Using Regression to learn to Sell

1.
Qwest (q)     Rq = 0.115 + 2.543*Rsp500

The estimated value of the intercept (alpha) represents the expected excess return for holding a stock in Qwest when the excess return on the market in negligible.  For example, if the S&P500 returns equal those of the current rate of long term government bonds over 1 year, then the expected return for holding Qwest stock over that same year would be 11.5%.

With a beta of 2.543 for Qwest, we would expect that the return on holding Qwest stock over 1 year would equal 2.543 times the returns on the market in excess of the long term government bonds over that 1 year, plus the 11.5%.  The beta reflects the systematic risk of Qwest.  Beta predicts the expected of returns of Qwest stock in response to rises and falls in the market.

2.
R - rf =  0.01055  +  0.00478[E(rm)-rf]
t-stat for beta =  -1.61764
t-stat for alpha = 2.92852

Ho: Beta = 0
H1: Beta ≠ 0

Ho: Alpha = 0
H1: Alpha ≠ 0

The absolute value of the t-stat for Beta à |-1.61764| < 2.00. Ho

This regression infers that beta in this example does not support the CAPM.  Predictions of the CAPM are insufficiently accurate substituting the index portfolio for the market. 

The absolute value of the t-stat for Alpha à |2.92852| > 2.00. H1

Since statically different from 0, there are excess returns beyond those predicted by CAPM.

 

 

 

3.
R – rf = 0.005746 - 0.00417[E(rm)-rf] +0.18667

t-stat for beta =   -1.48445
t-stat for residual variance = 2.07957

Ho: Beta = 0
H1: Beta ≠ 0

Ho: Res Var = 0
H1: Res Var ≠ 0

 

The absolute value of the t-stat for Beta à |-1.48445| < 2.00. Ho

This infers that systematic risk is not significant in the security market line, thus, discrediting CAPM theory.

The absolute value of the t-stat for Residual variance à |-2.07957| > 2.00. H1

Residual variance, or firm specific risk, sufficiently supports excess returns and further contradicts the CAPM.  

 

4. 
Step 1 – Retrieve the B/M ratios and P/E ratios for each month over the time period off the internet, and then find the average B/M ratio and P/E ratio for each company.

Step 2 - Run a regression with the Betas, the average B/M ratios and the average P/E ratios as the “x” variables, and average monthly return for each stock as the “y” variable.

Step 3 – Run hypothesis testing on the t-values associated with the Beta, average B/M ratios and the average P/E ratios.  Any absolute value of t > 2.00, would be considered to have a significant effect on the equation.

Y = Ao + A1X1 + A2X2 + A3X3