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 23.17% per annum.
- MRK price at the close of April 25, 2024 was $130.72 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 2.52% per annum.
- MRK price at the close of April 25, 2024 was higher than the top border of the secondary price channel by $16.69 (14.63%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 MRK 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: January 27, 2021
End date: July 25, 2023
a = 3.8525
b = 0.0006
s = 0.0551
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 23.17%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0551) – 1
= 24.67%
January 27, 2021 calculations
Top border of price channel:
Exp(Y442)
= Exp(a + b × X442 + 2 × s)
= Exp(a + b × 642 + 2 × s)
= Exp(3.8525 + 0.0006 × 642 + 2 × 0.0551)
= Exp(4.3293)
= $75.89
Bottom border of price channel:
Exp(Y442)
= Exp(a + b × X442 – 2 × s)
= Exp(a + b × 642 – 2 × s)
= Exp(3.8525 + 0.0006 × 642 – 2 × 0.0551)
= Exp(4.1088)
= $60.87
July 25, 2023 calculations
Top border of price channel:
Exp(Y1,068)
= Exp(a + b × X1,068 + 2 × s)
= Exp(a + b × 1,551 + 2 × s)
= Exp(3.8525 + 0.0006 × 1,551 + 2 × 0.0551)
= Exp(4.8483)
= $127.53
Bottom border of price channel:
Exp(Y1,068)
= Exp(a + b × X1,068 – 2 × s)
= Exp(a + b × 1,551 – 2 × s)
= Exp(3.8525 + 0.0006 × 1,551 – 2 × 0.0551)
= Exp(4.6278)
= $102.29
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 23.17% per annum.
- MRK price at the close of April 25, 2024 was $130.72 and was inside the primary price channel.
Secondary Trend
Start date: October 27, 2022
End date: December 29, 2023
a = 4.7853
b = -0.0001
s = 0.0394
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -2.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0394) – 1
= 17.08%
October 27, 2022 calculations
Top border of price channel:
Exp(Y884)
= Exp(a + b × X884 + 2 × s)
= Exp(a + b × 1,280 + 2 × s)
= Exp(4.7853 + -0.0001 × 1,280 + 2 × 0.0394)
= Exp(4.7747)
= $118.47
Bottom border of price channel:
Exp(Y884)
= Exp(a + b × X884 – 2 × s)
= Exp(a + b × 1,280 – 2 × s)
= Exp(4.7853 + -0.0001 × 1,280 – 2 × 0.0394)
= Exp(4.6170)
= $101.19
December 29, 2023 calculations
Top border of price channel:
Exp(Y1,178)
= Exp(a + b × X1,178 + 2 × s)
= Exp(a + b × 1,708 + 2 × s)
= Exp(4.7853 + -0.0001 × 1,708 + 2 × 0.0394)
= Exp(4.7448)
= $114.98
Bottom border of price channel:
Exp(Y1,178)
= Exp(a + b × X1,178 – 2 × s)
= Exp(a + b × 1,708 – 2 × s)
= Exp(4.7853 + -0.0001 × 1,708 – 2 × 0.0394)
= Exp(4.5871)
= $98.21
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 2.52% per annum.
- MRK price at the close of April 25, 2024 was higher than the top border of the secondary price channel by $16.69 (14.63%). This indicates a possible reversal in the secondary trend direction.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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