## Monday, November 20, 2017

### Lines Problem One

Question One:   Below are the median market return and median stock

 Median Return for S&P 500 and Apple by  S&P 500 Return Tercile Tercile Median Market Return Median Apple Return 1 -0.0061 -0.0034 2 0.0124 0.0147 3 0.0285 0.0569
Median monthly returns from 1980 to 2017.   Data was sorted by smallest to largest S&P 500 returns and placed into terciles by S&P 500 return.

Consider the market return variable to be your X variable and the median Apple return to be your Y variable.   Provide an equation of the form Y=mx+b with the slope defined by the third and first quartile and with the line running through (X,Y) of the second tercile.

Answer:  The slope of the line is 1.74 (0.0569- -0.0034)/(0.0285- -0.0061).  The  line goes through (0.0124, 0.0147) Using these values for X and Y and 1.74 for m we solve for b.

b=0.0147-1.74*0.0124) or b=-0.0070.

The equation is Y=-0.0070+1.74*X.

Readers interested in using median-median regression models to estimate betas of stocks can go to the following post.

Go here for more problems on lines:

http://www.dailymathproblem.com/p/questions-on-lines.html