Modeled share price of Franklin Resources (BEN) forecasts a fall

The price model for Franklin Resources (BEN) is a brand new one.  BEN is a financial company and was analyzed previously as a candidate for a bankruptcy [1]. The obtained model is based on is our stock pricing concept and includes the consumer price index of food at home (FH) and the index of tobacco and tobacco products (TOB). The former defining CPI component led the share price by 5 months and the latter one by 8 months. Therefore, the model has a natural 5-month forecast horizon. 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. The slope of time trend is positive and would provide a $55 increment per year if both CPIs are fixed. The best-fit 2-C model for BEN(t) is as follows:

BEN(t) = -6.33FH(t-5) – 0.27TOB(t-8) – 55.08(t-1990) + 547.67     

where t is calendar time.  The standard deviation of $7.21 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 $100 from the current $125, as follows from the predicted and observed curves presented in Figure 2.  Figure 3 displays the model error which was low after 2008.

Figure 1. The evolution of FH and TOB.

Figure 2. Observed and predicted BEN share prices.

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

AFL stock price model

Aflac Incorporated (AFL) is a financial company in the S&P 500 list. Using new CPI estimates published by the BLS on April 14 we have estimated a preliminary model.  The share price is defined by the consumer price index of household furnishing and operations (HFO) and that transportation services (TS). The defining time lags are as follows: the HFO index leads the share price by 2 months and the TS by 4 months.

Both coefficients in the obtained model are negative. Therefore any growth in both indices causes the share price to fall with a several month delay. The slope of time trend is positive and provides an increment of $20.4 per year. The intercept is $997.7. The best-fit 2-C model for AFL(t) is as follows:

AFL(t) =  -5.02HFO(t-2) – 2.87TS(t-6)  + 20.42(t-1990) + 997.71

where t is calendar time.

The predicted curve in Figure 1 leads the observed price by 2 months with the residual error of $3.94 for the period between June 2003 and March 2011. During the second quarter of 2001, the share price has to decrease to the level of $50.

Figure 1. Observed and predicted AFL share prices.

CVS Caremark Corporation in 2011Q2

CVS Caremark Corporation (CVS) is an old member of our list for stock price modeling. We have been following the CVS share  since 2009, i.e. since we started developing our concept of share pricing as related to consumer price indices. The original CVS model has been very stable over the past two years and it provides an overall validation for the deterministic share price setting. A very exciting feature of the CVS price model we developed two years ago is the possibility of prediction at a 3 months horizon.

Using new CPI estimates published by the BLS on April 14 we have updated the model and found that the CVS model has not been changing much and is still defined by the consumer price index of other food at home (OFH) and that transportation services (TS). A slight difference consists in smaller time lags: the OFH index leads the share price by 3 months and the TS - by 4 months.

Figure 1 depicts the overall evolution of both involved indices. These two defining components provide the best fit model between August 2009 and March 2011. Relevant coefficients are both negative. Therefore any growth in both indices causes the share price to fall with a several month delay. The slope of time trend is positive and provides an increment of $12 per year. The intercept of $199 is necessary to compensate the difference in the initial values of both indices.

The best-fit 2-C model for CVS(t) is as follows:

CVS(t) = -0.48OFH(t-3) – 1.26TS(t-4) + 12.11(t-1990) + 199.16

where t is calendar time.

The predicted curve in Figure 2 leads the observed price by 3 months with the residual error of $1.82 (was $1.88 in January 2011) for the period between June 2003 and March 2011. The model provides and an excellent and very stable prediction of the share price in the past.

In January we forecasted a period of no growth in the first quarter of 2011. This prediction was successful and thus validated the model. It is necessary to stress again that the model has been predicting the CVS share price since August 2009 with the same accuracy.

During the second quarter of 2001, the share price has to decrease by $2 according to an ace;eratedgrowth in the indices of other food at home and transportation services in Figure 1.

Figure 1. Evolution of the price of OFH and TS.

Figure 2. Observed and predicted CVS share prices. Black diamonds present the contemporary prediction shifted 3 months ahead to fit actual data.

Share price of Ashland Inc.

We have already presented a preliminary model for Ashland Inc (ASH). (The quantitative approach is described in [1].) Here we re-estimate the model using new BLS estimates of CPIs. Ashland is a chemical company in the S&P 500 list since 1983. The stock price was defined by the index of food without beverages (FB) and that of miscellaneous personal goods (MISG). Both indices might be directly related to major ASH products. Figure 1 depicts the overall evolution of both involved consumer price indices.  The best-fit 2-C model for ASH(t) is as follows:

ASH(t) = -4.06FB(t-2) – 3.11MISG(t-7) + 24.11(t-1990) + 719.56

Actually, the predicted curve in Figure 2 leads the observed price by 2 months with the residual RMS error of $4.23 (see Figure 3) for the period between March 2003 and March 2011. The evolution of the observed and predicted prices is synchronized and the model does predict the share price in the past and foresees at a two month horizon.

Both indices had a period of no growth between 2008 and 2010 and the price was driven by the time trend with the slope of +24.11. This effect resulted in the total growth of $50 during these two years. A slow growth in food price restarted in the end of 2010 and the share price stalled. In February and March 2011, the index of food grew from 222.9 to 225.3, i.e. by 3 units. All in all, the share has to fall by approximately $6 in the next two months.

Figure 1. Evolution of the price of FB and MISG.

Figure 2. Observed and predicted ASH share prices.

Figure 3. Residual error of the model.

References

1. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

CIGNA Corporation stock price

We have estimated a model for CIGNA Corporation (CI). The company is associated with health service. The model for CI is stable during the past ten months. It is a deterministic one and has been defined by the consumer price index of pets, pet products and services (PETS) and transportation services (TS). The former CPI component does not lead the share price and the latter one leads by 3 months. Figure 1 depicts both involved indices. Relevant coefficients are both negative. Therefore the growth in both indices causes the share price to fall. The slope of time trend is positive. The best-fit 2-C model for CI(t) is as follows:

CI(t) =  -2.72PETS(t) – 1.63TS(t-3)  + 28.20(t-1990) +  299.39

where t is calendar time.

The predicted curve in Figure 2 repeats the measured one. The residual error is $3.46 for the period between June 2003 and March 2011. The model does not include a slight fall in the price in the second quarter since the current level is underestimated and corresponding correction might be negative.  

Figure 1. Evolution of the price of PETS and TS.

Figure 2. Observed and predicted CI share prices.

Revisiting JNJ share price

Recently, the BLS has reported the CPI estimates for March 2011. It is natural to revisit our models for the first quarter. Johnson & Johnson (JNJ) is one of the companies we have been following since 2009. A preliminary model was obtained in September 2009. The latest model was reported in January 2011.  

Originally, the stock price was defined by the index of appliances (APL) and that of transportation services (TS). We have revisited the stock in September 2010 and found that the model did not change, except a slight change in coefficients well explained by the uncertainty of the monthly closing price as a parameter characterizing the stock behavior and the estimation accuracy of these two defining CPIs.

In the previous post on JNJ we presented a model based on the CPIs for November 2010 and the December closing price of JNJ. Our concept of share pricing and quantitative approach is described in [1]. Briefly, we decompose a share price into a weighted sum of two individual CPI components and minimize the RMS model error.

Figure 1 depicts the overall evolution of both involved consumer price indices. These two defining components provide the best fit model between March 2009 and March 2011, i.e. two years or 24 months.  Since the index of appliances has been on a steady decline since the early 2000s, its negative coefficient of -1.35 (-1.40 in January) has actually resulted in the growth of the share price. The negative influence of TS, -1.47 (-1.26), has been also compensated by all other terms in the model.  The best-fit 2-C model for JNJ(t) is as follows:

JNJ(t) = -1.35APL(t-2) – 1.47TS(t-6) + 11.13(t-1990) + 332.20

Actually, the predicted curve in Figure 2 leads the observed price by 2 months with the residual error of $2.35 (see Figure 3) for the period between March 2003 and March 2011. One may conclude that the price of a JNJ share is well defined by the behaviour of the two defining CPI components.

Comparing the evolution of the observed and predicted prices since the start of modelling (2008) we have found that the model does predict the share price in the past and foresees at a two month horizon.

In January, we expected that this share would experience a slight growth in the first quarter of 2011. The price actually has stalled at the level of $60. In the second quarter 2011, the price should not change much.

Figure 1. Evolution of the price of APL and TS.

Figure 2. Observed and predicted JNJ share prices. Red line – contemporaneous prediction which forecasts major pivot points in advance.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $2.35. The largest errors were observed in 2007 and 2010.  Currently, the model overestimates the share price.

References

Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.

BSX in Q1 and Q2

The price model for Boston Scientific (BSX) was reported in January 2011, as based on our stock pricing concept [1]. We expected a small rise in the price in 2011Q1.  The original model included the consumer price index of housing (H) and the index of durable goods (DUR). The former defining CPI component led the share price by 5 month and the latter one by 3 months. The updated model has the same defining components and time lags. Figure 1 depicts the overall evolution of the involved indices.

These two defining components provide the best fit model between March 2011 and January 2010.  Both coefficients are negative, and thus the increasing prices result in decreasing share price. The slope of time trend is negligible. The best-fit 2-C model for BSX(t) is as follows:

 BSX(t) = -1.41H(t-5) – 2.85DUR(t-3) – 0.09(t-1990) + 630.92     

 where t is calendar time.  Both models predicted the price at a three month horizon with standard deviation of $1.83 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 $5 from the current $7, as follows from the predicted and observed curves presented in Figure 2.

Figure 1. The evolution of H and DUR.

Figure 2. Observed and predicted BSX share prices. Red curve represents the contemporaneous prediction.

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