1. 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?
No, this is not a straight line. The X in each domain indicates dates, and the Y axis indicates stock prices. These three functions are in different domains.
2. 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?
Connect a straight line from starting coordinates (0, 10) to the final coordinates (89, 15). maybe this is a simplified solution.
3. Would a simple function hold up?
Yes. We can use the function to analyze the slope of the line and infer the stock's average change over the selected interval.
4. What is the simplest function to represent this situation?
Calculate the straight line function using the formula for calculating the slope between coordinates and the simplified line formula.
m = (y-y0)/(x-x0) (Abramson, 2017)
y-y0 = m(x-x0)
A(0,10) B(89,15)
m = (15-10)/(89-0)m ＝ 5/89
y-10 = 5/89(x-0)
y = 5/89x+10
5. Does your naïve initial and simplified model allow you to predict the behavior of the stock in the next month?
No, stock prices are unpredictable, and a straight line cannot predict the future.
6. 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.
By combining three different linear equations, each with a different domain corresponding to each period, we can see the price movement from early January to the end of March.
m = (y-y0)/(x-x0)
y-y0 = m(x-x0)
・January 1st to January 31
A(0,10) B(30,12)
m = (12-10)/(30-0)m ＝ 1/15
y-10 = 1/15(x-0)
y = 1/15x+10
Domain of x = [0;30]
・February 1st to February 28th
A(30, 12) B(58, 9)
m = (9-12)/(58-30)m ＝ 3/28
y-12 = -3/28(x-30)
y = -3/28x+12+90/28
Domain of x = [30;58]
・March 1st to March 31th
A(58, 9) B(89, 15)
m = (15-9)/(89-58)m ＝ 6/31
y-9 = 6/3(x-58)
y = 6/31x+9-348/31
Domain of x = [58;89]
Thank you guys. Have a nice day!! (390 words)
References
Abramson, J. (2017). Algebra and trigonometry. Opens tax, TX: Rice University. Retrieved from https://openstax.org/details/books/algebra-and-trigonometry
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