Goldman Sachs may rise to $133 in January 2013

We have been trying to build a preliminary pricing model for Goldman Sachs (NYSE: GS) since 2008. This company was included in our study of bankruptcy cases in the USA. All in all, the model was not stable over time and the prediction for 2009 was not fully correct.  Originally, the stock price was defined by the index of housing operations (HO) and that of food away from home (SEFV).  In January 2011, we presented an updated model as based on the CPIs available till November 2010 and the December monthly closing (adjusted for splits and dividends) price of GS. In the updated model, the defining CPIs are the index of other food at home (OFH) and the housing index (H). Thus, the difference between the preliminary and the updated model was not too large because the pairs of defining indices are very close. Here we present a revised model, which includes new data obtained since December 2010. The revised model shows that GS share may grow to $133 from its current level of $118. This might be a good long idea together with that for Prudential Financial.

The concept of share pricing based on the link between consumer and stock prices has been under development since 2008. In the very beginning, we found a statistically reliable relationship between ConocoPhillips’ stock price and the difference between the core and headline consumer price index (CPI) in the United States. Then we extended the pool of defining CPIs to 92 and estimated quantitative models for all companies from the S&P 500. The extended model described the evolution of a share price as a weighted sum of two individual consumer price indices selected from this large set of CPIs. We allow only two defining CPIs, which may lead the modeled share price or lag behind it. The intuition behind the lags is that some companies are price setters and some are price takers. The former should influence the relevant CPIs, which include goods and services these companies produce. The latter lag behind the prices of goods and services they are associated with. In order to calibrate the model relative to the starting levels of the involved indices and to compensate sustainable time trends (some indices are subject to secular rise or fall) we introduced a linear time trend and constant term. In its general form, the 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 (I=2 in all our models); b_i, c and d  are empirical coefficients of the linear and constant term; e_j is the residual error,  whose statistical properties have to be scrutinized.

By definition, the bets-fit model minimizes the RMS residual error. It is a fundamental feature of the model that the lags may be both negative and positive. In this study, we limit the largest lag to eleven months. System (1) contains J equations for I+2 coefficients. We start our model in July 2003 and the share price time series has more than 100 points. To resolve the system, standard methods of matrix inversion are used.  A model is considered as a reliable one when the defining CPIs are the same during the previous eight months. This number and the diversity of CPI subcategories are both crucial parameter.  For example, Table 1 lists defining parameters for GS between March and October 2012. For each month, the best model is based on the same defining CPIs – the consumer price index of food and beverages, F, and the index of owners’ rent of primary residence, ORPR.  In all cases, the lags are the same: three and two months, respectively. Other coefficients and the standard error suffer just slight oscillations or drifts (e.g. c and d).  It is important to stress again that all models for months except October also include those with future CPIs relative to the given month. Table 1 confirms that no future CPIs drive the share price in March 2012. The best fir model is always based on the past values of F and ORPR, at least since March 2012.

Figure 1 depicts the overall evolution of both involved consumer price indices: F and ORPR. It also presents the evolution of two defining indices from the previous model: the index of other food at home, OHF, which is a part of F, and the index of housing, H, with ORPR representing a part of H.  The OHF and H indices provided the best fit model between March 2010 and December 2010.  The best-fit models for GS(t) are as follows:  

GS(t) = -11.06OFH(t) +11.06H(t-12) - 1.82(t-2000) – 99.4, December 2010

GS(t) = -13.79F(t-3) +11.03ORPR(t-2) + 29.93(t-2000) + 33.75, October 2012      

The predicted curve in Figure 2 leads the observed price by two months. The residual error is of $14.52 for the period between July 2003 and October 2012. The price of a GS share is relatively well defined by the behaviour of the two defining CPI components. Figure 2 also depicts the high and low monthly prices for the same period, which illustrate the intermonth variation of the share price. These prices might be considered as natural limits of the monthly price uncertainty associated with the quantitative model. Since 2009, the predicted price is well within the high/low band. Figure 3 displays the residual error. 

Table 1. The evolution of GS model since March 2012

Month	CPI1	t1	b1	CPI2	t2	b2	c	d	sterr,$
October	F	3	-13.795	ORPR	2	11.026	29.934	33.75	14.52
September	F	3	-13.791	ORPR	2	11.013	29.992	35.82	14.58
August	F	3	-13.786	ORPR	2	11.002	30.023	37.10	14.64
July	F	3	-13.759	ORPR	2	10.978	30.018	37.64	14.70
June	F	3	-13.730	ORPR	2	10.933	30.124	41.98	14.75
May	F	3	-13.703	ORPR	2	10.876	30.342	48.75	14.76
April	F	3	-13.661	ORPR	2	10.818	30.449	53.17	14.80
March	F	3	-13.786	ORPR	2	10.942	30.439	48.63	14.76

 

 

Figure 1. Evolution of F and ORPR. Also shown are defining CPI of the 2010’s model:  OFH and H.

Figure 2. Observed and predicted GS share prices. The prediction horizon is two months.

Figure 3. Standard error of the model $14.52. 

TECO Energy - no big change is expected

In this article, we introduce a tentative pricing model for TECO Energy (NYSE: TE). This is one of many energy related companies in the S&P 500 index. Our pricing model is based on our concept of stock dependence on consumer price index.  The intuition is simple and clear, the evolution of a share price is inherently related some goods and services and thus the evolution of their relative prices.  For example, it is not easy to ignore the intuition that crude oil has to affect share prices of oil companies. We have reported that such a link exists for ConocoPhillips and formulated an empirical model. On the other hand, the oil price is not the only changing price and other goods and services should obviously affect share prices of oil companies. Thus one needs also some reference price, which best expresses the overall price evolution. An example from life, when one jumps in a moving elevator the net trajectory depends on both the person and elevator.    

Therefore, our model is seeking two CPI components from a large number of 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 October 2012. For TE, we use a set of 92 individual consumer price indices to select the best two CPIs in order to describe the evolution of the share price. Our two-component model also includes a free term (constant) and a linear time term, which compensates well know linear (time) trends between various CPI components. We allow the modeled share price to lead and lag behind one or both defining CPIs. When the price is lagged, the model is deterministic one and foresees at the horizon of the smallest lag. When the price leads both CPIs, one cannot predict the future of the price but get some information on the future CPIs.  In the case of TE, both CPIs are contemporary to the share price and the best-fit model is as follows:  

TE(t)= -1.43R(t-0) + 0.05E(t-0) + 1.49(t-2000)  + 150.92, October 2012 

where R(t) in the index recreation at time t, E is the index of energy also contemporary to the price, (t-2000) is the elapsed time.  

Figure 1 depicts the evolution of both CPIs.  The index of recreation evolves slowly and the energy index has been actually driving the TE price since 2003. Figure 2 depicts the observed and predicted (monthly closing) prices together with the monthly high/low prices, which are natural limits of the intermonth price uncertainty. Our model correctly predicted the price since 2003.  The model residual error is shown in Figure 3. It has standard deviation of $0.85 for the period between July 2003 and October 2012.  

For an investor, the evolution of TE is almost fully related to the price index of energy. Our model of oil price evolution implies a fall to $40 to $60 by 2016. This may induce a fall in energy prices in the long run and the TE price will be on a down ward trend as well. On this long term trend, there should be periods of high fluctuations associated with elevated market volatility. When the actual price is far below the predicted price, one may consider a profitable (in the short run) share purchase. When the actual price is far above the predicted price, it is best time to sell. Currently, the predicted and observed prices are almost equal. No action needed.

Figure 1. The evolution of defining CPIs.

 

Figure 2. Observed and predicted TE share prices.  

Figure 3. The model standard error is $0.85. 

 

Prudential Financial may rise to $64 in January 2013

In this article, we revisit our pricing model for the evolution of Prudential Financial (NYSE: PRU) stocks presented in March 2012. Prudential is a company from financial sector which provides various financial products and services. In March, we used the monthly closing prices between July 2003 and February 2012. PRU’s share was at about $57 with the predicted level of $44. The tentative model also predicted the price to grow in the first half of 2012 to $52. Therefore, we foresaw a negative correction in March-April. The actual price started to fall in the beginning of May and the monthly closing price for May was at the level of $45 per share. The updated model, as obtained with new data between March and October 2012, predicts a healthy growth in the price in 2012Q4. In January 2013, the price may reach the level of $64.  On November 20, the closing price was $50.78. There is some potential of a 10% to 15% return at a three month horizon. One may consider PRU as an investment idea at this horizon.    

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 intuition is clear – there is a set of goods and services which any company produces and this set defines the share price evolution of a given company relative to other companies. These other companies are also driven by prices for some goods and services. Hence, for a given company one needs two defining sets of goods and services to estimate its relative pricing power – one related and one as an independent reference. Thus, the relevant stock price can be defined by two CPIs which include corresponding goods and services. 

Many SA readers have reasonable doubts that some consumer price, which is not directly related to goods and services produced by a given company, may affect its price.  We allow the economy to be a more complex system than described by a number of simple linear relations between share prices and goods. The connection between a firm and its products may be better expressed by goods and services which the company does not produce or provide. The demand/supply balance is fragile and may evolve along many nonlinear paths. It would be too simplistic to directly define a company price only by its own products. 

Originally, we addressed the PRU model in 2009 and found two CPIs explaining the monthly closing prices of PRU since 2003. They were the consumer price index of food and beverages (F) and the index of transportation services (TS). The defining time lags were as follows: the food index led the share price by 5 months and the TS index led by 4 months: 

PRU(t) =  -6.09F(t-5) – 3.15TS(t-4)  + 59.76(t-1990) + 930.50,  September 2009 

In 2010 and 2012, we revisited the original model and estimated new coefficients and lags. These estimates were close to the original ones:  

PRU(t) =  -5.45F(t-5) – 3.98TS(t-3)  + 59.66(t-1990) + 1055.38,  September  2010

PRU(t) =  -5.14F(t-5) – 3.80TS(t-4)  + 56.20(t-1990) + 1005.63,  February 2012

 

Here we revisit the model. We have borrowed the time series of monthly closing prices of PRU from Yahoo.com and the relevant (seasonally not adjusted) CPI estimates through October 2012 are published by the BLS.  The best-fit model for PRU(t) is as follows:  

PRU(t) =  -5.09F(t-5) – 3.67TS(t-3)  + 55.44(t-2000) + 1531.31,  October 2012 

where PRU(t) is the PRU share price in U.S. dollars,  t is calendar time. One can conclude that the model has not been changing since January 2009 and thus provides a good estimate of the price at a three month horizon.   

Figure 1 displays the evolution of both defining indices since 2002.  Figure 2 depicts the high and low monthly prices for a share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The predicted prices are well within the limits of the high/low share price which might be considered as the actual price uncertainty.   

The model residual error is shown in Figure 3 with the standard deviation between July 2003 and October 2012 of $6.01 ($5.58 in March 2012).

 

Figure 1. The evolution of F and TS indices

 

Figure 2. Observed and predicted PRU share prices.

 

Figure 3. The model standard error is $6.01.

JPMorgan Chase is slightly overvalued

Banks have attracted special attention during the current period of socio-economic turbulence because of their deep involvement in both financial and economic components of the crisis. In 2009, we investigated and revealed the reasons behind bankruptcy of major banks and have been reporting on the evolution of many to-big-to-fall institutions since then. In March 2012, we presented a brand new model for JPMorgan Chase & Co. (NYSE: JPM) stock price and predicted a negative correction in April/May. This forecast was correct: the (monthly closing) price increased from $38.38 in February to $44.97 in March and then fell to $42.31 in April and to $32.63 in May. The closing price in October 2012 was $41.68, which is approximately $2 higher than predicted. Our updated model again shows the possibility of a negative correction in November-December down to $38. On November 17, the closing price is $39.53. We would not recommend buying JPM shares and consider them as reaching some stability level at a two month horizon, which is a natural horizon for our quantitative model.  

JPM is a company from financial sector which provides various financial products and services worldwide. The model has been obtained using our general concept of share pricing as based on a decomposition of a share price into a weighted sum of two consumer price indices. Our main assumption is a natural one – all goods and services produced (provided) by a given company should define the share price evolution relative to other companies. In other words, relative pricing power of the company is related to the pricing power of its G&S. Since other companies are also driven by prices for their goods and services, which compete with the studied company, one need two defining sets of G&S to estimate the relative pricing power. Presumably, the studied share price can be defined by two CPIs.  

The best CPIs are selected from a set of 92 CPIs with estimates available from 2000. In the tentative model presented in March 2012, the best fit (in the LSQ sense) consumer price indices are that of food and beverages (F) and the index of owner’s equivalent rent of residence (ORPR). In the updated model, the defining CPIs are the same and time lags of the price behind the CPIs are as follows: the food index led the share price by 4 months and the ORPR index led by 2 months. The tentative and updated models are as follows:   

JPM(t) =  -1.99F(t-3) + 1.15ORPR(t-2)  + 6.81ORPR(t-1990) + 39.30,  February 2012

JPM(t) =  -1.86F(t-4) + 0.99ORPR(t-2)  + 7.04(t-2000) + 116.91,  October 2012 

where JPM(t) is the JPM share price in U.S. dollars,  t is calendar time. As both models show, the increasing food index suppresses the share price and the rent index drives it up. Any big jump in food price results in a sharp fall in JPM price in four months. It is worth noting that we present only those price models which are stable over longer periods of seven and more months. This means that all models obtained since February 2012 are defined by the same CPIs with the same time lags when only contemporary data are used. The tentative model also covered the period seven months before February 2012. This makes the presented model to be the best in the LSQ sence since August 2011.

Figure 1 displays the evolution of both defining indices since 2002.  Figure 2 depicts the high and low monthly prices for a share together with the predicted and measured monthly closing prices (adjusted for dividends and splits). The measured price volatility is much higher than the predicted one. This means that large deviations from the predicted level are possible but such excursions are always ended on the predicted curve. One can use this observation for a qualitative forecast of price movements as we did in March 2012 and do in this post. The current deviation of the JPM price from its predicted level could be interpreted as a temporary one with the following return and dive below the line (dynamic overshooting) as was observed many times since 2003.  

The updated model validates the tentative one by the data measured during the eight month period. The model residual error is shown in Figure 3 with the standard deviation between July 2003 and October 2012 of $2.96.  

 Figure 1. The evolution of F and ORPR indices

 

 Figure 2. Observed and predicted JPM share prices.

 Figure 3. The model standard error is $2.96.