Share price of select energy companies

Since September 16, 2009 the readings of the headline CPI and its components for August 2009 are available (we retrieve all CPI data from http://www.bls.gov/data). We recalculate our model for selected stock prices from the S&P 500 list. First was ConocoPhillips since it provides a good example of a company, which share price has been leading defining components of the CPI. Here we present several companied from the “energy” subcategory of S&P 500. It is instructive that these companies are rather different than similar in the evolution of share price and thus in defining CPI components.

In the previous posts and articles [1,2] we introduced several models with varying number of CPI components. In our view, the best one, we call it 3-C model, is seeking those two CPI components from 34 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 August 2009. This model also includes free term (constant) and linear time term [3-6], which compensates well know linear (time) trends between various CPI components.

In the previous post we reported the empirical 3-C model for COP:

COP(t)= 3.41CF(t+1) - 7.17EC(t-6) + 7.22*(t-2000) + 145.76

where t is the calendar time, CF is the headline CPI less food, which lags behind COP by one months, and EC is the index for education and communication leading COP by six months. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009. Figure 1 displays the observed and predicted prices.

Figure 1. Observed and 3-C predicted COP’s share price.

Below we present analytic models and figures for several energy companies without comments. One can judge the accuracy of the predictions and the similarity/difference between the companies.
Figure 2. Observed and 3-C predicted Apache Corp.’s share price: APA(t) = 1.35*TPR(t+1) + 3.21*MCS(t-7) + 47.20*(t-2000) - 973, where TPR is the index of private transportation, MCS is the index of medical care services. Standard deviation is $6.36.

Figure 3. Observed and 3-C predicted Anadarko Petroleum Corp.’s share price: APC(t) = 3.31*EC(t+2) – 1.74*CSHF(t-5) + 5.49*(t-2000) + 58, where EC is the index of education and transportation, CSHF is the headline CPI less shelter and food. Standard deviation is $3.22.

Figure 4. Observed and 3-C predicted Baker Hughes’ share price: BHI(t) = 4.93*F(t-5) – 0.79*T(t+1) + 32.53*(t-2000) + 662, where F is the index of food and beverages, T is the index of transportation. Standard deviation is $5.30.

Figure 5. Observed and 3-C predicted Peabody Energy Corp.’s share price: BTU(t) = 0.64*FU(t-4) + 1.36*TPR(t+1) – 8.37*(t-2000) - 266, where FU is the index of (housing) fuels and utilities, TPR is the index of private transportation. Standard deviation is $4.35.

Figure 6. Observed and 3-C predicted Cameron Intl. CP share prices CAM(t) = 0.64*TPR(t+1) + 2.65*RENT(t-4) - 17.1*(t-2000) - 610, where FU is the index of (housing) fuels and utilities, TPR is the index of private transportation. Standard deviation is $3.38.

Figure 7. Observed and 3-C predicted Chesapeake Energy Corporation share price: CHK(t) = 0.41*E(t+1) - 1.50*ED(t-7) - 12.1*(t-2000) + 102.7, where E is the index of energy and ED is the index of education. Standard deviation is $2.70.

Figure 8. Observed and 3-C predicted Consol Energy share price: CNX(t) = 6.11*C(t+2) – 2.62*ED(t-5) – 2.81*(t-2000) - 767.5, where C is the headline CPI and ED is the index of education. Standard deviation is $5.65.

Figure 9. Observed and 3-C predicted Chevron share price: CVX(t) = 0.25*E(t+1) + 2.76*MCS(t+4) – 37.6*(t-2000) - 716.1, where E is the index of energy and MCS is the index of medical care services. Standard deviation is $3.26.

Figure 10. Observed and 3-C predicted Devon Energy Corp.’s share price: DVN(t) = 0.79*T(t-3) + 0.46*E(t+2) – 0.68*(t-2000) - 162.7, where E is the index of energy and T is the index of transportation. Standard deviation is $5.67.

Figure 11. Observed and 3-C predicted Ensco share prices: ESV(t) = 2.23*CSH(t+1) - 2.61*FB(t-5) + 8.89*(t-2000) + 65.9, where CSH is the headline CPI less shelter and FB is the index of food only. Standard deviation is $3.37.


References
[1] 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
[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., (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.
[4] 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
[5] 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
[6] 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

Predicting bank bankruptcy: Colonial Bank vs. CIT Group Inc.

We have described the evolution of a number of share prices for S&P 500 companies using empirical relationship between the prices and the differences between various CPI components [1-3], [Seeking Alpha posts]: Bank of America (BAC) and Goldman Sachs (GS, both financials), Microsoft (MSFT, information technology), and Alcoa (AA, materials), Boeing (BA, industrials), Exxon mobile (XOM, energy), ConocoPhillips (COP, energy), etc. All these companies were described with a reasonable accuracy considering the uncertainty associated with the monthly estimates of CPI expenditure subcategories and slightly stochastic character of the monthly closing price (adjusted for dividends and splits) as a representative of corresponding share price. All in all, the concept has demonstrated a high level of consistency.

This time our task is a more exciting and challenging one. Can our model describe the approach to bankruptcy? For a regular investor this question is of the top priority. The history of dramatic decline in share prices of financial companies in 2008 and 2009 dictates an inevitable choice – comparison of the Colonial Bank (CNB) and CIT Group (CIT), which both were beyond the edge of bankruptcy but with different outcome. In this study, all share prices are retrieved from YahooFinance.

Previously, we introduced and tested several models with varying number of defining CPI components. It was found that the best model includes two defining CPI components, free term (constant) and linear time term [4-6], which compensates well known the linear trends between the defining CPI components. For historical reasons we call it 3-C model. In this study, we are seeking for those two CPI components from a full set of components, which minimize the (RMS) difference between observed and predicted prices.

The 3-C model for a share price sp(t) is as follows:

sp(t) = A*CPI1(t+t1) + B*CPI2(t+t2) + C*(t-2000) + D (1)

where CPI1 and CPI2 are defining CPI components; t is the calendar time; A, B, C, and D are empirically determined coefficients. Because prices for good and services can lag or lead relevant share prices the time lags t1 and t2 are introduced. Both time lags can be positive or negative. In our model, we test all possible lags between 0 and +13 months. So, we chose the best from 34*33*14*14 ~ 200,000 possible models, with two extra degrees of freedom introduced by linear and free terms.

The full set includes 34 CPI components, which are tested as predictors for each share price. Among these components are major expenditure categories: the headline CPI (C), the core CPI, i.e. the headline CPI less food and energy (CC), food and beverages (F), housing (H), apparel (A), transportation (T), medical care (M), recreation (R), education (ED), communication (CO), and other goods and services (O). All components used in the model are not seasonally adjusted ones and retrieved from the Bureau of Labor Statistics.

In [4] we have revealed and explained the presence of linear trends in the differences between various components of the CPI. It was also found that the trends exist during long but finite periods and then their slops turn to opposite signs. Accordingly, the evolution of the differences between CPI components since 1960 can be approximated by a piece-wise linear function. When the trends turn, the coefficients in the link between CPI and share price also change. Because of this constraint we limit our modeling to the period between July 2003 and July 2009. The early date is a conservative estimate of the start of the current trend, and the latter one corresponds to the bankruptcy of Colonial Bank.

Here, we would like to emphasise that the usage of the differences instead of CPI components is caused by two crucial factors. First, we presume that the evolution of a share price depends only on the pricing power of goods and services associated with the company relative to other goods and services. Then, the difference in pricing powers of two companies should be directly mapped into the difference in the growth in relevant consumer price indices. Therefore, we assume that there exists a pair of CPI components, which reflect the best relative evolution of the share prices. Such a pair might not be always available among eight major expenditure categories. As a result, one needs two or more differences between CPI components to accurately predict the evolution of a share price.

Second factor consists in the presence of sustainable (linear and nonlinear) trends in the difference. This is the phenomenon we have described in [4-6]. Effectively, one can accurately decompose any share price using several CPI components. However, such decomposition does not allow forecasting without knowledge of the evolution of relevant CPI subcategories. The trends in the differences make it possible to predict at longer time horizons.

Now we apply the 3-C model (1) to the CNB’s and CIT Group’s share prices. The (LSQR) best-fit empirical relationship is as follows:

CNB(t) = 1.58*F(t) – 1.39*O (t-10) + 20.61*(t-2000) + 633 (2)
CIT(t) = -4.14*F(t-6) – 3.10*FB (t+4) + 43.18*(t-2000) + 1776 (3)

Empirical relationship (2) implies that CNB’s share price evolve in sync with the index of food and beverages (F), but lags behind the index for other goods and services (O) 10 months. Therefore, the share price depends on past and contemporary values of the defining CPI components. Effectively, it allows predicting CNB price only in the past. Figure 1 displays the observed and predicted price as well as their residual.

Empirical relationship (3) shows that CIT’s share price leads by six months the index of food and beverages (F) and lags four months behind the index for food only (FB). Therefore, the share price depends on past and future values of the defining CPI components. Effectively, it allows predicting CIT price only in the past.

Comparing the time histories of CNB and CIT one can conclude that the former sank right below the zero price and thus this bank deserved the bankruptcy. CIT has been closing the negative zone but still is slightly above it. The next several readings of FB will answer the question – Was it worth to bail out CIT Group? In other words, will the predicted price sink below the zero line?

Figure 1. Upper panel: Comparison of the observed and predicted CNB’s share price. The latter is obtained using (2). Lower panel: the difference between the observed and predicted price.

Figure 2. Upper panel: Comparison of the observed and predicted CIT’s (adjusted for dividends and splits) share price. The latter is obtained using (3). Lower panel: the difference between the observed and predicted price.

References
[1] Kitov, I., (2009). ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finances, v. 1, issue 2 (in press).
[2] Kitov, I., Kitov, O., (2009). Predicting share price of energy companies: June-September 2009, MPRA Paper 15863, University Library of Munich, Germany.
[3] Kitov, I., Kitov, O., (2009). Modelling selected S&P 500 share prices, MPRA Paper 15862, University Library of Munich, Germany
[4] 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.
[5] Kitov, I., Kitov, O., (2009a). A fair price for motor fuel in the United States, MPRA Paper 15039, University Library of Munich, Germany
[6] Kitov, I., Kitov, O., (2009b). Sustainable trends in producer price indices, Journal of Applied Research in Finance, v. 1, issue 1

The Phillips curve regains attention

Laurel Graefe, senior economic research analyst at the Atlanta Fed, wrote a short post on the Phillips curve for macroblog. The evolution of unemployment and inflation in the USA since 2008 actually needs a very detailed analysis.

I agree that the Phillips curve is not a productive idea since it does not explain observations in many countries. Moreover it is counterproductive because unemployment in the USA (and some other developed countries) lags behind inflation. We have published a number of papers on this issue. For example,"The Anti-Phillips curve" . It is funny, that Laurel being a Senior Economic Research Analyst does share our opinion on the helplessness of the conventional Phillips curve.

Also, we fully agreed that it is the best time to make deciding study of the link between inflation and unemployment - the change in both variables is fast and dramatic. Our generalized model, linking both inflation and unemployment to the change in the level of labor force, should also be tested against the most recent data. Usually, we do not use high-frequency data for our analysis because the uncertainty of the change over short periods is too high, but the rate of growth in unemployment and fall in inflation is really large to overcome this shortcoming.

We are in the initial stage of the analysis and will trace the near future developments. At this stage, the generalized model looks an adequate one - the drop in CPI fully compensates the rise in unemployment according to their coefficients in the relationship. In other words, the change in unemployment is driven by the change in inflation.

On the other hand, the time lag suddenly fell from 2.5 years to several months in 2008. We need more time to understand the causes of the shift. It is not excluded that the current state is related to panic deviation from the generalized equilibrium. Then the spike in unemployment and inflation are only a short one fluctuation.

CPI vs. core CPI: August 2009

Here we revisit our previous analysis of the difference between headline and core CPI in the USA [1]. Figures 1 and 2 illustrate the evolution of the difference which is apparently characterized by the presence of three distinct segments with linear trend and two short periods of change in the trends. Between 1960 and 1978, the difference is relatively stable and varies in a narrow range around +1 unit of index. Between 1979 and 1982, the curve falls to -2 and then suddenly changes its direction from downward to upward one.
Between 1982 and 1999, the core CPI was growing consistently faster and a gap of about 10 units was created through 1999. The curve between 1982 and 1999 is best represented by a straight line with small-amplitude deviations, the latter likely associated with measurement noise. The slope of the linear regression line presented in Figure 2 is -0.67 with R2=0.96. In other words, during these eighteen years the headline CPI was growing by 0.67 units of index faster than the core CPI.
If to assume that the evolution of both indices is driven by independent stochastic process like random walks, then the deviation between the indices would be a stochastic process itself. From Figure 2, it is more reasonable and reliable to assume, however, that there is a tight link between these variables, which provides the observed linear growth of the difference between them. For purely stochastic and independent variables such a linear behavior is highly unlikely. Because the CPI inflation is predefined by the labor force growth rate (Kitov, 2006ab) the evolution of the core CPI is also predefined.
There was another period of high volatility between 1999 and 2003 similar to that observed between 1979 and 1982. Between 2003 and 2008, the gap between the core CPI and CPI was closing in line with a faster growing CPI. In [1], we extrapolated the rate of convergence between the CPI and core CPI observed after 2003, as displayed in Figure 3, one can estimate the intercept time somewhere between 2009 and 2010. This linear trend of convergence is very robust with R2=0.86, as was the divergence trend between 1982 and 1999. The convergence is faster - approximately 1.6 units of index per year. This prediction was accurate in terms of the turn to a new positive trend but timing was slightly wrong. The turn started in the middle of 2008 with a severe fall in the difference down to -4. This early start of the transition to the new trend was accompanied by extraordinary volatility. After the difference reached the bottom at -4, it quickly (during six months) rebounded to +6. At this point we made (in this blog and several articles [2-4]) a new assumption that the difference would be freely falling since March 2009. Such behavior has been actually observed, as Figure 4 demonstrates. The return to the new linear trend may include a slight overshoot below the trend line in 2009 or early 2010.
What will happen after 2010? It is likely that the difference will fluctuate around the new trend, which characteristics have to be established yet.

Figure 1. The difference between the core CPI and headline CPI: update from October 2007 to August 2009.

Figure 2. Linear regression of the difference between the core CPI and CPI.

Figure 3. Extrapolation of the trend in the differnce between core CPI and CPI beyond 2007 [1].

Figure 4. The return to the new linear trend. An overshoot below the trend line may happen in 2009 or early 2010. Then, the differnce will align around the new trend, which will emerge promptly.


References
[1] 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. http://www.jaes.reprograph.ro/articles/Kitov.pdf

[2] 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

[3] Kitov, I., Kitov, O., (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/,
http://mpra.ub.uni-muenchen.de/13587/01/MPRA_paper_13587.pdf

[4] 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

Price inflation: Q&A

Sometimes Q&A is the best way to present new concepts. I expect this post to grow over time and welcome questions related to theoretical and empirical aspects of price inflation in developed countries. Emerging and developing countries are also of interest, especially the cases of hyperinflation.

Q1. What is it - price inflation?
In narrow sense, price inflation is a reaction of economic system to changing level of labor force. Inflation is the process which recovers personal income distribution to its natural and fixed (rigid) shape. As a monetary process, inflation is expressed in changing prices for goods and services (G&S), with the total cost of all these G&S exactly determined by real economic growth, if any, and inflation, as predefined by the change in labor force level.
In developed (capitalist) economies, prices for G&S have to interact and compete, i.e. to be governed by "invisible hand", in order to find some final (but not predetermined!) configuration, which corresponds to the total nominal cost of the G&S. This total cost (nominal GDP) is defined by real economic growth and inflation.
(Detailed explanation of price inflation as an economic phenomenon and process as well as relevant quantitative analysis are given in our papers.)

Q2. Is it possible to describe the link between inflation and labor force change using simple mathematical representation?
There exists a linear lagged relationship between inflation, π(t), unemployment, UE(t), and the change rate of labor force, dLF(t)/LF(t):

π(t+t1)= AdLF(t)/LF(t) + BUE(t+t2) + C

where A, B, and C are country-specific empirical constant (this relationship is normalized to inflation); t1 and t2 are time lags between the change in labor force and the reaction of inflation and unemployment. These lags may reach several years and there is no general rule which variable reacts first.

Q3. Is inflation an economic ill, constantly threatening economic stability?
There is no statistical or any quantitative link between inflation and real economic growth except the one, which is related to population changes. There is a formal statistical and econometric prove available in our papers that real economic growth depends only on the attained level of real GDP per capita and the change rate of population of a country-specific age. This defining age is nine years in the USA.

Q4. Is deflation harmful?
Since real economic growth and inflation are not directly related, the recession and deflation (like observed in Japan) have different sources. For example, the former process is approaching its end in Japan and real economic growth (per capita) is on its potential level (http://inflationusa.blogspot.com/2007/07/modelling-evolution-of-real-gdp-in.html). The latter process will last the next 40 years with increasing amplitude (http://inflationusa.blogspot.com/2007/08/prediction-of-cpi-inflation-in-japan.html )

Q5. Is inflation unpredictable?
Inflation can be accurately predicted at various time horizons in developed countries. Examples are the USA, Japan, France, Germany, Canada, Austria, and the UK. The accuracy of inflation prediction is completely defined by the accuracy of labor force measurements, as follows from the relationship in Q2. There are some simple means to improve current labor force estimates.

Q6. Do central bankers control inflation and inflationary expectations through clear inflation targeting?
Because inflation is completely defined by the change rate of labor force Central Banks do not control inflation as it is. They can potentially control the balance between inflation and unemployment, which are linear lagged function of the change rate of labor force.
Quantitative prediction of the history of inflation in USA is a good example that the Fed does not control inflation. The history of inflation in France demonstrates that the suppression of money supply results in elevated unemployment. So, this is an example of negative affect of central bank in sense of high unemployment balancing low inflation.

ConocoPhillips share price revisited

Since September 16, the readings of the headline CPI and its components for August 2009 are available (we retrieve all CPI data from http://www.bls.gov/data). We recalculate our model for selected stock prices from the S&P 500 list. First is ConocoPhillips since it provides a good example of a company, which share price has been leading defining components of the CPI. In the previous posts and articles [1,2] we introduced several models with varying number of CPI components. Here we compare two models. The first one, we call it 3-C model, is seeking those two CPI components from 34 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 August 2009. This model also includes free term (constant) and linear time term [3-6], which compensates well know linear (time) trends between various CPI components. The second model (5-C) uses four CPI components and free term. The number of potential defining components is reduced to ten: food (F), housing (H), apparel (A), transportations (T), medical care (M), recreation (R), education and communication (EC), other goods and services (O), the headline CPI (C), and the core CPI (CC). These components compile a full set of the CPI expenditure categories, and also comprise a subset of the 34-component set.
The 3-C model for COP is as follows:

COP(t)= 3.41CF(t+1) - 7.17EC(t-6) + 7.22*(t-2000) + 145.76 (1)

where CF is the headline CPI less food. It does not differ from the model presented in the previous post except the time shifts are +1 (was +2) month and -6 (was -5) months now. This is due to the inclusion on the CPI readings for August. Figure 1 shows the predicted and observed curves. Standard deviation between the curves is $3.96 for the period between July 2003 and August 2009.

Figure 1. Observed and 3-C predicted COP’s share prices.

The 5-C model does not include the linear time term, but two components extra to the 3-C model play this role. The best 5-C model also shows that the stock price leads all defining CPI components:

COP(t)= 1.53H(t+3) – 8.29R(t+1) – 4.90EC(t-6) + 3.53C(t+1) + 518.4 (2)

There components from the four defining lag behind COP share price and only the EC leads by six months. Figure 2 presents the model. Standard deviation between the curves is only $3.03 for the period between July 2003 and August 2009, which is better than the accuracy of the 3-C model.
Figure 2. Observed and 5-C predicted COP’s share prices.

At first glance, the 5-C prediction is better that the 3-C one. However, this conclusion is not fully correct. As mentioned above, the extra two components chiefly represent the linear trend. Figure 2 illustrates the phenomenon. The difference between R and EC actually provides a linear trend with small fluctuations, which slightly suppress the residual of the 3-C model. Among all pairs of CPI components -8.29R(t+1) – 4.90EC(t-6) suppresses the model residual (noise) the most efficient. It is a positive side of the 5-C model. It has a negative side as well. The difference may diverge from the linear trend in the next several months and will increase the residual and thus the accuracy of prediction instead of suppression. So, we do prefer using the 3-C model for the prediction of share prices. Figure 4 depicts both residuals.

Figure 3. Two differences between defining components in (2).

Figure 4. Residuals of the 3-C and 5-C models.

We will continue updating both empirical models. The next obvious date is October 1, 2009 with the next closing share price for September.

References
[1] 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
[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., (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.
[4] 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
[5] 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
[6] 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

Predicting Microsoft stock price

We continue modelling various stock prices. This post is devoted to Microsoft (MSFT). In my article on the prediction of stock prices for COP and XOM - “Predicting ConocoPhillips and Exxon Mobil stock price”, Journal of Applied Research in Finance, v.2, 2009 (a draft version is available here.), only a very crude model of the stock price evolution was presented. Now a more reliable model is available in the following form:

sp(t)= A1S1(t+t1) + A2S2(t+t2) + A3t +A4

where sp(t) is the stock price at time t, A1 through A4 are empirical coefficients, S1 and S2 are components of headline CPI, t1 and t2 are time difference (negative or positive) between the change in the stock price and relevant changes in the CPI components. Term A3t is introduced to compensate linear trends observed in the difference between the components.

For Microsoft, an accurate empirical model is as follows:

MSFT(t)= -3.61*R(t-1) – 1.22*MSC(t-11) + 23.5*(t-2000) + 680.5.

where t is the calendar time, R(t-1) is the index for recreation leading MSFT(t) by one month, MCS(t-11) is the index for medical service leading the MSFT(t) by eleven months. The linear trend term 23.5*(t-2000) compensates the trend term in the difference between R and MCS. Standard deviation between the curves is $1.75 for the period between July 2003 and August 2009.

Figure 1. Comparison of measured (open circles) and predicted (solid diamonds) stock prices of Microsoft