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 0.53% per annum.
- UNH price at the close of April 25, 2024 was $493.86 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.62% per annum.
- UNH price at the close of April 25, 2024 was inside the secondary price channel.
- 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 UNH 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: December 8, 2021
End date: April 25, 2024
a = 6.2004
b = 0.0000
s = 0.0500
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.53%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0500) – 1
= 22.12%
December 8, 2021 calculations
Top border of price channel:
Exp(Y661)
= Exp(a + b × X661 + 2 × s)
= Exp(a + b × 957 + 2 × s)
= Exp(6.2004 + 0.0000 × 957 + 2 × 0.0500)
= Exp(6.3142)
= $552.35
Bottom border of price channel:
Exp(Y661)
= Exp(a + b × X661 – 2 × s)
= Exp(a + b × 957 – 2 × s)
= Exp(6.2004 + 0.0000 × 957 – 2 × 0.0500)
= Exp(6.1143)
= $452.29
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(6.2004 + 0.0000 × 1,826 + 2 × 0.0500)
= Exp(6.3268)
= $559.34
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(6.2004 + 0.0000 × 1,826 – 2 × 0.0500)
= Exp(6.1269)
= $458.02
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.53% per annum.
- UNH price at the close of April 25, 2024 was $493.86 and was inside the primary price channel.
Secondary Trend
Start date: November 7, 2023
End date: April 25, 2024
a = 7.9113
b = -0.0010
s = 0.0289
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -29.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0289) – 1
= 12.25%
November 7, 2023 calculations
Top border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 + 2 × s)
= Exp(a + b × 1,656 + 2 × s)
= Exp(7.9113 + -0.0010 × 1,656 + 2 × 0.0289)
= Exp(6.3754)
= $587.22
Bottom border of price channel:
Exp(Y1,142)
= Exp(a + b × X1,142 – 2 × s)
= Exp(a + b × 1,656 – 2 × s)
= Exp(7.9113 + -0.0010 × 1,656 – 2 × 0.0289)
= Exp(6.2599)
= $523.15
April 25, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.9113 + -0.0010 × 1,826 + 2 × 0.0289)
= Exp(6.2118)
= $498.60
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.9113 + -0.0010 × 1,826 – 2 × 0.0289)
= Exp(6.0963)
= $444.20
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 29.62% per annum.
- UNH price at the close of April 25, 2024 was inside the secondary price channel.
- 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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