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# Ivan Kitov's  Instablog

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
My company:
Stock Market Science
My blog:
Economics as Classical Mechanics
My book:
Deterministic mechanics of pricing
• ##### 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 (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.

Disclosure: No positions

Disclosure: No positions
Tags: SPY
Mar 27 7:00 AM | Link | Comment!
• ##### 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 Mobile (NYSE: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 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.
[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

Disclosure: No positions
Tags: XOM, COP
Mar 27 3:49 AM | Link | Comment!
• ##### 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 (NYSE:XOM) and ConocoPhillips (NYSE: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 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.
[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

Disclosure: No positions
Tags: COP
Mar 21 4:49 AM | Link | Comment!

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