stock pricing model indicates that the stock market is likely an object of a hard science.

A model predicting stock prices in a deterministic way is a sensitive issue. It seems unfair to give advantages to randomly selected market participants. As thoroughly discussed in (Kitov, 2009b; Kitov and Kitov, 2008; 2009ab) the models are piecewise ones. A given set of empirical coefficients holds until the trend in the difference between defining CPI is sustained. Such sustainable trends are observed in a majority of CPI differences and usually last between 5 and 20 years (Kitov and Kitov, 2008). The most recent trend has been reaching its natural end since 2008 and the transition to a new trend in 2009 and 2010 is likely the best time to present our model. As a result, there is no gain from the empirical models discussed in this paper. Their predictive power has been fading away since 2008. When the new trend in the CPI is established, one will be able to estimate new empirical coefficients, all participants having equal chances.

The results of the presented research open a new field for the future investigations of the stock market. We do not consider the concept and empirical models as accurate enough or final. There should be numerous opportunities to amend and elaborate the model. Apparently, one can include new and improve available estimates of consumer price indices.

1. Model and dataKitov (2009b) introduced a simple deterministic pricing model. Originally, it was based on an assumption that there exists a linear link between a share price (here only the stock market in the United States is considered) and the differences between various expenditure subcategories of the headline CPI. The intuition behind the model was simple - a higher relative rate of price growth (fall) in a given subcategory of goods and services is likely to result in a faster increase (decrease) in stock prices of related companies. In the first approximation, the deviation between price-defining indices is proportional to the ratio of their pricing powers. The presence of sustainable (linear or nonlinear) trends in the differences, as described in (Kitov and Kitov, 2008; 2009ab), allows predicting the evolution of the differences, and thus, the deviation between prices of corresponding goods and services. The trends are the basis of a long-term prediction of share prices. In the short-run, deterministic forecasting is possible only in the case when a given price lags behind defining CPI components.

In its general form, the pricing model is as follows (Kitov, 2010):

sp(tj) = Σbi∙CPIi(tj-ti) + c∙(tj-2000 ) + d + ej (1)

where sp(tj) is the share price at discrete (calendar) times tj, j=1,…,J; CPIi(tj-ti) is the i-th component of the CPI with the time lag ti, i=1,..,I; bi, c and d are empirical coefficients of the linear and constant term; ej is the residual error, which statistical properties have to be scrutinized. By definition, the bets-fit model minimizes the RMS residual error. The time lags are expected because of the delay between the change in one price (stock or goods and services) and the reaction of related prices. It is a fundamental feature of the model that the lags in (1) may be both negative and positive. In this study, we limit the largest lag to fourteen months. Apparently, this is an artificial limitation and might be changed in a more elaborated model. In any case, a fourteen-month lag seems to be long enough for a price signal to pass through.

System (1) contains J equations for I+2 coefficients. Since the sustainable trends last more than five years, the share price time series have more than 60 points. For the current recent trend, the involved series are between 70 and 90 readings. Due to the negative effects of a larger set of defining CPI components discussed by Kitov (2010), their number for all models is (I=) 2. To resolve the system, we use standard methods of matrix inversion. As a rule, solutions of (1) are stable with all coefficients far from zero.

At the initial stage of our investigation, we do not constraint the set of CPI components in number or/and content. Kitov (2010) used only 34 components selected from the full set provided by the US Bureau of Labor Statistics (2010). To some extent, the original choice was random with many components to be similar. For example, we included the index of food and beverages and the index for food without beverages. When the model resolution was low, defining CPI components were swapping between neighbors.

For the sake of completeness we always retain all principal subcategories of goods and services. Among them are the headline CPI (C), the core CPI, i.e. the headline CPI less food and energy (CC), the index of food and beverages (F), housing (H), apparel (A), transportation (T), medical care (M), recreation (R), education and communication (EC), and other goods and services (O). The involved CPI components are listed in Appendix 1. They are not seasonally adjusted indices and were retrieved from the database provided by the Bureau of Labor Statistics (2010). Many indices were started as late as 1998. It was natural to limit our modeling to the period between 2000 and 2010, i.e. to the current long-term trend.

Since the number and diversity of CPI subcategories is a crucial parameter, we have extended the set defining components to 92 from the previous set of 34 components. As demonstrated below, the extended set has provided a significant improvement in the model resolution and accuracy. Therefore, we envisage the increase in the number and diversity of defining subcategories as a powerful tool for obtaining consistent models. In an ideal situation, any stock should find its genuine pair of CPI components. However, the usage of similar components may have a negative effect on the model – one may fail to distinguish between very close models.

Every sector in the S&P 500 list might give good examples of companies with defining CPI components lagging behind relevant stock prices. As of January 2010, there were 66 financial companies to model, with the freshest readings being the close (adjusted for dividends and splits) prices taken on December 31, 2009. (All relevant share prices were retrieved from http://www.finance.yahoo.com/.) Some of the modeled companies do present deterministic and robust share price models. As before, those S&P 500 companies which started after 2004 are not included. In addition, we have modeled Fannie Mae and Freddie Mac, which are not in the S&P 500 list, and Lehman Brothers and CIT Group (CIT) which are out of the S&P 500 list. Due to the fact that the latter three companies are both bankrupts, they have been modeled over the period of their existence. Apparently, there are many more bankrupts to be modeled in the future.

There are two sources of uncertainty associated with the difference between observed and predicted prices, as discussed by Kitov (2010). First, we have taken the monthly close prices (adjusted for splits and dividends) from a large number of recorded prices: monthly and daily open, close, high, and low prices, their combinations as well as averaged prices. Without loss of generality, one can randomly select for modeling purposes any of these prices for a given month. By chance, we have selected the closing price of the last working day for a given month. The larger is the fluctuation of a given stock price within and over the months the higher is the uncertainty associated with the monthly closing price as a representative of the stock price.
Second source of uncertainty is related to all kinds of measurement errors and intrinsic stochastic properties of the CPI. One should also bear in mind all uncertainties associated with the CPI definition based on a fixed basket of goods and services, which prices are tracked in few selected places. Such measurement errors are directly mapped into the model residual errors. Both uncertainties, as related to stocks and CPI, also fluctuate from month to month.

2. Model for AXP

American Express Company (AXP) has a model predicting at a four month horizon. The defining CPIs are the index for food and beverages leading by 4 months and the index for medical care leading by 10 months. In the previous study (Kitov, 2010) the model was essentially the same. So, the extended CPI set does not make a better model. The model is a robust one and minimizes the standard error for the period between July and November 2009 as well.

The best-fit 2-C model for AXP(t) is as follows:

AXP(t)= -3.71F(t-4) – 2.10M(t-10) + 50.59(t-2000) + 1127.9

where F in the index of food and beverages leading the stock price by 4 months, M is the index of medical care leading by 10 months, (t-2000) is the elapsed time. The predicted curve should lead the observed price by 4 months. In other words, the price of a AXP share is completely defined by the behaviour of the two CPI components. Figure 1 depicts the observed and predicted prices, the latter shifted four months back for synchronization. The model residual error, i.e. standard deviation, is of $2.64 for the period between July 2003 and February 2010.

The model does predict the share price. Therefore, it should be revisited at a monthly basis. In March and April 2010, the price is expected at $47.5 and $50.5, respectively. On the 26th of March, the price was at $41.12.

Figure 1. Observed and predicted AXP share prices.



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.

The evolution of Exxon Mobil share price

In the previous post, we described the pricing model for ConocoPhillips shares as based on the concept of stock dependence on consumer price index. He we apply the model to Exxon Mobil (XOM). As for COP, we will track the performance of the model and compare observed and predicted prices.

Since March 18, the readings of the headline CPI and its components for February 2010 are available (we retrieve all CPI data from http://www.bls.gov/data). Here we update our model for XOM as one of selected stocks from the S&P 500 list.

Exxon Mobil provides an example of a company, which share price has been leading defining components of the CPI. As always, the model is seeking those two CPI components from a large number of pre-selected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and February 2010. The original model [2-4] included only nine top CPI subcategories and that obtained in [1] - 34 different CPI indices. Currently, the set of CPI components is extended to 92. This is not the final set, however.

The two-component (2-C) model also includes free term (constant) and linear time term [5-8], which compensates well know linear (time) trends between various CPI components. The best-fit 2-C model for XOM(t) is as follows:

XOM(t)= 3.817RPR(t-4) – 3.983MVR(t-0) + 11.64(t-2000) – 26.88

where RPR in the index of rent of primary residency (CUUS0000SEHA) lagging the stock price by 4 months, MVR is the index of motor vehicle maintenance and repair (CUUR0000SETD) leading by 0 months, (t-2000) is the elapsed time. Therefore, the predicted curve should lag the observed price by 4 months. In other words, the price of a XOM share defines the behaviour of rent of primary residence. Figure 1 depicts the observed and predicted prices, the latter shifted four months ahead for synchronization. The model residual error, i.e. standard deviation, is of $2.76 for the period between July 2003 and February 2010.

The model does not predict the share price. Therefore, it will not be necessary to revisit this prediction before September 2010.
Figure 1. Observed and predicted XOM share prices.

References[1] Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Academic Publishing.
[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., (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
[4] Kitov, I., (2009). Predicting ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(2(2)_ Wint), pp. 129-134.
[5] 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.
[6] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf
[7] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf
[8] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf

3/21/10

ConocoPhillips price revisited

Lately, we have developed and tested a concept of stock pricing as based on the dependence on consumer price index [1]. The model was originally introduced by Kitov and Kitov [1,2] and then applied to Exxon Mobile (XOM) and ConocoPhillips (COP) [4]. It is instructive to track the performance of the model and compare observed and predicted prices.

Since March 18, the readings of the headline CPI and its components for February 2010 are available (we retrieve all CPI data from http://www.bls.gov/data). Here we update our model [1] for ConocoPhillips (COP), as one of selected stocks from the S&P 500 list.

ConocoPhillips provides a good example of a company, which share price has been lagging behind defining components of the CPI. The model is seeking those two CPI components from 92 pre-selected ones, which minimize the difference between observed (monthly closing price adjusted for dividends and splits) and predicted prices for the period between July 2003 and February 2010. The original model [1] included only nine top CPI subcategories and that obtained in [1] - 34 different CPI indices. Currently, the set of CPI components is extended to 92. This is not the final set, however.

The two-component (2-C) model also includes free term (constant) and linear time term [5-8], which compensates well know linear (time) trends between various CPI components. The best-fit 2-C model for COP(t) is as follows:

COP(t)= 2.792MCS(t-3) – 4.477PETS(t-2) - 10.964(t-2000) – 267.54

where MCS in the index of medical care services (CUUR0000SAM2) leading the stock price by 3 months, PETS is the index of pets and pet products (CUUR0000SERB) leading by 2 months, (t-2000) is the elapsed time. Therefore, the predicted curve leads the observed price by 2 (!) months, i.e. contemporary readings of relevant CPI subcategories allow the prediction at a 2-month horizon. Figure 1 depicts the observed and predicted prices, the latter shifted two months back for synchronization. Figure 2 presents the residual error, with standard deviation of $3.78 for the period between July 2003 and February 2010.

The model predicts the price to grow in March and April 2010 to the level of $55 and $60.7, respectively. We will revisit this prediction in May 2010.

Figure 1. Observed and predicted share prices.


Figure 2. Residual error of the model, σ=$3.78 for the period between July 2003 and February 2010.

References
[1] Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Academic Publishing.
[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., (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
[4] Kitov, I., (2009). Predicting ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finance, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. I(2(2)_ Wint), pp. 129-134.
[5] 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.
[6] Kitov, I., (2009). Apples and oranges: relative growth rate of consumer price indices, MPRA Paper 13587, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf
[7] Kitov, I., Kitov, O., (2009). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15039/01/MPRA_paper_15039.pdf
[8] Kitov, I., Kitov, O., (2009). Sustainable trends in producer price indices, MPRA Paper 15194, University Library of Munich, Germany, http://mpra.ub.uni-muenchen.de/15194/01/MPRA_paper_15194.pdf



3/20/10

PREDICTING REAL ECONOMIC GROWTH IN FRANCE, GERMANY, NEW ZEALAND, AND THE UNITED KINGDOM

Journal of Applied Economic Sciences (JAES) has published the spring issue with my paper:

Ivan O. KITOV, 2010. "Predicting Real Economic Growth In France, Germany, New Zealand, And The United Kingdom," Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. 5(1(11)_Spr), pages 48-54.


Abstract
The growth rate of real GDP per capita is modeled and predicted at various time horizons for France, Germany, New Zealand, and the United Kingdom. The rate of growth is represented by a sum of two components – a gradually decreasing trend and fluctuations related to the change in country-specific age population. The trend is an inverse function of real GDP per capita with constant numerator. Previously, similar models were developed and validated for the USA and Japan.

Keywords: real GDP per capita, modeling, prediction, population

JEL classification: E1, E3, O4, O5

3/18/10

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.