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.

CPI and core CPI

We have been reporting on the difference between the core CPI and headline CPI since we found a long-term linear trend in this difference [1].  Figure 1 reproduces the illustration from [1] and shows the change in the trend near 2000.

Figure 1. Linear regression of the difference between the core CPI and CPI for the period from 1981 to 1999 (R²= 0.96 the slope is 0.67) and linear regression of the difference between the core CPI and CPI between 2002 and 2009 (R²=0.91, and the slope is -1.59). 

Figure 2 displays the previous (negative) trend between 2002 and 2008 and the following evolution of the difference. We expected a new trend to be developed between 2008 and 2010 and this new trend should be positive, as shown by the solid red line. However, after a year of “right” evolution the difference has fell to the zero line again. This puts the overall evolution under question.

Figure 2. The evolution of the difference between the core and headline CPI since 2002.

To distinguish between a short-term excursion from the new trend and the development of long-term negative trend we present a broader view on the core and headline CPI and related rates of price inflation. Figure 3 depicts both indices since 1960. Between 1980 and 2009, the overall CPI was below the core CPI.  After the 2008/2009 spike in energy (oil) prices, the CPI fell again below the core CPI. Currently, a new spike is observed in oil price. Therefore, the CPI intersects the core CPI again. All in all, the CPI is more volatile than the core CPI and fluctuates with larger amplitudes.

Figure 3. The evolution of core and headline CPI since 1960.

Figure 4 provides a better view on the volatility in the CPI. The rate of CPI price inflation (monthly estimates of annual inflation) during the past 10 years fluctuates severely around the core inflation rate. In 2010, there were several months of the overall CPI deflation, which was replaced with a new spike in prices. The core inflation has been showing a steady decrease since 2005, however.

Hence, it is natural to expect the current surge in oil price to calm down and the CPI falling back below the core CPI in the next few quarter. In this case, the difference in Figure 1 will return to its new positive trend manifesting a progressive decrease in energy and food prices relative to other goods and services.

Figure 4. The rate of price inflation as defined by the headline and core CPI.

Therefore, we confirm our previous predictions and expect the new positive trend in Figure 1 to hold in the future. This trend repeats the trend observed between 1987 and 1999 rather than the mirror reflection of the previous negative trend between 2002 and 2009. Thus, the price indices of food and energy will not be falling too fast relative to the core CPI, but this period will likely last more than 10 years.
The core CPI inflation will fall below the zero line in 2012 manifesting the period of deflation predicted in 2006 [2].  

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
2. Kitov, I. (2006). Exact prediction of inflation in the USA, MPRA Paper 2735, University Library of Munich, Germany

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