Forecasting S&P 500 returns. Quarterly update

Three months ago we revisited our prediction of the S&P 500 return including the estimate of real GDP for the fourth quarter of 2010. Here, we update our model and include the GDP estimate for the first quarter of 2011 and the monthly closing prices through May 2011. As discussed in our working paper on S&P 500, there exists a trade-off between the growth rate of real GDP, G(t),  and the S&P 500 returns, R(t). The predicted returns, R_p(t), can be obtained from the following relationship: 

R_p(t) = 0.0064dlnG(t) - 0.03   (1) 

where G(t) is represented by the Q/Q (annualized) growth rate, because only quarterly readings of real GDP are published by the BEA. 

Figure 2 displays the observed S&P 500 returns and those obtained using real GDP. As before, the observed returns are MA(12) of the monthly returns. The period after 2003 is relatively well predicted. Therefore, it is reasonable to assume that G(t) can be used for modeling of the S&P 500 index and returns. Reciprocally, current S&P 500 may be used for the estimation of real GDP. The predicted return is lower than that observed in April and May 2011. We can assume that the level of S&P 500 should be corrected downwards or the preliminary estimate of GDP should be revised up.

Figure 1. Observed S&P 500 return and that predicted from real GDP. For a given quarter, all monthly values of the growth rate relative to the previous quarter are equal.  

The rate of unemployment in the U.S. may fall to 6% by the end of 2011

As in the previouspost, we refer to our model which links the rate of participation in laborforce, LFP, to the change in real GDP per capita. For short time intervals, one replaced labor force with employment, E, and GDP per capita with GDP. Now we use the rate of unemployment, UE, instead of the employment-population ratio, E/P. Unlike the E/P, unemployment negatively depends on real economic growth, i.e. should fall when dGDP/GDP is large. Thus, we scale the UE in the following way: dGDP/GDPdt = 1.1(8.0-UE), where coefficients 1.1 and 8.0 were estimated empirically.   Figure 1 shows the evolution of dGDP/GDPdt and UE) in the U.S. after 1990. The latter variable is shifted 12 months back in order to fit the peaks and troughs in the dGPG/GDP between 1990 and 2010.

 The overall agreement between the curves is excellent and allows forecasting the UE since the dGDP/GDPdt curve leads by 12 months. Then, the current UE (9.1%) value corresponds to May 2010 in the DGDP/GDP curve. Therefore, the rate of unemployment should fall to the level of 5% to 6% by the end of 2011.

Figure 1. The annual change rate of real GDP, dGDP/GDP, and the scaled rate of unemployment, UE.

The employment/population ratio may rise to 63% by the end of 2011

Our model links the rate of participation in labor force, LFP, to the change in real GDP per capita. The latter leads by two years, and we have successfully predicted the fall in LFP in 2009. For short time intervals, one can replace labor force with employment, E, and GDP per capita with GDP. Figure 1 shows the evolution of dGDP/GDPdt and E/P (employment population ratio) in the U.S. after 1990. The latter variable is reduced by 60% and shifted 12 months back in order to fit the level of dGPG/GDP between 1990 and 2010.

The overall agreement between the curves is excellent and allows forecasting the E/P, the dGDP/GDPdt curve leads by 12 months. Then, the current E/P value corresponds to May 2010. Therefore, the E/P should jump to the level of 63% by the end of 2011.

Figure 1. Annual change rate of real GDP, dGDP/GDP, and the monthly estimated ratio of employment and working age population, E/P.

Why the employment situation is not disappointing

The Bureau of Labor Statistics has published an “Employment Situation Summary” for May. The nonfarm payroll employment has increased by 54,000. The number of employed in the U.S. increased by 105,000; from 139,674,000 to 139,779,000.  These low numbers have come as a surprise for many experts, who predicted 170,000 (http://online.wsj.com/mdc/public/page/2_3064-446888.html) for the nonfarm payroll employment in May. Therefore, the market and general public feel some disappointment> Should they?

In the previous post, we demonstrated that the level of labor force in the U.S. has been experiencing an unprecedented fall since 2008. Figure 1 reminds us that the reason for the fall is not the current financial crisis and recession but rather a new trend in the rate of labor force participation, LFP. This is not a short- or mid-term transient process but the change in the long-term tendency. The LFP had been growing between 1955 and 2000, when it reached its peak. One can consider 2001 as a pivot point manifesting a fundamental change in the labor market behavior in the U.S. It is worth noting that the change in LFP behaviour started ten years ago, not in 2008. (The reader might be interested in the explanation of this phenomenon. We had accurately predicted the 2010/2011 fall in the LFP many years before it happened.)

As a result of the new long-term tendency, one should not expect the same pace of employment growth as it was between 1960 and 2000. In addition to the fundamental shift in the secular LFP evolution, one should not forget another source of employment growth – the level of working age population. Figure 2 depicts monthly increments of the working age population, i.e. 16 years old and over.  One can clearly see that the influx of the population has been decelerating since 2000 as well. The deep negative corrections in Figure 3 are associated with annual revisions to population controls. It is not wise to wait that the growth in employment will exceed the influx of working age population in the situation with the falling LFP.   

It is important that even decreasing unemployment can not compensate the effects of LFP and population. Figure 3 shows the evolution of monthly increments in employment, E, after 2003 with MA(12). One should not expect that E will be growing at a pace which was considered as a healthy one before 2000 any time soon. In that sense, the today’s BLS news is not disappointing. Really disappointing is the unjustified expectation of any large increase in the U.S. employment.  

Figure 1. Measured LFP in the U.S.

Figure 2. Monthly increment in working age popualtion (16 years of age and over) in the U.S.

 

Figure 3. Monthly increment of employment in the US with its MA(12). 

Catastrophic fall in labor force in the U.S.

Labor force in the U.S. experiences unprecedented fall. With total population growing at a healthy pace of ~1% per year, the number of people in labor force has been physically decreasing since 2009. The reason behind this effect is the labor force participation rate, LFP, plummeting down. Figure 1 shows that LFP dropped from 66.4% in 2008 to 63.9% in the first quarter of 2011. This 2.5% is equivalent to 6,000,000 people out of the working force in 2011 relative to 2008.  Event the growth in the total working age population from 235,000,000 to 239,000,000 has failed to compensate the fall in the LFP. Figure 2 shows that the decline in the labor force, LF, is a unique feature since the very beginning of observations in 1948.  Except the current fall, there were only two short intervals with dLF/LFdt<0 after WWII, in 1951 and 1962, as Figure 3 shows.

The negative growth rate of labor force is the cause of a higher rate of unemployment and lower rate of price inflation. It should be noted that we predicted the current decline in the LFP many years ago. 

However, the fall in LFP is not the cause but a consequence of the low rate of real GDP  (per capita) growth after 2008. When the growth rate of real GDP per capita regains its normal pace of 2% per years the LFP will start to increase, with a two-year delay.

 

Figure 1. Measured LFP in the U.S.

Figure 2. Labor force in the US.

Figure 3. The change rate of labor force, dLF/LFdt

Motor fuel price to fall in the near future

Our task is to estimate relative growth in a given price with time.  We use the ratio of price index, P(t), and GDP per capita in current prices, Y(t) (the idea borrowed from V.Kossov): 

Z(t)=P(t)/Y(t)

Figure 1 presents the evolution of the price index of motor fuel since 1935 (obtained from the BLS) and Figure 2 – nominal GDP per capita.   The share of motor fuel price in GDP per capita can be presented as a function of Y as well as time.  Figure 3 shows that there exist a long-term negative trend for Z(t) (notice the log-log scale) with two major fluctuations.  The trend looks sustainable and deviations seem to be of transient character.  Therefore, one can expect the fall in Z in the near future – motor fuel will be falling against GDP per capita. Oil price is likely to fall as well.  Figure 4 presents log(Z) as a function of time.

Figure 1. The consumer price index of motor fuel (not seasonally adjusted).

Figure 2. Nominal GDP per capita

Figure 3. LogZ vs. GDP per capita.

Figure 4. LogZ vs. time

Food is getting cheaper

Food is getting more and more expensive. Everybody knows that.  Figure 1 illustrates the evolution of the price index of food since 1913. At the same time, the US economy also grows including the growth in real GDP per capita which is shown in Figure since 1929 (chained, in 2005$).  One can easily estimate which of these two variables grows faster. Figure 3 depicts the ratio of CPI and GDP per capita relative to that in 1929. Overall, the food price falls relative to the GDP per capita, i.e. one has to pay a lower share of income (a fixed portion of GDP per capita)  for the same amount of food (we do not consider nomenclature and quality of food here).  Food is getting cheaper with time. It is interesting that the ratio in Figure 3 has not been falling much since 1975.

Figure 1.

Figure 2.

Figure 3.