Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 38.20% per annum.
- ORLY price at the close of November 8, 2022 was $833.51 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.49% per annum.
- ORLY price at the close of November 8, 2022 was higher than the top border of the secondary price channel by $41.47 (5.24%).
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of ORLY price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: February 21, 2020
End date: April 27, 2022
a = 5.1482
b = 0.0009
s = 0.0638
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 38.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0638) – 1
= 29.05%
February 21, 2020 calculations
Top border of price channel:
Exp(Y572)
= Exp(a + b × X572 + 2 × s)
= Exp(a + b × 834 + 2 × s)
= Exp(5.1482 + 0.0009 × 834 + 2 × 0.0638)
= Exp(6.0150)
= $409.54
Bottom border of price channel:
Exp(Y572)
= Exp(a + b × X572 – 2 × s)
= Exp(a + b × 834 – 2 × s)
= Exp(5.1482 + 0.0009 × 834 – 2 × 0.0638)
= Exp(5.7600)
= $317.35
April 27, 2022 calculations
Top border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 + 2 × s)
= Exp(a + b × 1,630 + 2 × s)
= Exp(5.1482 + 0.0009 × 1,630 + 2 × 0.0638)
= Exp(6.7207)
= $829.37
Bottom border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 – 2 × s)
= Exp(a + b × 1,630 – 2 × s)
= Exp(5.1482 + 0.0009 × 1,630 – 2 × 0.0638)
= Exp(6.4656)
= $642.67
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 38.20% per annum.
- ORLY price at the close of November 8, 2022 was $833.51 and was inside the primary price channel.
Secondary Trend
Start date: June 29, 2021
End date: October 21, 2022
a = 5.9397
b = 0.0003
s = 0.0510
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 13.49%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0510) – 1
= 22.63%
June 29, 2021 calculations
Top border of price channel:
Exp(Y913)
= Exp(a + b × X913 + 2 × s)
= Exp(a + b × 1,328 + 2 × s)
= Exp(5.9397 + 0.0003 × 1,328 + 2 × 0.0510)
= Exp(6.5023)
= $666.65
Bottom border of price channel:
Exp(Y913)
= Exp(a + b × X913 – 2 × s)
= Exp(a + b × 1,328 – 2 × s)
= Exp(5.9397 + 0.0003 × 1,328 – 2 × 0.0510)
= Exp(6.2983)
= $543.64
October 21, 2022 calculations
Top border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 + 2 × s)
= Exp(a + b × 1,807 + 2 × s)
= Exp(5.9397 + 0.0003 × 1,807 + 2 × 0.0510)
= Exp(6.6684)
= $787.12
Bottom border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 – 2 × s)
= Exp(a + b × 1,807 – 2 × s)
= Exp(5.9397 + 0.0003 × 1,807 – 2 × 0.0510)
= Exp(6.4644)
= $641.87
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.49% per annum.
- ORLY price at the close of November 8, 2022 was higher than the top border of the secondary price channel by $41.47 (5.24%).
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