The Basics
If a stock’s growth/decay factor is between 0 and 1, the values of the function are said to do this.
Decay
To find a growth or decay factor for a given year, you divide the current year's price by this value.
The previous year's price.
When calculating the geometric mean of 6 years of growth factors, which root must you use on your calculator?
6th Root
Write an exponential equation (y=a(b)^x): A $2,500 investment losing 8% annually.
y=2500(0.92)^x
Between "Stock A" (steady growth factor of 1.06) and "Stock B" (volatile, average growth of 1.12), which is generally safer for a short-term 2-year investment?
Stock A
This term refers to how much a stock's price "swings" up and down over a period of time.
Volatility
A stock was priced at $540 in 2020 and $450 in 2021. What is the decay factor (rounded to four decimal places)?
0.8333
Find the geometric mean of: 2 and 0.5.
1
Write an exponential equation (y=a(b)^x): A $2,500 stock portfolio growing by 92% annually.
y=2500(1.92)^x
Between "Stock A" (steady growth factor of 1.06) and "Stock B" (volatile, average growth of 1.12), which is predicted to have the higher return after 20 years?
Stock B
In the exponential model y=a(b)^x, what do the variables a and b represent?
a= Initial Amount
b= Growth/Decay Factor
Calculate the growth factor for "Green Tech" from 2021 to 2022 if the price rose from $150.00 to $168.00.
1.12
Find the geometric mean of: 1.08, 1.08, and 1.08.
1.08
If the "Green Tech" stock starts at $150.00 (year 0) and has a geometric mean of 1.0645, write the exponential function y=a(b)^x.
y=150(1.0645)^x
In the exponential function y=a(b)^x, if the value of b is exactly 1.00, what does this tell you about the stock price over time?
It stays the same.
If a stock has a growth factor of 0.88, by what specific percentage is the price changing?
Decaying by 12%.
Find the geometric mean of 1.04 and 0.96. Round your answer to four decimal places.
0.9992
Using the model y = 450(1.1215)^x, what does the x represent if the data starts in the year 2020?
Years since 2020
Find the geometric mean of: 1.15, 0.88, 1.04, and 0.97. Round your answer to four decimal places.
1.0104
Why do we use the geometric mean instead of a simple average to find the "average annual growth factor" for a stock?
(Answers Vary)
Using a growth factor of 1.12, if you invest $10,000, what is the predicted value after 20 years?
$96,462.93