You are working on designing a factor models for MSFT and UPS stocks.  After preliminary analysis you’ve settled on the following factors that you are considering might help to estimate MSFT and UPS returns.

The factors for MSFT are: S&P 500 returns, NASDAQ returns, changes in PPI (Producer Price Index) and changes in St. Louis Financial Stress Index.

The factors for UPS are: S&P 500 returns, US Regular All Formulations Gas Price changes, changes in Retail Sales: Total (Excluding Food Services).

Take the following steps and write up the answers.  Include your graph and regression results.  Use excel file.

I.    MSFT analysis:

1. Prepare a scatter graph of S&P 500 returns vs. MSFT returns, add the trend line and estimated equation.  What is Beta estimate for MSFT based on the equitation you’ve got?

1. Run regression of MSFT returns vs. S&P 500 returns and write out the resulting equation:

RMSFT = α + βi (RS&P 500) + εi

a.    What is your Beta estimate?  Compare to part 1 Beta estimate.

b.    What is R2?  Explain, what does it tell you?

c.    What is P-value? Explain, what does it tell you?

1. Run regression of MSFT returns vs. NASDAQ returns and write out the resulting equation:

RMSFT = α + βi (RNASDAQ) + εi

a.    Is NASDAQ a better factor for MSFT returns estimate?  Why or why not?

1. Choose the better factor for MSFT returns estimate (S&P 500 or NASDAQ returns).  Add changes in PPI to your regression estimates and write out the resulting equation:

RMSFT = α + β1i (RS&P 500 or RNASDAQ) + β2i (Δ PPI) + εi

a.    Should you keep changes in PPI as a factor in the model for MSFT Risk Premium estimates?  List 2 reasons.

1. Now, instead of changes in PPI,  add changes in St. Louis Financial Stress Index to your regression estimates and write out the resulting equation:

RMSFT = α + β1i (RS&P 500 or RNASDAQ) + β2i (Δ St. Louis Fin Stress Index) + εi

b.    Should you keep changes in St. Louis Fin Stress Index as a factor in the model for MSFT Risk Premium estimates?  List 2 reasons.

1. Write down the best regression for estimating MSFT returns.  List 2 reasons why you have chosen this regression.

II.  UPS analysis:

1. Prepare a scatter graph of S&P 500 returns vs. UPS returns, add the trend line and estimated equation.  What is Beta estimate for UPS based on the equitation you’ve got?

1. Run regression of UPS returns vs. S&P 500 returns and write out the resulting equation:

RUPS = α + βi (RS&P 500) + εi

a.    What is your Beta estimate?  Compare to part 1 Beta estimate.

b.    What is R2?  Explain, what does it tell you?

c.    What is P-value? Explain, what does it tell you?

1. Now add changes in the US Regular All Formulations Gas Price to the previous regression and write out the resulting equation:

RUPS = α + βi1 (RS&P 500)  + βi2 (Δ US Gas Prices) + εi

a.    Should you keep changes in US Gas Prices as a factor in the model for UPS returns estimates?

1. Now instead of changes in the US Regular All Formulations Gas Price, add changes in the Retail Sales: Total (Excluding Food Services) to the S&P 500 returns and write out the resulting equation:

RUPS = α + βi1 (RS&P 500)  + βi2 (Δ Retail Sales) + εi

1. Now run a regression with all 3 factors and write out the resulting regression:

RUPS = α + βi1 (RS&P 500)  + βi2 (Δ Retail Sales) + βi3 (Δ US Gas Prices) + εi

a.    What can you conclude about the resulting regression?  Check the correlation between changes in the Retail Sales and changes in the US Gas Prices.  What happens to the regression estimates when two highly correlated factors are used for estimating UPS returns (in this particular example)?

1. Choose the best factor model for UPS returns estimates.  Write out 2 reasons for why you chose that particular factor model.