Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 28.74% per annum.
- BMY price at the close of April 26, 2024 was $44.85 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.12% per annum.
- BMY price at the close of April 26, 2024 was lower than the bottom border of the secondary price channel by $4.06 (8.29%). 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 BMY 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: October 26, 2022
End date: March 4, 2024
a = 5.5110
b = -0.0009
s = 0.0347
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -28.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0347) – 1
= 14.89%
October 26, 2022 calculations
Top border of price channel:
Exp(Y882)
= Exp(a + b × X882 + 2 × s)
= Exp(a + b × 1,276 + 2 × s)
= Exp(5.5110 + -0.0009 × 1,276 + 2 × 0.0347)
= Exp(4.3958)
= $81.11
Bottom border of price channel:
Exp(Y882)
= Exp(a + b × X882 – 2 × s)
= Exp(a + b × 1,276 – 2 × s)
= Exp(5.5110 + -0.0009 × 1,276 – 2 × 0.0347)
= Exp(4.2570)
= $70.60
March 4, 2024 calculations
Top border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 + 2 × s)
= Exp(a + b × 1,771 + 2 × s)
= Exp(5.5110 + -0.0009 × 1,771 + 2 × 0.0347)
= Exp(3.9362)
= $51.23
Bottom border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 – 2 × s)
= Exp(a + b × 1,771 – 2 × s)
= Exp(5.5110 + -0.0009 × 1,771 – 2 × 0.0347)
= Exp(3.7975)
= $44.59
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 28.74% per annum.
- BMY price at the close of April 26, 2024 was $44.85 and was inside the primary price channel.
Secondary Trend
Start date: October 27, 2023
End date: April 10, 2024
a = 3.4585
b = 0.0003
s = 0.0252
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 10.12%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0252) – 1
= 10.61%
October 27, 2023 calculations
Top border of price channel:
Exp(Y1,134)
= Exp(a + b × X1,134 + 2 × s)
= Exp(a + b × 1,642 + 2 × s)
= Exp(3.4585 + 0.0003 × 1,642 + 2 × 0.0252)
= Exp(3.9426)
= $51.55
Bottom border of price channel:
Exp(Y1,134)
= Exp(a + b × X1,134 – 2 × s)
= Exp(a + b × 1,642 – 2 × s)
= Exp(3.4585 + 0.0003 × 1,642 – 2 × 0.0252)
= Exp(3.8418)
= $46.61
April 10, 2024 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,808 + 2 × s)
= Exp(3.4585 + 0.0003 × 1,808 + 2 × 0.0252)
= Exp(3.9865)
= $53.87
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,808 – 2 × s)
= Exp(3.4585 + 0.0003 × 1,808 – 2 × 0.0252)
= Exp(3.8857)
= $48.70
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 10.12% per annum.
- BMY price at the close of April 26, 2024 was lower than the bottom border of the secondary price channel by $4.06 (8.29%). 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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