Multiple Regression Model

Project: Multiple Regression Model Introduction Today’s stock market offers as many opportunities for investors to raise money as jeopardies to lose it because market depends on different factors, such as overall observed country’s performance, foreign countries’ performance, and unexpected events. One of the most important stock market indexes is Standard & Poor's 500 (S 500) as it comprises the 500 largest American companies across various industries and sectors. Many people put their money into the market to get return on investment.Investors ask themselves questions like how to make money on the stock market and is there a way to predict in some degree how the stock market will behave? There are lots and lots of variables involved in how the stock market behaves at a specific time. The stock market is in a way an information agency. Based on new information, whether good or bad regarding almost everything from political issues to interest rates and inflation, the stock market can go up or down. The market is anticipating economic occurrences proactively, ignoring already occurred events that were predicted before.This way it is very hard to predict how it is going to move in the future. As S 500 is considered to be the most reliable benchmark  for the overall U. S. stock market, we decided to study what factor has the most impact on it. We created two regression models and included the economic indicators, such as Consumer Price Index, Producer Price Index, House Price index, Interest Rate, Unemployment Rate, and Gross Domestic Product of some countries. Model Specification and Data How accurately can we predict the stock market behavior?People working in the finance industry have been trying to estimate or predict the behavior of stock market for a long time, or maybe some of them already have a very long and complex model of predicting the behavior of a stock market based on many factors and variables. We decided to use the US econo mic indicators and the other countries’ GDP. With this research we are hoping to find a statistically significant model that would describe what affects the stock market. We used the average annual data from 1980 to 2011 to track the influence on the US market. Our data is a time-series data.It is very interesting since within these 31 years there were a lot of changes in the countries’ economies, financial regulations and policies. At the very beginning, we assumed that the following factors may have influence on stock market: S (Percentage Change) = ? 0 + ? 1*(Annual CPI) + ? 2*(Annual Average PPI) + ? 3*(Annual Average House Price Index) + ? 4*(Annual Average Interest Rate) + ? 5*(Percentage Change of Annual Average GDP of US) + ? 6*(Percentage Change of Annual Average GDP of Spain) + ? 7*(Percentage Change of Annual Average GDP of Germany) 1: Consumer Price Index reflects the state of inflation in the country’s economy. That indicator is very important in th e assessment of the stock market performance. If inflation grows, the interest rate rises and this prevents the companies to borrow money for further development of their businesses. This entire situation may hurt the stock prices of the companies and that’s why we wanted to see how big the impact is. We assume that this variable is going affect the dependent variable a lot. ?2: Producer Price Index indicates early state of inflation.Therefore, if investors know that the PPI heralds a strong economy with no increase in an interest rate, then they feel confident to invest in the businesses what means increased positive activity in the market. We assume that this variable is going to have some impact on the dependent variable however; it is not going to be crucial. ?3: House Price Index is an analytical tool for estimating changes in the rates of mortgages. If mortgage rates are high, then housing market is weak because demand for houses drops due to expensive loans, therefore HPI drops.In 2008 mortgage default affected stock market very severely because before that period house prices went down because people couldn’t pay their mortgage payments and banks collapsed. Decrease in house prices is one of the possible contributors to recession because the home owners lose their equity in their houses. Considering such recession scenario, the stock market always becomes bearish. Additionally, house market is considered more stable investment than stock market. When stock market drops, people are willing in the houses and HPI goes up.We assume that HPI and stock market shouldn’t move in the same direction thereby we don’t take into consideration the complex scenario of 2008. ?4: 10-Year Treasury Constant Maturity Rate impacts on the number of issued bond and is used as risk free rate to calculate the excess return on the investment. It also has an influence on the stock market. ?5: Gross Domestic Product of the US is important for business profit and this can drive the stock prices up. Investing in the stock market seems reasonable when the economy is doing well.If the economy is growing fast then the stock market should be affected positively, the investors are more optimistic about the future and they put more money into market more. This variable is crucial for the dependent one. ?6: Gross Domestic Product of Spain. Since Europe is currently in a recession, we wanted to include the GDP of Spain, as one of the weakest economies in Europe now, to check if there is any relationship between Spain’s economy and the US stock market performance. Very small percentage of US investments goes to Spain.Compared to Germany, which is the 5th country the USA invests into, Spain is the 31st country on the list. There should not be any correlation between these two variables, so we included Spain’s GDP into our regression to check our hypothesis. ?7: Gross Domestic Product of Germany is an indicator of Germany is the 5th largest economy in the world and is the largest European trade and investment partner of the US. Germany is the largest economy in Europe and almost 1/5 of GDP of the European Union is that of Germany alone. We assume that this variable has to have an impact on the US stock market.The second regression model is the following: S (Annual Average) = ? 0 + ? 1*(Annual CPI) + ? 2*(Annual Average House Price Index) + ? 3*(Annual Average Interest Rate) + ? 4*(Average Annual Unemployment Rate) + ? 5*(Annual Average GDP of US) + ? 6*(Annual Average GDP of Germany) + ? 7*(Annual Average GDP of China) After we run the regression of the second model, it resulted in improving of our model accuracy. We excluded PPI, GDP of Spain because it came out that these variables have no impact on the US stock market.Also, we added the unemployment rate and GDP of China because it is the largest US business partner. Here is the explanation of the new variables: Unemployment Rate is one of the most impo rtant factors of the economy’s performance. High unemployment rate decreases the buyer power of the consumers. 2/3 of the US economy is consumer based and it influences the stock market negatively. We assume that there is a relationship between these two variables. Gross Domestic Product of China affects the US economy because cheap export from China prevents inflation in the US.China is a huge buyer of the US Treasuries. It lowers the interest rate and companies borrow money to invest in development hence, it directly affects the stock market. We assume that GDP of China and US stock market move in the same direction, meaning if China does well, it has money to buy US Treasuries. Additionally, the US stock market increases because production of those US companies that is outsourced to China grows. Results The First Model [pic] Looking at this model, we see that only the interest rate and GDP of US are statistically significant because they have P-values lower than 0. 05.The rest variables do not correlate with S because their P-values are high. Our assumption about Spain’s economy affecting the US stock market was proved. The coefficient we got for GDP of Spain is statistically insignificant. Looking at the US and Spain investment relationships in the broad aspect we see that Spain’s performance has no significant impact on the US stock market even considering its economic situation. PPI is a fraction of inflation and CPI also reflects inflation, so we decided to exclude one variable because two variables together cancelled each other out and we got defected result.As P-value is smaller compared to P-value of PPI, we decided to keep it in the second model. Looking at the adjusted R square which is 26 %, we concluded that model is deficient and we have to change the variables. The Second Model [pic] Each estimated coefficients we can interpret as follows: -For every 1 unit increase in Annual CPI, the S will go down by -25. 68 S points. Whe n inflation goes up, it causes interest rate to go up, therefore companies are not willing to borrow money and invest. Hence the S index moves in the opposite direction to CPI.The P-value of 0. 000368 implies that the results are statistically significant and it coincides with our assumption. -For every 1 unit increase in House Price Index, the S goes down by -7. 97 units, which tell us that when the price of houses rises, the stock market moves in the opposite direction and it shrinks because people invest in the housing market. The P-value of 0. 000028 shows it is a statistically significant outcome. -For every 1 unit increase in Annual Average 10-Year Treasury Constant Maturity Rate, the S index goes up by 27. 4 units. It would imply that when interest rates go up then the stock market goes up as well, but the p-value of 0. 154 tells us the results are not statistically significant and we should not rely on this outcome. There is no correlation. -For every 1 unit increase in Annu al Average Unemployment Rate in US, the S goes down by 40. 44 units. The p-value of 0. 043 shows what we consider a statistically significant correlation. We can conclude that unemployment rate has a reverse impact on the stock market.When more people have jobs, more people have money to spend and to invest, hence the economy speeds up and the stock market goes up. -For every 1 unit increase in Annual Average GDP of US, the S goes up by 0. 601 index units. The p-value of 0. 00000069 shows the outcome is statistically significant, and implies that when the GDP of US grows meaning that the economy is doing better, investors are more confident and invest more and stock market also goes up. -For every 1 unit increase in Annual Average GDP of Germany, the S goes up by 0. 224 units.We assumed that when Germany is producing more products and their economy is doing well, then the stock market in US does somewhat better too because Germany and US have an economic interaction. The P-value of 0. 155 tells us that the relationship is not statistical significant to conclude the Annual Average GDP of Germany has a positive relationship with S. -For every 1 unit increase in Annual Average GDP of China, the S goes down by . 154 units. US economy as we know is affected by Chinese economy. When US companies move production overseas, specifically to China, the stock market in US does poorly.The P-value of 0. 005 means that this results is statistically significant. We did not find any violations with SLR/MLR assumptions. There appears to be no problem with the data and all the results are relevant. Summary The adjusted R2 of . 96 means that our regression of 96% explains the changes in S. We found out that the biggest correlation is observed between US GDP, CPI, HPI, and China’s GDP. We found out that the GDP of Germany and Interest Rate has no significant correlation with S predicted performance.As we explained above in the result section, the investors should look at US economy performance as well as China’s economic performance, CPI and HPI to try to predict the stock market behavior. References: 1. http://www. infoplease. com/ipa/A0774473. html 2. Federal Housing Finance Agency Web Site 3. U. S. Department of Commerce: Bureau of Economic Analysis Web Site 4. U. S. Department of Labor: Bureau of Labor Statistics Web Site 5. mhttp://research. stlouisfed. org/fred2/series/SP500/downloaddata? cid=32255