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Ivan Kitov
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I am a Doctor of Physics and Mathematics, Lead Researcher at the Institute for the Geospheres' Dynamics, Russian Academy of Sciences. Founding member of the Society for the Study of Economic Inequality Published three monographs in economics and finances: Deterministic mechanics of pricing... More
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Stock Market Science
My blog:
Economics as Classical Mechanics
My book:
Deterministic mechanics of pricing
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  • Predicting Stock Prices: General Electric Company To Hold

    It is time to model the stock price evolution of General Electric Company (NYSE: GE). GE is a company from Industrial Goods sector which "operates as an infrastructure and financial services company worldwide". Among others, the studied company has a Transportation segment covering a wide range of transportation services. This observation is important for understanding the model.

    All models have been obtained using our concept of stock pricing as a decomposition of a share price into a weighted sum of two consumer price indices. The background idea is a simplistic one: there is a trade-off between a given share price and goods and services the relevant company produces or provides. For example, the energy consumer price should influence the price of energy companies. Let's assume that some set of consumer prices (as expressed by an appropriate consumer price index, CPI) drives the company stock price. The net effect of the relevant CPI change can be positive or negative.

    In real world, each company competes not only with those producing similar goods and services, but also with all other companies on the market. Therefore, the influence of the driving CPI should also depend on all other goods and services, and thus, relevant CPIs. To model the net change in the market prices we introduce just one reference CPI. In quantitative terms, it has to best represent the dynamics of changing price environment. Hence, our pricing model includes two defining CPIs: the driver and the reference. Because of possible time delays between action and reaction (the time needed for any price changes to pass through), the defining CPIs may lead the modeled price or lag behind.

    We have borrowed the time series of GE monthly closing prices (through March 2014) from CPI estimates (not seasonally adjusted) through February 2014 are published by the BLS. According to the procedure described in Appendix, the evolution of GE share price is defined by the index of transportation services (TS) and the index of pets, pet products and services (PETS). These indices were selected from a large set of 92 CPIs covering all consumer price categories. All possible CPI pairs with all possible time lags and leads were tested one by one. The TS/PETS set, which minimizes the model error, is considered as the defining pair. For GE, the time lags are 6 and 2 months, respectively, and the best-fit model is as follows:

    GE(t) = -1.536PETS(t-2) - 0.631TS(t-6) + 11.805(t-2000) + 291.08, February 2014 (1)

    where GE(t) is the GE share price in U.S. dollars, t is calendar time. All coefficients in the above relationship were estimated together with their uncertainties using the linear regression technique . Table 1 confirms that all coefficients are statistically significant.

    Table 1. Statistical estimates for the model coefficients

     CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

    Figure 1 displays the evolution of both defining indices since 2003. Figure 2 depicts the high and low monthly prices for GE share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The model prediction is best described by the coefficient of determination Rsq.=0.93. The predicted and observed time series are cointegrated. Thus the Rsq. estimate is not biased.

    From relationship (1), it seems that the index of pets, pet products and services define the evolution of GE price. Actually, the model implies that PETS index does NOT affect the share price. This index provides a dynamic (price) reference rather than the driving force. Here is a simple example how to understand the term "dynamic reference". Imagine that a swimmer needs to swim 20 km along a river. Let's assume that for this experienced swimmer the average speed is 5 km/h. How much time does s/he need? The quick answer 4 hours is wrong. One cannot calculate the time needed without knowing the stream speed and direction. This stream is the dynamic reference (or moving coordinate reference system) for the swimmer. The stream speed can also vary over time producing a non-stationary coordinate reference system. The intuition behind our pricing concept is similar - the driving CPI is not enough to calculate the price change, one needs to know "the stream speed", i.e. the market movements. The CPI representing "dynamic reference" for GE was selected from 91 CPIs.

    The model is stable over time: it has the same defining CPIs, coefficients and time lags for longer periods of time. Table 2 lists the best fit models, i.e. slopes, b1 and b2, for two defining CPIs, time lags, slope of time trend, c, and free term, d, for 7 months between July 2013 and February 2014. It is instructive that the same model was obtained in 2012, 2011, and 2010, also listed in Table 2. Therefore, the estimated GE model is reliable over 50+ months. The model residual for February 2014 is shown in Figure 3. Between July 2003 and February 2014, the model standard error is $1.51.

    Overall, the model does not foresee any big change in GE price. One may expect some price fluctuations within the bounds of intermonth changes observed in the past. The predicted value for May 2014 is $27.7 (+-$1.5).

    Table 2. The best fit models for the period between May 2010 and February 2014


    Figure 1. The evolution of TS and PETS indices

    Figure 2. Observed and predicted GE share prices.

    Figure 3. The model residual error: sterr=$1.51.


    The concept of share pricing based on the link between consumer and stock prices has been under development since 2008. In the very beginning, we found a statistically reliable relationship between ConocoPhillips' stock price and the difference between the core and headline consumer price index in the United States. Then we extended the pool of defining CPIs to 92 and estimated quantitative models for all companies from the S&P 500 list. The extended model described the evolution of a share price as a weighted sum of two individual consumer price indices selected from this large set of CPIs. We allow only two defining CPIs, which may lead the modeled share price or lag behind it. The intuition behind the lags is that some companies are price setters and some are price takers. The former should influence the relevant CPIs, which include goods and services these companies produce. The latter lag behind the prices of goods and services they are associated with. In order to calibrate the model relative to the starting levels of the involved indices and to compensate sustainable time trends (some indices are subject to secular rise or fall) we introduced two additional terms: linear time trend and constant. In its general form, the pricing model is as follows:

    sp(tj) = Σbi∙CPIi(tj-ti) + c∙(tj-2000 ) + d + ej (2)
    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 (I=2 in all our models); bi, c and d are empirical coefficients of the linear and constant term; ej is the residual error, whose statistical properties have to be scrutinized.

    By definition, the bets-fit model minimizes the RMS residual error. It is a fundamental feature of the model that the lags may be both negative and positive. In this study, we limit the largest lag to eleven months. System (2) contains J equations for I+2 coefficients. We start our model in July 2003 and the share price time series has more than 130 readings. To resolve the system, standard methods of matrix inversion are used. A model is considered as a reliable one when the defining CPIs are the same during the previous seven months.

    Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

    Apr 06 2:18 AM | Link | Comment!
  • Increasing Income Inequality Is A Political (Taxation) Problem

    Here we show that the source of increasing income inequality in the tax law. At the end of the day, the whole set of US politicians is responsible for the increase in the portion of personal income for the richest families. This is good news since the return to "normal" income distribution is a political procedure. There are no economic forces behind the change, which would be much more difficult to overcome.

    According to the reports of the Bureau of Economic Analysis (BEA), the proportion of personal (money) income in the Gross Domestic Product has not been changing since 1947. This is the year when the BEA started to measure personal incomes. We have revealed the source of virtual increase in income inequality - private companies redistribute their income in favor of personal income of their owners. The question is - how do they get extra money to redistribute to their private owners? This post answers this question - the US tax system started to reduce the level of tax for private companies. Primarily, it is made by increasing the rate of depreciation, which enterprises are officially permitted to charge for tax purposes (usually fixed by law). Hence, the tax law in responsible for the increasing income inequality.

    We start with a graph showing the growth in GDP, gross personal income (GPI) and compensation of employees (paid) since 1929. Figure 1 demonstrates that the level of GPI has been rising faster than that of the GDP (and the compensation) since 1979. (The share of GPI in the GDP has been rising since 1979!) The difference between the GPI and GDP curves depicted in Figure 2 has a striking kink around 1979. And this is the start of the current rally in the rich families' personal income. In other words, a new political (taxation is a political issue) era started in 1979. We would like to stress again the proportion of the compensation of employees in the GDP has not been changing since 1929, with a small positive deviation in the end of 1990s and a negative deviation since 2009. This observation supports our previous finding that the proportion of personal (money) income in the GDP has not been changing.

    So, where the extra money is from? The level of personal income has been actually increasing faster than that of the GDP and it should be the last fool, who lost its share in the GDP. Figure 3 shows two major components of the GPI. The net operating surplus (private) has been changing at the same rate as the GDP since 1929, while the proportion of taxes on production and imports has been growing at lower rate since 1980. We have allocated the source of income for rich families. They take money from the decreasing taxes. But what is the mechanism of money appropriation? Figure 4 demonstrates that the decrease in taxes goes directly into the increasing share of consumption of fixed capital.

    This is the force behind the increasing income inequality.

    The increasing share of the consumption of fixed capital is successfully converted in private money, not in investments! This is a political problem started in 1979.

    It seems that there is no economic problem behind increasing income inequality.

    Figure 1. GDP, GPI, and compensation of employees normalized to their respective levels in 1960.

    Figure 2. The difference between the GPI and GDP curves in Figure 1.

    Figure 3. GDP, net operation surplus (private), and taxes (on production and imports) normalized to their respective levels in 1960.

    Figure 4. GDP and consumption of fixed capital normalized to their respective levels in 1960.

    Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

    Tags: demographics
    Mar 10 9:52 AM | Link | 5 Comments
  • Time To Sell The S&P 500

    In the middle of December 2012, we reported on the evolution of the S&P 500 index and decided to sell it at 1430. We had bought the index at 1352 in November. Due to technical reasons not related to our investing decisions we were able to sell the whole lot only on December 15 at 1420. The return from November was 4.7%; and from May 2012, when we first formulated our investment tactics, we made around 15%. We also decided to buy the S&P 500 at ~1400. This level was touched on December 28.

    Right after this fall, we predicted a rally to 1550 according to our simple and straightforward investing tactics - we follow the trajectory of the S&P 500 observed during the rally between 2002 and 2007. In March 2013, the S&P 500 exceeded 1560 and currently we expect it to fall to 1450 at a one month horizon. If to follow up our procedure, as explained in Figures 1 through 6, it's time to sell and wait for a new short-term rally in June-October 2013. Then a tremendous fall down to 750 in 2015 is not excluded. Since 2009, the S&P 500 has been following the previous (2002-2007) trajectory up. This observation is the basis of our best guess that the index should not stay high after October 2013? Currently, I am in bonds and look for 1.5% to 1.7% yield to sell them in June.

    In March 2012, we first published a graph which showed that the S&P 500 index would have a local fall in May 2012 at the level 1300. In a few sessions, we bought the S&P 500 index in May/June 2012 at the level 1287 to 1322. The initial idea was to sell by the end of 2013 at 1525 and get a 12% to 14% return. In September 2012, the S&P was at 1450, which was far above the expected level, and we decided to sell and wait a negative correction to 1350 to 1375 to re-enter the index. Selling at ~1460, we obtained an approximately 10% return in September. In October, the S&P 500 fell to 1350 as had been predicted in September and we re-entered in two sessions at 1348 and 1355. By the end of November the S&P 500 regained 4.5% (1416). Two weeks ago, we expected the index to rise to 1430 to 1450 in December 2012. This was considered as the best time to sell before the next negative correction in December 2012/ January 2013. In reality, this correction to 1400 was very short.

    Below we present the evolution of the S&P 500 and the step-by-step assumptions illustrating the decisions we have made since March 2012.

    Figure 1 shows the evolution of the S&P 500 index since 1980. After 1995, the index behavior reveals some saw teeth with peaks in 2000 and 2007. The current growth resembles those between 1997 and 2000 and from 2003 and 2007. There are two deep troughs in 2002 and 2009 which are marked by red and green lines. For the current analysis we assume that the repeated shape of the teeth is likely induced by a degree of similarity in the evolution of macroeconomic variables. The intuition behind such an assumption is obvious - in the long run the stock market depends on the overall economic growth.

    Having two peaks and troughs between 1995 and 2009, what can we say about the current growth in the S&P 500? Before making any statistical estimates, in Figure 2 we have shifted forward the original curve in Figure 1 in order to match the 2009 trough (blue line). When the 2002 and 2009 troughs are matched, one can see that the current growth path closely repeats that after 2002. The first big deviation from the blues curve in Figure 2 started in 2011 and had amplitude of 150 units (from 1210 to 1360). The black curve returned to the blue one in August/September 2011. From December 2011, we observed a middle-size deviation of about 100 units.

    (click to enlarge)

    Figure 1. The evolution of the S&P 500 market index between 1980 and 2012.

    In April 2012, we predicted a drop in the S&P 500 to the level of 1300 by the end of May. Figure 2 shows the predicted behavior in April and May 2012, with the predicted segment shown by red line. We expected that the path observed in the previous rally would be repeated with the bottom points coinciding. When this prediction realized, we invested at the average price 1320. In May 2012, the expected exit level was 1500 in October 2013.

    (click to enlarge)

    Figure 2. The original S&P 500 curve (black line) and that shifted forward to match the 2009 trough (blue line). Red line - expected fall in the S&P 500: from 1400 in March to 1300 in May.

    Figure 3 shows the evolution of the S&P 500 monthly closing price between May and August 2012. The S&P 500 closing level for August was 1430 and reached 1469 in the middle of September. This level provided a ten percent return over approximately 4 months. One can see that the observed level was far above the expected level (blue line). The return and the deviation from the expected level both made us think that this was the best time to exit. We sold the index on September 21 (1460) anticipating strong turbulence (economic, financial, and political) and an overall fall to 1375 at a few month horizon.

    (click to enlarge)

    Figure 3. Same as in Figure 2 with an extension between May and August.

    Figure 4 shows the evolution of the S&P 500 monthly closing price in September-November 2012. The October's closing level was 1411. On October 26, we put the November's level down to 1375. One can see that the red line intersects the blue curve. The previous history of the black and red lines intersection with the blue one made us think that the time to enter the market (S&P 500 index) was approaching. We expected to buy at 1350 to 1375.

    (click to enlarge)

    Figure 4. Same as in Figure 2 with an extension between September and November 2012.

    Figure 5 depicts the state of the S&P 500 on December 15, 2012. The index had a local minimum of 1347 in the middle of November and recovered to 1416 on November 30. This was 15 points less than the expected level of 1430 in December 2012. The red line intersects the blue one in January 2013 and a negative correction to 1400 (or less) was expected.

    (click to enlarge)

    Figure 5. Same as in Figure 4 with an extension into December 2012.

    Figure 6 displays the current situation with the S&P 500. As in a few cases after 2010, the actual index (red line) leads the expected one (blue) by a month or so. It has reached the (closing) level 1563 on March 14 and has been falling since then. As in April and November 2012, we expect the index to fall. The level is likely around 1455. Then it might regain its power and have a final spurt to 1560 in October 2013. Do not miss this last opportunity.

    (click to enlarge)

    Figure 6. Same as in Figure 5 with an extension into March 2013.

    Mar 20 2:08 PM | Link | 1 Comment
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