# Is There A Formula To Predict The Dow, S&P For 2014?

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by: Sanjeev Sharma

## Summary

Disposable Income is the amount of money left from the wages, after spending on essential needs like housing, food and fuel.

Using the different factors affecting disposable income, the author has been writing many articles predicting the stock market movement six months to one year in advance on seekingalpha.com, since 2009.

Using the same factors, the author has utilized historical data to find if it can be proven statistically that the stock market moves with the changes in disposable income.

With 70% of the US economy based on consumer spending, disposable income of the masses is the primary fuel for demand of new goods and services. If the amount of money left after spending on essential needs like housing, food and fuel is higher, people tend to spend higher on new goods and services. This grows the economy and the stock market reflects it in medium term of six months to one year. For more than last 5 years, I have been utilizing disposable income to predict the US stock market on seekingalpha.com, six months to an year ahead. These predictions have turned out to be accurate. A summary of theses previous articles are in the 'Previous Predictions' section.

This time, I have tried to use some of the factors affecting disposable income and find their relation with the changes in the stock market, using statistical analysis.

The following factors have been utilized in this multivariate regression analysis, from 1982-2010 (example: Row 27 in the data below is for 2008) (data from January-December for each year):

• Percentage increase in the median wages (average of all except the top 5%) during the year
• Percentage increase in CPI during the year
• Percentage increase in the 10 year treasury yield. Example, if it increases from 2.7 to 3.7, we take the difference of 1. It is assumed that other interest rates like mortgage rates would also move in the same direction as the ten year treasury, and higher interest rates would impact the ability of people to borrow and spend
• Percentage increase in median home price during the year (using census.gov data)
• Percentage increase in Gas Price during the first 4 months of the year (Jan-April). As gas prices can quickly move in the same direction as economy and stock market by end of the year, thus confusing between the cause and the effect, I decided to use only the first 4 months of change
• To ensure that the non liner impact of change in interest rates is considered, the squares of percentage increase in ten year treasury was used. To consider the cumulative impact of increased cost of mortgage due to increase in home prices as well as interest rates, percentage increase in Home price * percentage increase in ten year treasury were used

We need to acknowledge that these are only some of the factors, as many other factors are difficult to be applied in data format. For example:

• Political and economic issues in other countries (like Euro) that impact the flow of money is difficult to be expressed in numeric form
• Dollar strength compared to a large basket of currencies, which impacts the import prices
• The exact process and time utilized to collect data by various agencies is not clearly known, which may impact our analysis
• Our arbitrarily using the time period (from beginning of year to end of the year) would impact the analysis
• Factors impacting the mood of the people, thus increasing spending (example: huge increase in home equity last year impacted people's spending) is difficult to be expressed in numeric form

I utilized SAS software to generate a regression analysis with these factors and the results are attached below. Readers who are not interested in detailed analysis may directly jump to the INFERENCES section below.

PREVIOUS PREDICTIONS:

• May 2009 article - US economy will recover in next 3 months
• Jul 2009 article - There will little inflation despite the Fed's printing of trillions of dollars
• Jan 2010 article - The Dow will be around 12000 by the end of 2010
• Dec 2010 article - Dow will not go up in 2010, but will go lower in 2011
• Oct 2011 article - Dow will be between 12500 and 13000 after Q1 2012
• Jun 2012 article - Dow will be closer to 14000 by end of 2012

INPUT DATA FOR REGRESSION ANALYSIS:

 year S&P Increase Income Increase 10 year Increase CPI Increase Home Price Increase Gas Increase 4 months(Jan-Apr) 1982 14.76132 6.679306 -0.91 8.390805 0.580552 -8.17 1983 17.27105 5.347035 -1.91 3.711559 8.658009 -4.46 1984 1.400594 7.244441 1.36 4.192229 6.108898 0.8 1985 26.33341 5.83459 -1.84 3.532875 5.506884 5.69 1986 14.62041 5.824635 -2.95 3.886256 9.134045 -44.8 1987 2.027501 5.3675 0.72 1.459854 13.58696 10.68 1988 12.40084 4.958316 0.46 4.046763 7.655502 3.35 1989 27.25047 7.35863 -0.36 4.667243 6.666667 -6.67 1990 -6.55914 2.416731 0.06 5.202312 2.416667 -4.5 1991 26.3067 1.38652 -0.69 5.651491 -2.35964 8.89 1992 4.464264 2.421311 -0.85 2.600297 1.25 -4.13 1993 7.055151 6.663268 -1.14 3.258508 4.115226 -3.3 1994 -1.53929 4.115111 1.22 2.524544 2.766798 5.66 1995 34.11065 4.18477 -0.52 2.804378 3 7.69 1996 20.26367 4.862743 -0.13 2.727878 4.555639 14.29 1997 31.00818 5.452138 -0.09 3.044041 4.285714 -0.71 1998 26.66859 4.352008 -1.09 1.571339 4.452055 -2.34 1999 19.52604 5.557848 0.39 1.670792 5.57377 11.96 2000 -10.1392 4.380981 0.38 2.738892 4.968944 11.89 2001 -13.0427 1.879422 -1.01 3.732227 3.668639 16.88 2002 -23.366 -0.61194 -0.41 1.142204 7.077626 27 2003 26.3804 2.099488 -0.6 2.597403 3.944563 -3.53 2004 8.993453 2.369182 0.26 1.926252 13.33333 19.28 2005 3.001023 4.759684 0.02 2.969762 9.004525 20.22 2006 13.61943 5.09281 0.51 3.985317 2.324616 31.94 2007 3.529578 1.559857 -0.17 2.075643 0.567951 33.34 2008 -38.4858 1.206651 -0.97 4.280294 -6.37354 26.59 2009 23.45419 -0.65503 -0.4 0.029847 -6.63507 19.03 2010 12.78271 -0.85912 -0.04 2.625709 2.353484 7.55

SAS COMMAND USED :

The following SAS command generates a multivariate regression analysis to identify the impact of the various factors explained earlier on the percent increase in S&P during an year.

PROC GLM DATA=Economicdata;

MODEL spincrease = incomeincrease cpiincrease Homepriceincrease Gasinc4mon

Homepriceincrease*tenyearincrease

tenyearincrease*tenyearincrease ;

RUN;

OUTPUT:

This output from the regression analysis gives the impact of each of the factors on the percent increase in S&P and also explains how much is it reliable. A low p-value below (0.05) would be considered very good statistically and would show these factors are able to predict the changes in the stock market. A high R-square(coefficient of multiple determination) (above 0.9) would mean we can ignore all other factors besides these factors for making predictions about the stock market.

The GLM Procedure

Dependent Variable: spincrease spincrease

Sum of

Source DF Squares Mean Square F Value Pr > F

Model 6 3234.843234 539.140539 2.50 0.0534

Error 22 4740.412342 215.473288

Corrected Total 28 7975.255576

R-Square Coeff Var Root MSE spincrease Mean

0.405610 149.8398 14.67901 9.796468

Source DF Type I SS Mean Square F Value Pr > F

incomeincrease 1 865.187370 865.187370 4.02 0.0576

cpiincrease 1 145.752535 145.752535 0.68 0.4196

homepriceincrease 1 131.787990 131.787990 0.61 0.4425

gasinc4mon 1 674.023817 674.023817 3.13 0.0908

homeprice*tenyearinc 1 45.229600 45.229600 0.21 0.6513

tenyearin*tenyearinc 1 1372.861923 1372.861923 6.37 0.0193

Source DF Type III SS Mean Square F Value Pr > F

incomeincrease 1 976.151638 976.151638 4.53 0.0447

cpiincrease 1 563.520677 563.520677 2.62 0.1201

homepriceincrease 1 278.004492 278.004492 1.29 0.2682

gasinc4mon 1 733.565847 733.565847 3.40 0.0785

homeprice*tenyearinc 1 901.937433 901.937433 4.19 0.0529

tenyearin*tenyearinc 1 1372.861923 1372.861923 6.37 0.0193

Standard

Parameter Estimate Error t Value Pr > |t|

Intercept 20.21154545 9.50196422 2.13 0.0449

incomeincrease 3.44301333 1.61762102 2.13 0.0447

cpiincrease -3.44312502 2.12909276 -1.62 0.1201

homepriceincrease -0.84986754 0.74820750 -1.14 0.2682

gasinc4mon -0.50681605 0.27468031 -1.85 0.0785

homeprice*tenyearinc -1.41142413 0.68986808 -2.05 0.0529

tenyearin*tenyearinc -7.41233880 2.93655778 -2.52 0.0193

INFERENCES from statistical analysis:

It is obvious that the model is significant (p-value =0.05), despite a low coefficient of multiple determination (R-square=0.4). The R-square value is explainable by the reasons discussed earlier, as we are utilizing only a few factors available in numeric form and the stock market gets impacted by other factors.

Overall, the following can be inferred from this analysis:

• The model has an intercept of 20.2
• An increase in median incomes by 1 percent would increase S&P by 3.4 percent
• An increase in CPI by 1 percent decreases S&P by 3.4 percent
• Home price increase by 1 percent decreases S&P by 0.84 percent
• Square of increase in 10 year Treasury yield by 1 percent decreases S&P by 7.4 percent (cost of interest charges increases, thus decreasing the disposable income)
• Increase in gas prices of 1 percent in the first 4 months decreases S&P by 0.5 percent
• Cumulative impact of home price and ten year treasury by 1 percent decreases S&P by 1.4 percent
• The p-values for Home price increase (0.26) and CPI (0.12) are high, which show that these factors are statistically less significant than other factors. We can explain the home price factor as the home price increase also increases home equity which boosts the spending power of the consumer in certain years.

CONCLUSION:

Thus, most factors impacting disposable income like wage increase, CPI, gas price and home prices are statistically proven to be impacting S&P as we expected. This equation would work in normal conditions but unusual events like a war, a terrorist attack, a special economic event, an election year would skew the outcome. For example, in 2013, we saw the housing market turn around ( increase in home equities by more than 13 percent by some estimates and one of the highest in the recorded data here). An event like this impacts the mood of the people which impacts the market.

The FORMULA:

Ignoring other factors, the impact of disposable income on S&P can be explained in the previous regression analysis by the following formula:

S&P increase = 20.2 + 3.4* percent increase in Wages -3.4 * percent increase in CPI -0.8 * percent increase in Home prices - 0.5* percent increase in gas prices in first 4 months of the year - 1.4 *(percent increase in home prices * percent increase in ten year yield ) -7.4 *(percent increase in ten year treasury yield * percent increase in ten year treasury yield )

SHOW ME THE PROOF?

To test the formula, I applied this formula to each of the years in the test data and compared the predicted percent change in the S&P with the actual change. With so many other variables impacting the market, we can not expect an accurate outcome every year. It is apparent that around 40% times the predicted output is good indicator of what actually happened during the year. What is more important to notice is the last row, where the sum of all changes predicted during these years is compared to the actual changes that happened and there is almost no difference. This tells me that the impact of all other factors on the stock market are temporary, and in the long run, get evened out:

 Year Actual S&P Increase (in percent) Income Increase 10 year Increase CPI Increase Home Price Increase Gas Increase 4 months(Jan-Apr) S&P predicted by the Formula (in percent) 1982 14.76 6.679306 -0.91 8.390805 0.580552 -8.17 12.61 1983 17.27 5.347035 -1.91 3.711559 8.658009 -4.46 17.22 1984 1.40 7.244441 1.36 4.192229 6.108898 0.8 -0.03 1985 26.33 5.83459 -1.84 3.532875 5.506884 5.69 9.91 1986 14.62 5.824635 -2.95 3.886256 9.134045 -44.8 15.21 1987 2.03 5.3675 0.72 1.459854 13.58696 10.68 -0.26 1988 12.40 4.958316 0.46 4.046763 7.655502 3.35 9.00 1989 27.25 7.35863 -0.36 4.667243 6.666667 -6.67 29.75 1990 -6.56 2.416731 0.06 5.202312 2.416667 -4.5 10.82 1991 26.31 1.38652 -0.69 5.651491 -2.35964 8.89 -2.66 1992 4.46 2.421311 -0.85 2.600297 1.25 -4.13 16.80 1993 7.06 6.663268 -1.14 3.258508 4.115226 -3.3 27.08 1994 -1.54 4.115111 1.22 2.524544 2.766798 5.66 4.82 1995 34.11 4.18477 -0.52 2.804378 3 7.69 18.83 1996 20.26 4.862743 -0.13 2.727878 4.555639 14.29 17.37 1997 31.01 5.452138 -0.09 3.044041 4.285714 -0.71 25.79 1998 26.67 4.352008 -1.09 1.571339 4.452055 -2.34 25.26 1999 19.53 5.557848 0.39 1.670792 5.57377 11.96 18.81 2000 -10.14 4.380981 0.38 2.738892 4.968944 11.89 12.15 2001 -13.04 1.879422 -1.01 3.732227 3.668639 16.88 0.16 2002 -23.37 -0.61194 -0.41 1.142204 7.077626 27 -2.11 2003 26.38 2.099488 -0.6 2.597403 3.944563 -3.53 17.77 2004 8.99 2.369182 0.26 1.926252 13.33333 19.28 -3.95 2005 3.00 4.759684 0.02 2.969762 9.004525 20.22 8.72 2006 13.62 5.09281 0.51 3.985317 2.324616 31.94 2.55 2007 3.53 1.559857 -0.17 2.075643 0.567951 33.34 1.24 2008 -38.49 1.206651 -0.97 4.280294 -6.37354 26.59 -14.06 2009 23.45 -0.65503 -0.4 0.029847 -6.63507 19.03 8.76 2010 12.78 -0.85912 -0.04 2.625709 2.353484 7.55 2.81 SUM: 284.10 290.40

NOW, PREDICT FOR 2014 :

We can plug and play with different numbers for the various factors, in the equation for 2014. Here are my assumptions for 2014:

• Median Wages should increase around 5 percent this year, due to lower unemployment numbers and some signs of slowdown in outsourcing of jobs.
• percent increase in CPI will be around 2% this year ( due to weakness in emerging markets, strong dollar and import costs being lower)
• Gas prices would not increase, due to increased production of fuels in US
• Home Prices would increase around 7 percent this year (in line with the long term historical trends, and still low mortgage rates)

As is obvious by plugging and playing with these numbers , a lot depends on the interest rates this year: an increase in interest rates by 1 percent could increase the S&P by 7 percent, but if the interest rates stay the same, we can see an increase in the S&P by more than 20 percent in 2014.

The fed has been pretty vocal about keeping low interest rates. If the interest rates are indeed kept at current levels, I would go with the latter.

Disclosure: I am long SPXL. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.