Oil price in 2012-2013

This is a revision to our oil price prediction as based on the difference between the overall PPI and the index of crude oil. Figure 1 compares our previous prediction in May 2011 with actual oil price in 2011 and 2012. In August 2011, the predicted price was a bit higher than the measured one. We expected the price to fall by approximately $5 per month to the level of ~$70 by December 2011. In reality, the price reflected from the high bound of the expected price (dashed line) and grew during the end of 2011. This effect reflects the high level of price volatility during short time intervals. Since February 2012, the price has been returning to the expected price range which expresses the slow fall through 2016, with the uncertainty bounds for the long-term trend in oil price shown in Figure 1. The level of oil price in 2016 is expected between $30 and $60 per barrel.

Here we confirm the oil price trend and its bounds. Red squares show our prediction of oil price through February 2013. Despite local fluctuations, the trend is negative and will bring the price to $45 (±$15) per barrel in 2016.  

Figure 1. The evolution of oil price since 2001 as estimated from the differnce of the overall PPI and the PPI of crude petroleum.

Economic growth: Russia vs Russia vs USA

There are several ways to estimate real economic performance of a given country. Here we present three different approaches to the case of Russia.

We have modelled the transition from socialism to capitalism in a number of socialist countries. Figure 1 displays the observed and predicted GDP per capita. We used the total economy database published by the Conference Board in 2011 (GK PPPs, 1990 US dollars). Both curves are normalized to their values in 1991. This is the start point of the transition, which was effectively finished around 2000. Since then the Russian economy has been evolving according to general rules applied to capitalist countries. The long term rate of growth was estimated as 0.033 1/y. Figure 1 shows that this rate is likely a good estimate irrelevant to shirt-term deviations. Thus, one can expect that the Russian economy will return to the trend in the near future.

Figure 1. Observed and predicted evolution of real GDP per capita (Geary- Khamis PPPs) in Russia.

Several posts in May 2011 were devoted to the evolution of real GDP per capita in developed countries. We have shown that the difference between the US and other countries has quasi-linear trends. This observation followed from our general (empirically derived) concept of constant annual increment in GDP per capita. This should also work for all former socialist countries turned to the capitalist railway. Russia is not an exclusion as Figure 1 confirms. Thus, Figure 2 compares the mean annual GDP increment for the USA (between 1950 and 2010), which is $387 in 1990 US dollars, and the estimates of annual increment in Russia since 1989. Obviously, it was very slow start because of the transition; real GDP in 1998 was ~60% of its value in 1991.  After 2003, Russia has experienced a period of quick growth with annual increments well above $387. This was a period of good performance. In 2009, all countries suffered a deep fall in real GDP per capita. The year of 2010, looks very average.

Figure 2. Annual increment of real GDP per capita in Russia compared to the long-term average in the USA.

The above comparison with the long-term average demonstrates the healthy pace of the Russian economy in the long-run. This is also valid for the short run. Figure 3 depicts the difference between GDP per capita in the US and Russia between 1990 and 2010. The concept of the constant increment implies that the gap in real GDP can be never decreased since the rate of growth falls inversely proportional to the level of GDP. This means that all former socialist countries will never approach the most developed countries. According to this principle, the gap in Figure 3 must return to the level between $13000 an $1500 in the near future. Russia has been growing too fast in the 2000s. This growth is not likely to be repeated.   

 Figure 3. The difference between real GDP per capita in the USA and Russia.

Ireland and Solow's exogenous growth model

Three months ago we revisited the evolution of real GDP per capita in Ireland. This was an example of a country which demonstrated an extremely high annual increment of GDP per capita growth between 1990 and 2005. This observation undermined our concept of constant increment in GDP per capita in developed countries which expresses the idea of inertia in economic growth (see our post on theory of economic growth).  In this post, we present an updated version of the previous post on Ireland with new estimates of GDP per capita as published by the Conference Board in 2011. The newly published set includes readings for 2010 and also revises the previous estimates, sometimes severely. It allows seeing the case of Ireland in some new light and strongly supports our concept. As we supposed 5 years ago, Ireland GDP was highly overestimated and has fallen quickly to fit the concept of constant annual increment or inertial growth.  

Originally, the concept of constant annual increment in real GDP per capita, G, as observed in all developed countries, was introduced 5 years ago in a working paper [1] and then published in the Journal of Applied Economic Sciences [2]. We found that in the long run the trajectory of GDP growth is a linear function of time:

G(t-t₀)= G₀+B(t-t₀)

where G₀ is the initial level of GDP per capita at time t₀ in a given country, B is the country dependent increment measured in dollars. Therefore, the rate of growth of real GDP per capita, dlnG/dt, has a decelerating trend:

dlnG/dt = B/G

This assumption gives excellent statistical results and explains the evolution of real GDP per capita in the biggest developed countries. There were two exceptions – Ireland and Norway. (The latter economy is likely driven by oil demand.) Before 1990, Japan also demonstrated a larger positive deviation from the constant trend but then quickly returned to it during the 1990s and 2000s. We foresaw the same effect for Ireland.

So, five years ago, I wrote 

An opposite example of an excellent recovery gives Ireland with corresponding results displayed in Figure 11. A slow start was quickly compensated and the last twenty years of an extremely fast growth resulted in the leading position in the world economy with the mean increment $678. There are some doubts, however, that future will be so successful. Such a long and quick growth always ends up in a depression. This was observed in Japan and is related to the long-term decrease in the number of the specific age population [Kitov, 2005a]. Ireland has managed to increase birth rate for a very long period and has an age structure similar to that observed in Japan 20 years ago. The population distribution is currently peaked near 20 years with the defining age of 18 years. The years to come will demonstrate only decrease in the defining age population.

Fig. 11. Same as in Figure 4 for Ireland. The mean value is $678. The growth of the real GDP per capita is outstanding during the last twenty years. There is a downward tendency during the last four years, however.

In Figure 11 borrowed from the paper, one can observed an extremely high deviation of constant increment. Nevertheless, we put the progress of the Irish economy under doubt. The reason was its similarity to the Japanese case and the underlying model of real GDP growth, which includes population of a country specific age. In January 2011, we presented a new version of the curves in the above Figure (see Figure 1 below) with data up through 2009 which were available in January 2011. The slope of the trend was +0.0272 instead of +0.0608 in 2004, i.e. fell by a factor of 2. This slope is much close to the zero value.

Figure 1. Same as in Fig. 11  above with data between 1950 and 2009. The increment of real GDP per capita vs. real GDP per capita in Ireland. All data are borrowed from the Conference Board data base (http://www.conference-board.org/economics/database.cfm).

The revised GDP per capita data and one new reading present a quite different picture in Figure 2. The positive excursion between $30000 and $50000 in the curve does not look so dangerous for our concept and the slope now is only +0.0155, i.e. by a factor of 3 lower than in 2004. Hence, the Irish GDP per capita is not an exclusion form the general rule that real GDP per capita does grow with a constant increment in the long run, as other developed countries.

This observation makes Solow's model of economic growth empirically inconsistent, and thus, void.  

 

Figure 2. Same as in Figure 1 for the 2011 version of the Conference Board Total Economic Database

The near future of the Irish GDP per capita is under question as well: it will likely decrease or increase just marginally in 2011 and in the next several years. We will keep reporting on the case.   Ireland provides a higher volatility in the GDP growth, which is driven by unusual population pyramids with a strong peak at one age. (Same shape is observed in Japan, but the peak age is 25 years larger.) 

References

[1] Kitov, I., (2006). Real GDP per capita in developed countries, MPRA Paper 2738, University Library of Munich, Germany, http://ideas.repec.org/p/pra/mprapa/2738.html

[2] Kitov, I., (2009). The Evolution of Real GDP Per Capita in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. IV(1(8)_ Summ), pp. 221-234.

Novellus Systems share predicted

An investor is usually interested to know the future evolution of stock prices. The current stock pricing paradigm does not allow to see far enough and not much helpful for a small/middle size investors. (Very big investors can always play nasty games in their favour.) Therefore, only deterministic pricing model can equalize chances. We propose such a concept which  is very simple and is based on deterministic links between share prices and prices of goods and services included in the consumer price index, CPI.

Literally, we decompose a share price (monthly closing price adjusted for splits and dividends) into a weighted sum of two individual CPI components, linear time trend component and constant free term. We allow positive and negative time lags between all variables in the relationship and seek to minimize the RMS model error by varying the involved coefficients. The set of CPI components consists of 92 independent price indices of different level: from major (overall and core CPI) to very small (e.g. photo and related materials). When the modeled share lags behind both defining CPI components we have a deterministic model predicting at a horizon of the smallest time lag. This concept gives excellent results in terms of the model error and very stable pricing models which are valid during several years. In 2008, the model successfully predicted bankruptcy of some major banks, including Lehman Brothers. Fannie May and Freddie Mac. We were able to forecast negative share prices several months ahead [1].  One can also find in [1] a formal model description. 

In this blog, we present and track successful models from the S&P 500 list. They are numerous. For other companies from the S&P 500 list, we also have accurate quantitative models, but they are not deterministic since at least one of defining CPI components lags behind the modeled price. We revisit (recalculate) all models every quarter using new data and report on successful models. In some cases, a model should hold for a year before we publish it.

In this post, we present a share pricing model for Novellus Systems (NVLS). It belongs to Technology sector and is specialized in semiconductor equipment and material.  A preliminary model was obtained in September 2009 (18 months ago) and covered the period from January 2009 (25 months!). This old model included the same indices as the current one: the price index of food less beverages (FB) and the index of motor vehicle parts (MVP).  Both indices seem to be not related to the major product of this company, but define a very reliable stock price model.

The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. Both indices lead by 4 months the NVLS share price.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between January 2009 and March 2011.  The model is as follows:

NVLS (t) = -2.62FB(t-4) + 2.34MVP(t-4) + 4.21(t-1990) + 196.8

where NVLS(t) is a share price in US dollars, t is calendar time.

It is interesting that food related indices have negative coefficients in our models. This means that increasing food price suppresses the growth in all shares on the market. This effect has perfect sense because the food demand is likely not very flexible and is considered as a major threat to the growth of real U.S. economy and stock market.

The observed and predicted models are depicted in Figure 2. The residual error is of $2.52 for the period between July 2003 and March 2011. From Figure 2, one can expect the share will drop to the level of $30 by the end of 2011 Q2, and then even lower.

Figure 1. Evolution of the price indices MVP and FB.

Figure 2. Observed and predicted NVLS share prices.

 

1. Kitov, I. (2010). Modelling share prices of banks and bankrupts, Theoretical and Practical Research in Economic Fields, ASERS, vol. I(1(1)_Summer) pp. 59-85

A preliminary model for Cephalon share

After the model for Altero Corporation, we present a share pricing model for Cephalon (CEPH). The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. The tenants' and household insurance index (THI) leads by 2 months and the index of prescription drugs (PDRUG) leads by 9 months the CEPH share price.  The latter index might be directly related to Cephalon product. Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between November 2010 and March 2011.  The model is as follows:

CEPH(t) = -3.94THI(t-2) + 1.61PDRUG(t-9) – 10.04(t-1990) + 120.83

where CEPH(t) is a share price in US dollars, t is calendar time.

Both models are depicted in Figure 2. The residual error is of $5.00 for the period between July 2003 and March 2011.  2009. Notice that the PDRUG index has been growing at a high rate since the beginning and any fluctuation in this index has been directly mapped into the price, which is characterized by high volatility. The THI index has been rising steadily but slowly. 

Figure 1. Evolution of the price indices THI and PDRUG.

Figure 2. Observed and predicted CEPH share prices.

Celgene Corporation stocks will not be growing

Here we present a share pricing model for Celgene Corporation (CELG). A preliminary model was obtained in September 2009 and covered the period from October 2008. This old model included the same indices as the current one: the price index of food at home (FH) and the index of housing (H). The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. The FH index leads by 6 months and the H index is synchronized with the CELG share price.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011.  The model is as follows:

CELG(t) = -1.87FH(t-6) + 2.86H(t-0) +4.21(t-1990) – 247.59

where CELG(t) is a share price in US dollars, t is calendar time.

The observed and predicted prices are depicted in Figure 2. The residual error is $3.91 for the period between July 2003 and March 2011.  Since the dependence on time is weak ($4.2 per year) and the index of food at home had a spurt during the last four months ($7 since December 2010), one can expect a fall by $10 in the next half a year. We assume that the housing index is not going to grow fast.

Figure 1. Evolution of the price indices FH and H.

Figure 2. Observed and predicted CELG share prices.

Loews Corporation share price

Here we present a share pricing model for Loews Corporation (L) (see a brief description of the concept here). A preliminary model was obtained in September 2009 and covered the period from October 2008. This old model included the index of food without beverages (FB) and the index of transportation service (TS).

The most recent model also uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. Currently, the defining indices are almost the same: the index of food (F) and the TS index. The F index leads by 5 months and the TS index by 4 months.  Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between December 2009 and March 2011.  The models are as follows:

L(t) = -2.03F(t-5) – 2.12TS(t-5) +28.23(t-1990) +448.98

where L(t) is the share price in US dollars, t is calendar time.

Both models are depicted in Figure 2. The predicted curves lead the observed ones by 4 months. The residual error is of $2.46 for the period between July 2003 and March 2011.  In the second quarter of 2011, the model foresees a fall to the level of $39 per share. 

Figure 1. Evolution of the price indices F and TS.

Figure 2. Observed and predicted L share prices.

Cardinal Health in Q2 2011

Cardinal Health (CAH) is one of the companies with a long story of successful modeling. In September 2009, we first estimated a preliminary two-component model from the full set 73 CPI components. As in all our models, we predict the monthly closing price adjusted for splits and dividends. Here, we revisit the previous model using all data available on April 24^th and an extended set of CPIs.  Also, all time series are 18 months longer what provides a better resolution and reliability.

For CAH, the defining indices are as a year and two years ago: the index of dairy and related products (DAIRY) and the index of pets, pet products and services (PETS). The CPI components are both leading by 2 months. Figure 1 depicts the evolution of both indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011:  

CAH(t) = -0.38DAIRY(t-2) – 1.69PETS(t-2) +11.33(t-1990) + 136.12

      

where CAH(t) is the share price in US dollars, t is calendar time.

The predicted curve in Figure 2 is synchronized with the observed one. The residual error is of $2.58 for the period between July 2003 and March 2011.  The next move in the price is likely down according to the growth in both defining indices.

Figure 1. Evolution of the price indices DAIRY and PETS.

Figure 2. Observed and predicted CSC share prices.

Computer Science Corporation will not be growing

A year ago, we first presented a share price (monthly closing price adjusted for splits and dividends) model for Computer Science Corporation (CSC). In this post, we revisit the previous model using all data available on April 24th.  Longer time series provide a better resolution between defining CPIs and higher model reliability.

For CSC, the defining indices are as a year and two years ago: the index of motor vehicle parts (MVP) and the index of sporting goods (SPO). The CPI components are leading by 0 and 5 months, respectively. Figure 1 depicts the evolution of both indices which provide the best fit model, i.e. the lowermost RMS residual error, between July 2008 and March 2011:  

CSC(t) = -3.83MVP(t-0) + 3.16SPO(t-5) +16.31(t-1990) – 137.20

where CSC(t) is the share price in US dollars, t is calendar time.

The predicted curve in Figure 2 is synchronized with the observed one. The residual error is of $3.28 for the period between July 2003 and March 2011.  Since the MVP index has been growing since 2002 and the SPO index has a slight negative trend, the share price will not be growing in the near future.

Figure 1. Evolution of the price indices MVP and SPO.

Figure 2. Observed and predicted CSC share prices.

Comparison of SunTrust Banks (STI) and Franklin Resources (BEN) models

The price model for SunTrust Banks (STI) is a brand new one.  Like Franklin Resources (BEN) reported four days ago, it is a financial company and was analyzed previously as a candidate for a bankruptcy [1]. The newly obtained model is based on is our stock pricing concept and includes the consumer price index of food less beverages (FB) (it was food at home, FH,  for BEN) and the index of tobacco and tobacco products (TOB). The former defining CPI component led the share price by 4 months and the latter one by 6 months (5 and 8 months, respectively for BEN). Therefore, the model has a natural 4-month forecast horizon. It is worth noting that there are two financial companied driven by the same CPIs.

Figure 1 depicts the overall evolution of the involved indices. These two defining CPI components provide the best fit model between March 2011 and July 2010.  Both coefficients are negative, as in many models already reported in this blog, and thus the increasing prices result in decreasing share price. (However, the sensitivity to the TOB index is much lower than to the FB index, as was also valid for BEN). The slope of time trend is positive and would provide a $36 increment per year if both CPIs are fixed. The best-fit 2-C model for STI(t) is as follows:

STI(t) = -5.46FB(t-4)  – 0.19TOB(t-6) + 36.07(t-1990) + 627.06     

where STI(t) is a share price in US dollars, t is calendar time.  The standard deviation of $3.77  between July 2003 and March 2011. There was no growth during  the first quarter of  2011 since no one of the defining indices has demonstarted any big movement. In the second quarter of 2011, the price may drop to the level of $23 (and then to $18) from the current $28, as follows from the predicted and observed curves presented in Figure 2.  Figure 3 displays the model error.

Figure 1. The evolution of the difference between FB and TOB.

Figure 2. Observed and predicted STI share prices. The predicted curve leads by 4 months and was shifted ahead for synchronization with the observed one. Notice excellent prediction of major turns in the price.

Figure 3. The model residual, i.e. the difference between the observed and predicted STI

1. Kitov, I. (2010). Modelling share prices of banks and bankrupts, Theoretical and Practical Research in Economic Fields, ASERS, vol. I(1(1)_Summer) pp. 59-85

Allergan (AGN) share price model

It’s time to revisit the price model for Allergan (AGN) first estimated in January 2011.  As before, we model the monthly (adjusted for dividends and splits) closing prices between July 2003 and March 2011. It is found that the best fit model obtained in January is still valid in April 2011 with almost the same coefficients and time lags (see Appendix for details of our deterministic share pricing concept).

Briefly, we decompose a share price into a weighed sum of two individual CPI components, linear time trend component and constant free term. We allow positive and negative time lags between variables and seek to minimize the RMS model error by varying all involved coefficients. The set of CPI components consists of 92 independent price indices of different level: from major (overall and core CPI) to very small (photo and related materials). When both defining components lead the modeled price, one can predict future evolution of the stock; at least in the near future. The bets-fit two-component (2-C) model for AGN is as follows:

AGN(t)= -1.90FH(t-3) – 1.63THI(t-0) +16.56(t-1990) + 337.58       

where AGN(t) is the price of a share in US dolars, FH in the index of food at home leading the stock price by 3 months, THI is the index of tenants’ and household insurance, (t-1990)  is the elapsed time. Quantitatively, the best fit model provides RMSE=$3.37 for the period between July 2003 and March 2011. Also, it has been valid during the past seventeen months and we expect it to be valid in the first half of 2011, at least.  The defining CPI indices are displayed in Figure 1. The FH index has been growing at a high rate during since December 2011. This effect did not overcome the positive time trend of $16.6 per year and the fall in the THI during the same time. The share may grow in the second quarter if all the observed trends hold.

Figure 1. The price indices THI and FH between 2002 and 2011

Figure 2. Observed and predicted share prices AGN.

 Appendix

In its general form, our pricing model is as follows:

sp(t_j) = Σb_i∙CPI_i(t_j-t_i) + c∙(t_j-2000 ) + d + e_j                                                              (1)

where sp(t_j) is the share price at discrete (calendar) times t_j, j=1,…,J; CPI_i(t_j-t_i) is the i-th component of the CPI with the time lag t_i, i=1,..,I; b_i, c and d  are empirical coefficients of the linear and constant term; e_j 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 eleven months. Apparently, this is an artificial limitation and might be changed in a more elaborated model.

System (1) contains J equations for I+2 coefficients. For POM we use a time series from July 2003 to March 2011, i.e. 94 monthly readings.  Due to the negative effects of a larger set of defining CPI components 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. In the POM model, we use 92 CPI components. They are not seasonally adjusted indices and were retrieved from the database provided by the Bureau of Labor Statistics.

Due to obvious reasons, longer time series guarantee a better resolution between defining CPIs. In general, there are two sources of uncertainty associated with the difference between observed and predicted prices. 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. Second source of uncertainty is related to all kinds of measurement errors and intrinsic stochastic properties of the CPI and its components. 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.

Does crude drive the price index of steel and iron? (update)

We have been following the link between price indices of iron&steel and crude oil (domestic production) since 2009. This is a quarterly update. The previous update included PPI data as of November 2010. Here we extend the set by data available after April 13, 2011. Otherwise, we retain the form of the report untouched.

Historically, we first reported that the price index of crude oil had been likely evolving in sync with that of iron and steel, but with a lag of two months in September 2009  [1].  In order to present both indices in a comparable form, the difference between a given index, iPPI (i.e. iron&steel and crude), and the overall PPI was normalized to the PPI: (iPPI(t)-PPI(t))/PPI(t). The normalized differences represent the evolution of the rate of deviation from the PPI over years.  

Figure 1 depicts the corresponding time histories of the normalized deviations from the PPI, including the most recent period since December 2010.  Simple visual inspection reveals the following feature: the (normalized deviation from the PPI of the) index of iron and steel lags by approximately two months behind the (normalized) index of crude oil.

Figure 1. The deviation of the iron and steel price index and the index of crude oil from the PPI, normalized to the PPI.

In order to reduce both deviations to the same scale we additionally normalized the curves in Figure 1 to their peak values between 2005 and 2011

(iPPI(t)-PPI(t))/[PPI(t)*max{iPPI-PPI)}]

This scaling allows a direct comparison of corresponding shapes. In Figure 2, we display the normalized index of iron and steel shifted by two months ahead to synchronize its peak with that observed in the normalized index for crude petroleum. The scaled index of crude demonstrates just short-term deviations from the index of iron and steel in the overall shape and timing of the peak and trough. Simple smoothing with MA(3) makes the curves resemblance even better. As an invaluable benefit of the resemblance, one can use the two-month lag to predict the future of the iron and steel price index.

Figure 2. Deviation of the iron and steel price index from the PPI, normalized to the PPI and the peak value after 2005 as compared to the deviations of the index for crude petroleum normalized in the same way. The normalized index for iron and steel is shifted two months ahead.

Conclusion

Between 2006 and 2011, the deviation of the price index of iron and steel from the PPI in the USA repeats the trajectory of the deviation of the index of crude petroleum (domestic production) with a two-month lag. Therefore, the prediction of iron and steel price for at this horizon is a straightforward one.  

References

1. Kitov, I., Kitov, O., (2009). 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

Yahoo! share in Q2 2011

In January 2011, we wrote about YHOO share in 2011 Q1:

Currently, the predicted price shows no tendency to rise. All in all, one should not expect the YHOO price to grow fast.

This prediction was right and YHOO shares stalled in Q1. Here we update the underling model and give a forecast for 2011Q2.

Since the last revision in January 2011, the model for Yahoo! (YHOO) had no significant changes and still is a slightly weird example of the deterministic character of share price evolution.  The YHOO model is stable over the past year and a half and is defined by somewhat unexpected indices: the consumer price index of meat, poultry, fish and eggs (MEAT) and the index of motor vehicle parts and equipment (MVP). Both defining indices seem to have no visible relation to the internet services. On the other hand these CPIs are the most basic ones and are in the root of any economic activity.

In the new model, the MEAT index leads the share price by 5 months (6 months in January) and the MVP has no lead (1 month in January). Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between June 2010 and March 2011.  The MEAT coefficient is positive and thus the increasing price of meats, poultry, fish and eggs causes the share price to grow at a slow pace. The MVP index has a negative coefficient and causes the share to fall. The slope of time trend is positive revealing the price tendency to increase over time. The best-fit 2-C model for YHOO(t) is as follows:

YHOO(t) =  0.49MEAT(t-5) – 3.25MVP(t-0)  + 10.66(t-1990) + 145.61

where YHOO(t) is the price of a share in US dollars, t is calendar time.

The predicted and observed curves are presented in Figure 2. The residual error is of $2.56 for the period between June 2003 and March 2011 (see Figure 3). In the second quarter of 2011, the price of food will likely be growing and the MVP has a tendency to fall. This may introduce a positive force into the share and it will be growing through the quarter.

Figure 1. Evolution of the price of MEAT and MVP.

Figure 2. Observed and predicted YHOO share prices.

Figure 3. The model residual. Currently, the price is underestimated.

COP, XOM, CVX, DVN, and HAL stocks

Two years ago we presented several models linking share prices of companies to the difference between the headline and core CPI (Kitov and Kitov 2009c) including Halliburton (HAL), Devon Energy (DVN), and Chevron (CVX). Before that paper, we had modeled and predicted the evolution of share prices of ConocoPhillips (COP) and Exxon Mobil (XOM) (Kitov 2009).

It was demonstrated that the time history of these prices could be accurately approximated by a linear function of the difference between core CPI (cCPI) and headline CPI (CPI) in the United States. This difference is found to be the best to predict share prices in the energy subcategory of the S&P 500. The underlying model was an intrinsically deterministic and described the evolution of share prices along predetermined trajectories.

Here we revisit all five models using new estimates of the core and headline CPI and the previously obtained coefficients.  In that sense, we validate the models with new data. Our pricing model is simple. It states that a share price, for example that of ConocoPhillips, COP(t), can be approximated by a linear function of the difference between the core and headline CPI:

COP(t) = A + BdCPI(t + t₁)                                                  (1)

where dCPI(t) = (cCPI(t) – CPI(t)), A and B are empirical constants (for COP, A=72 and B=-5.5 for the period between 1999 and 2009); t is the elapsed time; and t₁=1/6 year is  the time delay between the share and the  dCPI changes, i.e. the dCPI has a lag behind the share price. For other four energy-related companies, the models were as follows: 

XOM= -6.0dCPI(t+1/12) +90; 1999-2009

CVX = -5.0dCPI(t+0) + 85; 1999-2009

DVN = -7.5dCPI(t+1/6) + 93; 1999-2009

HAL = -3.5dCPI(t-1/6) + 43; 1999-2009

Figure 1. The observed and predicted share prices.

Figure 1 displays all five models with coefficients obtained in 2009. All in all, the prediction was excellent and these prices are likely defined by the difference between the core CPI and the headline CPI. Considering increasing oil price, the rise in the share prices is not surprising. When oil price is down, the share will fall.  

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. 

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.

Kitov, I., Kitov, O. (2009a). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany,

Kitov, I., Kitov, O. (2009b). 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. (2009c). Predicting share price of energy companies: June-September 2009, MPRA Paper 15863, University Library of Munich, Germany