AutoNation's share price: no large change is expected

We have been modeling AutoNations’ (NYSE: AN) stock price since 2009. This is a company from services sector (as defined by the S&P 500) and operates as an automotive retailer in the U.S. here we present the current model which has been obtained by decomposition of the time series of monthly closing share prices (adjusted for splits and dividends) into a weighted sum of two consumer price indices. One might presume that a fast growth in the CPI inherently linked to the AN share price (e.g. energy consumer price for energy companies) relative to some independent by dynamic reference should be manifested in a higher pricing power for the company. Therefore, the task is to find two best (say, in sense of RMS residual error) defining CPIs. It allows testing of the underlying concept (decomposition into CPIs) and to estimate time lags and coefficients for AN.

We have borrowed the time series of monthly closing prices of AN from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS. The evolution of AN share price is defined by the consumer price of rent of primary residence (RPR) and the index of financial service (FS). The defining time lags are as follows: the RPR index leads the price by 10 months and the FS index leads by 5 months. The relevant best-fit model for AN(t) is as follows:

AN(t) = -1.89RPR(t-10) – 0.36FS(t-5) + 15.47(t-1990) + 270.31, February 2012

where AN(t) is the AN share price in U.S. dollars, t is calendar time. This model is valid since August 2011 with the same lags and coerffcients. Figure 1 displays the evolution of both defining indices since 2002. Due to the negative coefficient (slope), the sharp drop in the FS index in 2009 best explaines the jump in the share price five months later.

Figure 2 depicts the high and low monthly prices for the share together with the predicted and measured monthly closing prices. The predicted prices are well within the bounds of the share price uncertainty. The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $1.63.

Both CPIs have negative influence on the share price. Therefore, the price should decrease when the indices grow fast. From Figure 2, we expect no large changes in the first half of 2012. At least the price will be inside the uncertainty bounds defined by monthly high/low prices, which were volatile during the previous 4 to 6 months.

 

Figure 1. The evolution of the index of rent of primary residency (RPR) and the index of financial service (FS).

Figure 2. Observed and predicted AN share prices.

Figure 3. The model residual error: stdev=$1.63.

Putin proves that the Duma elections were falsified

We wrote several posts of the falsification of the State Duma elections in December 2011. The main argument was statistical. For a fair voting process with choices driven by a multitude of factors, e.g. age, income, sex, social status, place of birth and residency, etc., one can expect a normal distribution of shares of votes in favor of a given candidate over polling stations. The statistical background was the Central Limit Theorem, CLT. All parties did follow this rule and demonstrated Gaussian distribution. Except United Russia. This was the argument in favor of falsification which can also call a controlled choice.  

Our opponents defended their position by the argument that the CLT does not and should not work for elections. And the Duma elections were fair and right. 

The movement for fair elections and opposition as a whole has done a lot to make the presidential election fair. Half a million people have been sent as observers to polling stations. Putin has added his twenty cents and … voila. The presidential election was fairer. The overall distribution of votes for Putin is much closer to normal now (thanks Maxim Pshenichnikov).  The great effort was in Moscow, which has demonstrated a textbook Gaussian.   

Hence, the central limit theorem and normal distribution do work where the voting process was fair and well controlled. As expected.  

Now we can conclude and demand. The results of the presidential election proves that the Duma elections were falsified by approximately 15,000,000 votes. If Putin is the President of the Russian Federation, we have inherent rights for Duma re-elections in a year. Putin has proved the Duma elections were a fraud.   

We do not consider the election campaign to be a fair one. The candidates were not given equivalent possibilities: TV, newspapers, administrative pressure, etc. were all given to Putin.    

Putin has likely got around 55%

Putin has won. Some preliminary (and statistically sound) results show that he has got around 55%. Max Pshenichnikov has promptly provided an intermediate version of the percentage of polling stations as a function of the share for Putin. It seems peaked at 55% with a much lower high-vote tail than  United Russia had in December 2011. This time the election procedure was cleaner, but the election compain was not fair. Apparently, the latter is my personal judgement.

P.S. Statistics has shown its key role in the assessment of social processes. The lower level of falcification during the presidential elections confirms the high level of falcifications during the Duma elections. When two curves from the Max's post are compared, one can judge that the fight against dirty tricks has helped a lot. At the same time, these tricks were undoubtedly in play in December 2011.
Also, the Central Limit Theorem works and the absolutely fair election procedures (not election compains) can be verified.

Real GDP per capita in developed countries

Angus Maddison did a wonderful job recovering the evolution of real GDP per capita before 1950. Various historical estimates are available now at the website of Groningen University. The estimates after 1950 with the most recent updates are published by the Total Economy Database maintained by the Conference Board.  

We have demonstrated real GDP per capita, G, in developed countries follows a linear trend in the long run: 

G(t) = At + C                             (1) 

where the slope A and free term C have to be determined by linear regression.  

In other words, real GDP per capita has a constant annual increment over the previous 130 to 150 years at least. There is a break between 1940 and 1950. After the break, the annual increment jumped up by a factor of 10 in all developed countries. We have attributed this change to the revision of inflation definition around 1950. By extrapolating the linear regression line obtained before 1940, we have found that the true level of real GDP per capita in the U.S. should be around $11000. The official value is ~$31,000  (Geary–Khamis 1990 US dollars).

Here we apply the same procedure and estimate the true values of real GDP per capita in the U.K., France, Italy, Switzerland and Austria. In five Figures we depict both relevant segments, i.e. from 1870 to 1940 and from 1950 to 2011, and regression lines with their equations. We also reproduce one Figure from our previous post on the US. Table 1 lists the official and true estimates. The difference between these estimates is completely attributed to the mistakes in definition of price inflation.

Table 1. Official and true GDP per capita in GK dollars as of 2011

	Official	True	Ratio
Austria	24702	5041	4.90
France	21792	7093	3.07
Italy	18293	5451	3.36
Switzerland	25640	10524	2.44
UK	22377	8699	2.57
USA	30928	10956	2.82

All in all, the biggest countries have dramatically biased estimates of real GDP per capita. The rate of price inflation (i.e. the GDP deflator) has been underestimated and has affected the perception of real growth.  

Economics - a balloon expanding under the pressure of vacuum

All economists remember the years of so called “Great Moderation”. It was time when any mainstream theory (Keynesian or neoclassic) was right because they all predicted no change. The essence of conventional economics consists in the feedback loop when actual economic behavior can be partially controlled by economic/financial authorities like central banks, broader government and so on. The Great Moderation was the triumph of orthodox (and also heterodox) economic theory. All articles in major economic journals paid tribute to smart monetary/economic policies in developed countries and seriously declared cloudless future. Where are these happy years now?

What one sees now is a severe internal divergence in the economics domain. Previously peacefully co-existing “schools of economic thought” really fight without captives. Their opinions have polarized on all issues, from the reasons of the crisis to the influence of inequality on real economic growth.  Every action of monetary/economic authorities is criticised from all sides  and the authorities cynically ignore academic economists.

Unfortunately, nobody  explains anything  helpful in terms of strict science or even common sense. Nonetheless, the discussion is getting hotter. It seems to be a balloon expanding under the pressure of vacuum – such an anti-scientific allegory.    

Abbot Laboratories’ share price

Here we model the evolution of Abbot Laboratories’ (NYSE: ABT) stock price since July 2003. Abbot is a company from healthcare sector of the S&P 500 index. We model a share price decomposing it into a weighted sum of two consumer price indices. Our concept presumes that there exist a trade-off between a given share price and goods and services the relevant company produces and/or provides. Obviously, the defining consumer price (or CPI) has to rely to some independent and dynamic reference, which can also be a consumer price index. The pricing power is related to the difference between the defining and reference CPIs. 

We have borrowed the time series of monthly closing prices of ABT from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS.  Instructively, the evolution of ABT share price is defined by the consumer price index of medical care commodities (e.g. the discovery, development, manufacture, and sale of health care products) and the index of transportation services (TS). The defining time lags are as follows: the MCC index leads the share price by 9(!)  months and the TS index leads by 8 (!) months. The relevant best-fit model for ABT(t) is as follows:  

ABT(t) =  0.93MCC(t-9) – 1.00TS(t-8)  + 1.92(t-1990) – 22.62,  February 2012 

where ABT(t) is the ABT share price in U.S. dollars,  t is calendar time. Figure 1 displays the evolution of both defining indices since 2002.  Figure 2 depicts the high and low monthly prices for an ABT share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the bounds of the share price uncertainty and lead by 8 months.  However, the price has not been changing much since 2010 and the knowledge of the lead can not bring high return. 

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $2.38. Currently, the price is overestimated relative to its expected value and one can foresee a negative correction (~$3) in the first half of 2012.  From Figure 2, the uncertainty of $5 (between the low and high monthly prices) is applicable to our prediction. It means that one may act on the price when it is beyond the $5 range relative to the expected level.  

Figure 1. The evolution of MCC and TS indices

Figure 2. Observed and predicted ABT share prices.

Figure 3. The model residual error: stdev=$2.38.

Allstate Corporation's share price

Here we model the evolution of Allstate Corporation’s (NYSE: ALL) stock price. Allstate is a company from financial sector which is associated with “the personal property and casualty insurance, life insurance, and retirement and investment products business primarily in the United States”. The model has been obtained using our concept of share 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 potential trade-off between a given share price and goods and services the company produces and/or provides. For example, the energy consumer price does influence the price of energy companies. It should be taken into account that the defining consumer price (or relevant CPI) has to be related to some independent and dynamic reference, which can also be a consumer price index. A higher relative growth of the defining CPI should be manifested in a higher pricing power for the company.  

We have borrowed the time series of monthly closing prices of ALL from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through January 2012 are published by the BLS.  The evolution of ALL share price is defined by the consumer price index of food without beverages (FB) and the index of information and information processing (INF). The defining time lags are as follows: the FB index leads the share price by 4 months and the INF index leads by 6 months. The relevant best-fit model for ALL(t) is as follows:  

ALL(t) =  -1.83FB(t-4) – 4.05INF(t-6)  + 6.21(t-1990) + 634.40,  February 2012

where ALL(t) is the ALL share price in U.S. dollars,  t is calendar time. Figure 1 displays the evolution of both defining indices since 2002.  Figure 2 depicts the high and low monthly prices for an ALL share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the bounds of the share price uncertainty and lead by 4 months.  

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and January 2012 of $2.74. 

One can foresee the price evolution at a 4 months horizon. Currently, the share price is expected to decline in the first half of 2012.   

Figure 1. The evolution of FB and INF indices

Figure 2. Observed and predicted ALL share prices. 

Figure 3. The model residual error: stdev=$2.74.