Answer to Question #269837 in Linear Algebra for David

Question

If a stock price goes from $10 to $12 from January 1st to January 31, from $12 to $9 from February 1st to February 28th, and from $9 to $15 from March 1st to March 31th is the price change from $10 to $15 a straight line?

It is clear that in each of the three time intervals mentioned there was a complex daily variation of prices as in an electrocardiogram. But what would be a simplified solution for a first naive view of the situation? Would a simple function hold up? What is the simplest function to represent this situation? Does your naïve initial and simplified model allow you to predict the behavior of the stock in the next month?

How can I use three “pieces” of lines to describe the price movements from the beginning of January to the end of March? Show the graph for the price movement.

Answer 1

for january we have points (1,10) and (31,12)

for february we have points (1,12) and (28,9)

for march we have points (1,9) and (31,15)

slope (m) = (y₂-y₁)/(x₂-x₁)

slope of january = (12-10)/(31-1) = 2/30 =1/15

slope of febraury = (9-12)/(28-1) = -3/27 = -1/9

slope of march = (15-9)/(31-1) = 6/30 =1/5

equation of line for january is y=(x/15)+b

use first january point

10=(1/15)+b , b=9.93

january line formula y = (x/15)+9.93

equation of line for february is y=(-x/9)+b

use first february point

12=(-1/9)+b , b =12.11

february line formula y=(-x/9)+12.11

equation of line for march is y=(x/5)+b

9=(1/5)+b , b= 8.8

march line formula y = (x/5)+8.8

now graph for these three line is

red line for january

blue line for february

green line for march