An estimate of Morgan Stanley share price in 2011

We introduced a simple deterministic pricing model in 2009 [1]. Originally, it was based on an assumption that there exists a linear link between a share price (here only the stock market in the United States is considered) and the differences between various expenditure subcategories of the headline CPI. The intuition behind the model was simple - a higher relative rate of price growth (fall) in a given subcategory of goods and services is likely to result in a faster increase (decrease) in stock prices of related companies. In the first approximation, the deviation between price-defining indices is proportional to the ratio of their pricing powers. The presence of sustainable (linear or nonlinear) trends in the differences allows predicting the evolution of the differences, and thus, the deviation between prices of corresponding goods and services. The trends are the basis of a long-term prediction of share prices. In the short-run, deterministic forecasting is possible only in the case when a given price lags behind defining CPI components.

In its general form, the pricing model is as follows (Kitov, 2010):

sp(tj) = Σbi∙CPIi(tj-ti) + c∙(tj-2000 ) + d + ej     (1)

where sp(tj) is the share price at discrete (calendar) times tj, j=1,…,J; CPIi(tj-ti) is the i-th component of the CPI with the time lag ti, i=1,..,I; bi, c and d are empirical coefficients of the linear and constant term; ej 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 fourteen months. Apparently, this is an artificial limitation and might be changed in a more elaborated model. In any case, a fourteen-month lag seems to be long enough for a price signal to pass through.

System (1) contains J equations for I+2 coefficients. Since the sustainable trends last more than five years, the share price time series have more than 60 points. For the current recent trend, the involved series are between 70 and 110 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.

For the sake of completeness we always retain all principal subcategories of goods and services. Among them are the headline CPI (C), the core CPI, i.e. the headline CPI less food and energy (CC), the index of food and beverages (F), housing (H), apparel (A), transportation (T), medical care (M), recreation (R), education and communication (EC), and other goods and services (O). In this 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 (2011). Many indices were started as late as 1998. It was natural to limit our modeling to the period between 2000 and 2010, i.e. to the current long-term trend.

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. Without loss of generality, one can randomly select for modeling purposes any of these prices for a given month. By chance, we have selected the closing price of the last working day for a given month. The larger is the fluctuation of a given stock price within and over the months the higher is the uncertainty associated with the monthly closing price as a representative of the stock price.

Second source of uncertainty is related to all kinds of measurement errors and intrinsic stochastic properties of the CPI. 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.

Morgan Stanley (MS) is an example of a changing pricing model. In [3] we reported that the defining CPIs in 2008 were the index of housing operations (HO) and the index of food away from home (SEFV). However, through the second half of 2010 the defining indices are different: the index of food less beverages (FB) and the index of information technology, hardware and software (IT), which is a part of the communication index. The former CPI component is contemporaneous with the share price and the latter one leads by 1 month. Figure 1 depicts the evolution of both indices. As discussed in our previous posts on food, it is likely that the index for food will be slowly growing during the next two years. This growth has a negative influence on the share price – the fall in the share price in 2008/2009 is clearly associated with the spike in the food price index. Same effect was well described by the SEFV index in the previous model. The IT index is characterized by a long term decline and will hardly be growing during the next several years. Both, linear trend and constant term, have positive influence on the price.

These defining components provide the best fit model, i.e. the lowermost RMS residual error, between July 2010 and December 2010. The best-fit 2-C model for MS(t) is as follows:

MS(t) = -3.32*FB(t) – 17.34*IT(t-1) +0.68(t-2000) +904.4

The predicted curve in Figure 2 is in sync with the observed one. The residual error of $3.98 for the period between July 2003 and December 2010. The model accurately predicts the share price in the past. From the overall behaviour of the defining CPIs one may expect that the MS price will be stalled or slightly growing in the first quarter of 2011.

Figure 1. Evolution of the price index of food less beverages (FB) and information technology (IT).

Figure 2. Observed and predicted MS share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $3.98.

References

1. Kitov, I. (2009). Predicting ConocoPhillips and Exxon Mobil stock price, Journal of Applied Research in Finance, v., issue 2(2), Winter 2009, pp.129-134.

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

3. 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

Legg Mason may spurt

It is a great pleasure to revisit the previous version of the pricing model of Legg Mason (LM). During the last two years it has been stable and is based on the index related to food (food at home, FH) and the index of appliances (APL) from the housing index. Due to the uncertainty in the defining indices and closing prices as the parameter characterizing given shares, the lead of the FH has slightly changed from 4 months in the previous model to 5 months in the current model. The appliance index still leads by 13 months.

Overall, the predicted time series is very close to the observed one in Figure 1, with standard deviation of $7.33 between July 2003 and December 2010. The largest input to the standard deviation comes from a short period in 2006. Otherwise, both curves are very close even during the dramatic fall from $80 per share in the end of 2007 to $10 per share in February 2009 and during the fast recovery in 2009. The best-fit 2-C model [1] for LM(t) is as follows:

LM(t)= -3.61*FH(t-5) – 9.30*APL(t-13) + 16.62(t-2000) + 1317.6

The predicted curve actually leads the observed price by 5 months, as red line in Figure 1 illustrates. Therefore, one can foresee all major changes in the price. Without loss of generality, the LM price is completely defined by the behaviour of the two defining CPI components.

Currently, the model predicts a quick growth in the share price. Therefore, it would be instructive to revisit the prediction at a monthly rate. In January and February 2011, the price is expected at $45 and $56, respectively. Today, the price is at $36.

Figure 1. Observed and predicted LM share prices.

References

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

Xilinx share

This is a good example of a stable pricing model [1]. We already reported on this case in July 2010. The model for Xilinx (XLNX) is defined by the index of communication (CO-CUUR0000SAE2) and that of information and information processing (INF-CUUR0000SAE21). The former CPI component leads the share price by 4 months and the latter one leads by 11 months. From our past experience, the larger is the lag the more unreliable is the model, but this specific model has been valid since 2008.

These defining components provide the best fit model, i.e. the lowermost RMS residual error, between August 2009 and December 2010. The best-fit 2-C model for XLNX(t) is as follows:

XLNX(t) = -3.57*CO(t-4) + 4.21*INF(t-4) +1.88(t-2000) – 55.32

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $1.89 for the period between July 2003 and December 2010. The model accurately predicts the share price in the past and foresees increasing price in the first quarter of 2011.

Figure 1. Evolution of the price index of communication (CO) and information (INF).

Figure 2. Observed and predicted XLNX share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $1.89. The largest errors were observed in 2004 and 2009.

References

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

Real GDP in New Zealand - a decade of slow growth ahead

Following the post on the German real GDP per capita, we present a model for New Zealand. It was also obtained by the trial-and-error method [1]. Empirical constant A and the specific age, Ns, in the defining equation:

g(t) = dlnG(t)/dt = A/G(t) + 0.5dlnNs(t)/dt (1)

have been varied in order to fit amplitude and major features of the observed curve. The best fit annual increment value is A=$220 (1990 US$), i.e. less than in France and Germany. Surprisingly, the specific age population in New Zealand is 14 years, which is different from that in the US, Japan, France, and Germany. The age pyramid enumerated by the 2006 census was extrapolated in the past and in the future in order to estimate the number of 14-year-olds in (1).

Figure 1 presents the observed and predicted GDP growth rates for New Zealand. As for the other countries, all original readings of GDP were obtained from the Conference Board database. Both curves in the upper panel are characterized by high-amplitude oscillations likely associated with measurement errors. Therefore, in the lower panel of Figure 1, the annual curves are smoothed with MA(5) and MA(3), respectively.

Without prejudice, we have failed to find such a good prediction of real GDP elsewhere and would appreciate any information on a better model. The shape, amplitude and timing of the curves are in an excellent agreement after 1980.

Overall, there is no danger of a deep recession in New Zealand, but the rate of real economic growth will be very low (on average ~0.5% per year) in the years to come. Before 1980, data are likely not reliable due to significant revisions to relevant definitions.

Figure 1. Upper panel: Observed and predicted growth rate of real GDP per capita in New Zealand. Lower panel: The observed curve is smoothed with a 5-year moving average. The predicted rate is smoothed with MA(3). One can observe an outstanding agreement between the smoothed curves.

German GDP and WWII

Several days ago we presented in this blog an empirically correct model of real economic growth. The concept describing the evolution of real Gross Domestic Product (per capita) is very simple and is based solely on the age structure in a given developed country. It was empirically and statistically proved that the growth rate, g(t), of real GDP per capita, G(t), is driven by the attained level of real GDP per capita and the change in a specific age population, Ns. According to this model, the asymptotic growth rate of real GDP in developed countries can be completely characterized by constant annual increment A = const. All fluctuations around this constant increment can be explained by the change in the number of people of the country-specific age:

g(t) = dlnG(t)/dt = A/G(t) + 0.5dlnNs(t)/dt (1)

Equation (1) is the quantitative model that has been constructed empirically and tested statistically.

It is important to stress that the mainstream models such as Solow model and its successors are all based on an assumption that the rate of real economic growth is asymptotically constant. This assumption is empirically wrong and is rejected by statistical tests. We made no theoretical assumptions and our model came directly from data and was formulated at the initial stage of our empirical study. Therefore, we have a model that fits observations best.

We have already presented the cases of US, Japan, and France in this blog. The next country under investigation is Germany. The best fit constant increment is (A=) $260 (1990 US dollars) and the defining age is eighteen years, as in France. The age distribution from 2002 allows a prediction at an 18-year horizon. Figure suggests a slow-down in 2009 and likely a deeper recession in 2011, with a year of growth in 2010. On average, the beginning of 2010s will be characterized by very poor performance of the German economy. It will be even worse than in the 1990s. The population trough in N18 observed the 2010s is likely a remote and decaying echo of the WWII, which was amplified by the reunification turbulence in the early 1990s. The rate of birth was suppressed by the uncertainty of socio-political future of Germany. In the late 2000s and early 2010s, the drop in N18 might be compensated by immigration. In that case, real GDP may grow due to the rising working age population, i.e. due to extensive factors.

Here, we would like to emphasise that the prediction of the 2009 slowdown could be easily obtained in 2002, i.e. seven years before it happened! The estimates of population age structure are slightly noisy, however. Otherwise, the agreement between the observed and predicted curves is excellent after some years of turbulence associated with the reunification.

Figure 1. Observed and predicted rate of real GDP growth in Germany after the reunification. The predicted curve is obtained from relationship (1) with A=$260. Upper panel: Original curves. Lower panel: The original curves smoothed with MA(3). One should not expect a recession period before 2011, but the year of 2009 is very close to recession.

The rate of participation in labor force: an accurately predicted fall

In August 2009, we made a short term (five years) prediction of the rate of labor force participation, LFPR, in the US as based on our model [1]. A prediction at a longer horizon is also available from the population age pyramid. The contemporary level of LFPR was 65.4%, as reported by the Bureau of Labor Statistics (http://data.bls.gov/cgi-bin/surveymost). We predicted a quick fall in the level of LFPR in 2010:

In order to predict the evolution of the LFPR we used projections of real GDP based on the projections of population. Figure 4 depicts the predicted and observed LFPR curves for the years between 2000 and 2014. In 2010, the rate should drop by approximately 1.3%. When translated into absolute numbers, it gives more than 2,500,000 people leaving the labor force in 2010 at once. Really, the wave of the boomer’s retirement has just started and it is likely that nobody will replace many of them in the labor force.

Figure 4. Prediction of the LFPR evolution in the USA between 2000 and 2014 from the number of 3-year-olds. Flat segment between 2004 and 2009 will end up in a rapid drop by 1.3% after 2010. This is the effect of an elevated (above potential) real economic growth in 2010.

In 2011, the BLS reported the level of LFPR in December 2010. It is 64.3%, i.e. only 0.2% higher than predicted in August 2009. We consider this prediction as an excellent one and thus the model is validated and having a godd predcitive power. Has anybody made a better prediction?

References

1.  Kitov, I., Kitov, O., (2008). The Driving Force of Labor Force Participation in Developed Countries, Journal of Applied Economic Sciences, Spiru Haret University, Faculty of Financial Management and Accounting Craiova, vol. III(3(5)_Fall), pp. 203-222.

Goldman Sachs pricing model

We have been trying to build a preliminary pricing model for Goldman Sachs (GS) since 2008. This company was included in our study of bankruptcy cases in the USA [1]. All in all, the model was not stable over time and the prediction for 2009 was wrong. Originally, the stock price was defined by the index of housing operations (HO) and that of food away from home (SEFV).

In this post we present a new model as based on the CPIs available till November 2010 and the December closing price of GS. Now, the defining CPIs are the index of other food at home (OFH) and the housing index (H). Thus, the difference between the preliminary and current models might be not large because the original indices are very close to the new ones. Our quantitative approach is described in [1,2].

Figure 1 depicts the overall evolution of both involved consumer price indices. These two defining components provide the best fit model between March 2010 and December 2010 and the best-fit 2-C model for GS(t) is as follows:

GS(t) = -11.06*OFH(t) +11.06H(t-12) - 1.82(t-2000) – 99.4

The predicted curve in Figure 2 does not lead the observed price. The residual error is of $14.45 for the period between March 2003 and December 2010. The price of a GS share is relatively well defined by the behaviour of the two defining CPI components but the model does not foresee the price. During the last quarter of 2010, the predicted price is well below the observed one and the residual error is large. We expect the residual to return to the zero line in the first or second quarter of 2011. A drop in the actual price is likely but the predicted price might rise as well.

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

Figure 2. Observed and predicted GS share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $14.45.

References

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

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