Aflac may grow to $45 in December 2011

Here we revisit the stock price model for Aflac Incorporated (AFL) which we obtained in April2011 using our concept of share pricing. Accordingly, our goal is to test the original model and to update time lags and coefficients.

Last time we predicted the AFL price using the CPI estimates published by the BLS for March 2011. It was a preliminary model.  The share price was 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 led the share price by 2 months and the TS by 4 months. Adding new data for the period between April and September 2011, we re-estimated the model and found some changes in the time lags: zero and five months, respectively; and in the estimated coefficients. The relevant best-fit 2-C models for AFL(t) are as follows: 

AFL(t) =  -5.02HFO(t-2) – 2.87TS(t-6)  + 20.42(t-1990) + 997.71,  March 2011

AFL(t) =  -4.63HFO(t-0) – 2.90TS(t-5)  + 20.41(t-1990) + 953.49, September 2011 

where AFL(t) is the AFL share price in U.S. dollars,  t is calendar time. The changes in time lags are shown in red.  

In July2011, we reported that the original model gave a correct prediction of the fall in Q2 2011. Here we show that the current fall in the price has to stop and expect a positive correction in Q4 2011. Figure 1 depicts the high and low monthly prices for an AFL share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). As a rule, the predicted prices are well within the bounds of the share price uncertainty.  However, the price has fallen too much in Q3 and the model residual error (Figure 2) is negative what indicates a positive correction any time soon, if the model is right.  

Figure 1. Observed and predicted AFL share prices. 

Figure 2. The model residual error.

Alcoa share price may fall to $5 in December

Six months ago we reported a share price model for Alcoa (AA), which is company from Materials subcategory of the S&P 500 list specialized in aluminum. Here we test and update the model using new data, including the monthly closing price in September 2011 and the estimated CPI components for August. The principal result is that we accurately predicted the behavior in Q2 and Q3 and the updated model has the same defining CPI components and time lags with slightly shifted coefficients. Therefore, the model is a reliable tool to predict the evolution of Alcoa at a two month horizon.

According to our general approach to share price modeling we decompose the observed time history of the monthly closing AA stock price (adjusted for splits and dividends) into a weighted sum of two CPI components, time trend and free term.  Two defining CPI components are selected to minimize the model (RMS) error and may lead or lag behind the share.  

The original and current AA model is defined by the (not seasonally adjusted) index of food away from home (SEFV) and the price index of rent of primary residence (RPR), as reported by the US BLS. The former CPI component leads the share price by 2 months and the latter is 4 months ahead of the share price. Figure 1 depicts the overall evolution of both involved indices through August 2011. It seems these indices have been evolving in sync since 2002 with the only step-like change in the SEFV index in 2008.  We present two empirical models as estimated in April and October 2011: 

AA(t) =  -6.71SEFV(t-2) + 3.34RPR(t-4)  + 19.23(t-1990) + 298.87, Aril 2011

AA(t) =  -6.61SEFV(t-2) + 3.22RPR(t-4)  + 19.51(t-1990) + 300,89, October 2011 

where AA(t)  is a share price in US dollars, t is calendar time. Figure 2 illustrates the observed and predicted models for October 2011. The residual error is $3.04 ($3.12 in April) for the period between July 2003 and September 2011. Figure 2 also shows monthly high and low prices as the uncertainty in the monthly closing price as the best share price estimate. Since the closing price has to characterise the whole month by one value the high and low prices might serve as statistical bounds.  

One can expect the share price to fall to the level of $5 in December 2011. 

 

Figure 1. Evolution of the price of SEVF and RPR. 

Figure 2. Observed and predicted AA share prices.  

Predicting Harley-Davidson share price

Harley-Davidson (HOG) is one of the best illustrations of our concept (see a brief description of the concept in Appendix) linking stock prices to CPI components. For HOG, the model is stable for many years. The first model was obtained in September 2009 and covered the period from October 2008. Here we revisit the HOG model using the monthly closing price for September 2001 and the CPI estimates published for August 2011.  

For HOG, the defining indices are as follows: the index of rent of primary residence (RPR) and the index of owners' equivalent rent of residence (ORPR). Both CPI components are leading the 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 September 2011.  The models are as follows: 

HOG(t) = -13.82RPR(t-3) +12.77ORPR(t-4) +17.82(t-1990) – 163.94, before September 2009

HOG(t) = -11.30RPR(t-3) + 9.83ORPR(t-3) +17.53(t-1990) – 36.34, July 2011

HOG(t) = -11.27RPR(t-3) + 9.55ORPR(t-3) +19.35(t-1990) – 8.57, September 2011 

where HOG(t) is the share price in US dollars, t is calendar time. The model is characterised by standard deviation of $4.33 for the period between July 2003 and September 2011.   

Two recent models are depicted in Figure 2. The predicted curves lead the observed ones by 3 months. We do not foresee any further fall in the stock price.  Figure 3 displays the residual error.

Figure 1. Evolution of the price indices ORPR and RPR.

Figure 2. Observed and predicted POM share prices. Upper panel – the model for March 2011. Lower panel – the model for September 2011.

Figure 3. The model residual error.  

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-1990 ) + 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. 

Hewlett Packard should not fall below $20 per share

Hewlett Packard (HPQ) provides a good example of a successful share price prediction at a several month horizon.  We have already published our predictions at a four month horizon four times (July 2010, January 2011, March 2011, and July 2011). All predictions were based on our concept of share pricing as decomposition into a weighted sum of two CPI components.  We calculated the evolution of the monthly closing price (adjusted for dividends and splits). Here we test and update the model using data through September 2011.  

Originally, the long term model for HPQ share price was defined by the index of food without beverages (FB) and that of rent of primary residency (RPR). The former CPI component led the share price by 4 months and the latter one led by 5 months. Figure 1 depicts the overall evolution of both involved indices through August 2011. Below we present three best-fit 2-C models for HPQ(t) obtained at different times:  

HPQ(t) = -3.20FB(t-4) + 2.91RPR(t-5) + 3.64(t-1990) - 50.82, July 2010

HPQ(t) = -3.34FB(t-4) + 3.41RPR(t-5) + 0.51(t-1990) - 85.44, June 2011

HPQ(t) = -3.46FB(t-4) + 3.68RPR(t-5) – 0.72(t-1990) - 99.88, September 2011

where HPQ(t) is the price in US dollars, t is calendar time. All coefficients have been slightly drifting. This process expresses the trade-off between the linear trend in the difference between  the defining CPIs and the time trend term in the above equtions.  

The predicted curves are shown in Figure 2 (March and September 2011). In the second quarter of 2011, the model predicted the share price to fall to the level of $37 in June 2011 and then to $33 by the end of July 2011.   

From Figure 2, we predict the price to stabilize around $20 because the current price level is below the predicted one. Therefore, one can expect the price not to drop below $20 per share.    

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

Figure 2. Observed and predicted HPQ share prices in March (upper panel) and September (lower panel) 2011. The contemporaneous prediction is shown by red line. In March, we expect the price to fall down to $33 in July 2011. In September, we predict the price to stabilize around $20.

Is Boston Scientific on the brink?

We posted on Boston Scientific (BSX) in January and April 2011 and presented a share price model for Boston Scientific as based on our stock pricing concept.  Both models were similar and included the consumer price index of housing (H) and the index of durable goods (DUR). (Figure 1 depicts the overall evolution of the involved indices.) The former defining CPI component led the share price by 5 month and the latter one by 3 months.  Here we update the original model using data through September 2011. The updated model has the same defining components and time lags with slightly different coefficients. Therefore, the original model provided a reliable prediction through the past year and further in the past. Currently, the best fit model predicts the share to fall below zero in the near future what is equivalent to bankruptcy. A similar prediction (negative share price) was obtained for Lehman Brothers and other financial institutions before they failed.  As an alternative, our model may fail with the change in the overall CPI trends.

                                                                                                                                                

The best-fit 2-C models (March and September) for BSX(t) are as follows:

BSX(t) = -1.41H(t-5) – 2.85DUR(t-3) – 0.09(t-1990) + 630.92, March 2011

BSX(t) = -1.46H(t-5) – 2.71DUR(t-3)  + 0.36(t-1990) + 615.69, September 2011   

where BSX(t) is the (monthly closing adjusted for splits and dividends) share price in US dollars,  t is calendar time.  Both coefficients are negative, and thus the increasing consumer prices result in decreasing share price. The slope of time trend is negligible.

Both models predicted the price at a three month horizon with standard deviation of $1.94 between July 2003 and September 2011 ($1.83 in March). The currently observed growth in the defining consumer price indices should drive the share price down. In the fourth quarter of 2011, the price may drop below zero.    

   

Figure 1. The evolution of H and DUR.  

Figure 2. Observed and predicted BSX share prices. Upper panel: March model with red curve representing the contemporaneous prediction. Lower panel: the updated prediction. The price is negative by the end of 2011.

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

Avery Dennison share price will likely be falling further

In April 2011, we presented a model for Avery Dennison Corporation (AVY) based on our concept linking share pieces and consumer price indices. The share price model for Avery Dennison Corporation was defined by the index of food (F) and that of new and used motor vehicle (NUMV). In the original model, the former CPI component led the share price by 4 months and the latter one led by 2 months.

Here we revisit the model using the monthly closing prices (adjusted for splits and dividends) and CPIs for the period through September 2011. (The CPIs are available only for August 2011.) The principal result is that the underlying model is practically the same as six months ago with the same time lags but slightly different coefficients. In March 2011, we predicted a fall in the price which actually happened. Currently, the share price is overestimated if to consider that the predicted price expresses the right behavior. We expect that AVY stocks will be falling by the end of 2011 down to $16 per share from the September closing level $25.08.  

Figure 1 depicts the overall evolution of both involved indices between July 2005 and August 2011. These two defining components provide the best fit model between January 2010 and September 2011.  Both models, the original and the updated one, are shown below. The best-fit 2-C models for AVY(t) are as follows 

AVY(t) =  -4.24F(t-4) – 3.23NUMV(t-2)  + 23.29(t-1990) + 799.24 , March2011

AVY(t) =  -3.92F(t-4) – 2.70NUMV(t-2)  + 21.60(t-1990) + 710.60 , September 2011 

where AVY(t) is a share price in US dolalrs, t is calendar time. Relevant coefficients are both negative. The slope of time trend is positive.  There is some fluctuation in the coefficients caused by the uncertainty in measurements of both the stock prices and CPIs.  Nevertheless, both models provide an accurate prediction at a two-month horizon.  

The predicted curve in Figure 2 (both versions are depicted) leads the observed price by 2 months with the residual error of $2.57 ($2.68 in April) for the period between July 2003 and September 2011. The model residual for the same period is shown in Figure 3. The original model predicted the share price in the past and foresaw a fall in 2011 Q2.  

Figure 1. Evolution of the price of F and NUMV. 

Figure 2. Observed and predicted AVY share prices. Upper panel – March 2011; lower panel – September 2011. 

Figure 3. The residual error of the model. The mean residual error is 0.0 with the standard deviation of $2.57. Currently, the price is slightly overestimated.  

Another chance to sell oil futures

Two weeks ago, when oil was at $84,  I recommended  to sell oil futures before oil price falls to $79 and even lower. After this recommendation, oil actually fell down to $76 and could bring a 10% return. Today, oil is approaching $83, as we predicted five days ago. Therefore, a good time to sell oil futures is coming again. Below I reproduce some details of the model predicting oil price.

In May 2011, we predicted oil (WTI) price to fall to the level of $70 per barrel by the end of 2011. This is a monthly revision for September 2011. We consider the average oil price of $84 per barrel what is equivalent to the producer price index of 244 in September. (Actual estimate will be published by the Bureau of Labor Statistics in the middle of October.)
        Figure 1 compares our prediction with actual oil price in 2011. In August 2011, the predicted price is a bit higher than the measured one. In any case, we expect the price to fall by approximately $5 per month to the level of ~$70 in December 2011. We also expect the price to slowly fall through 2016 and put the uncertainty bounds for the long-term trend in oil price. The level of oil price in 2016 is between $30 and $60 per barrel. These bounds are also shown in Figure 1.

       

This part is the prediction of the current growth in oil price given days ago.

 A week ago, when oil price was at ~$79 per barrel, we recommended buying oil futures. The intuition behind this idea was that $79 is approximately $5 below the expected price for September. This is a disequilibrium which should be recovered in the short run. Today, oil price is at the level of ~84. This is the equilibrium level for September. A small hike in oil price is possible during the next few days. However, at a two-week horizon, oil price should fall again. Therefore, I recommend selling now and buying in approximately two weeks or when the price will be around $75. It will grow to the level of ~$82 to $85 in October or November.

Figure 1. Oil price prediction in 2011. The price is expected to fall by $5 per month between June and December 2011. The price level is ~$70 in December 2011. We also show the range of expected price evolution by 2016.