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 7.05% per annum.
- ODFL price at the close of August 4, 2023 was $407.11 and was higher than the top border of the primary price channel by $13.11 (3.33%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 430.74% per annum.
- ODFL price at the close of August 4, 2023 was inside the secondary price channel.
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 ODFL 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: March 30, 2021
End date: June 26, 2023
a = 5.4246
b = 0.0002
s = 0.1056
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.05%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1056) – 1
= 52.58%
March 30, 2021 calculations
Top border of price channel:
Exp(Y666)
= Exp(a + b × X666 + 2 × s)
= Exp(a + b × 967 + 2 × s)
= Exp(5.4246 + 0.0002 × 967 + 2 × 0.1056)
= Exp(5.8164)
= $335.75
Bottom border of price channel:
Exp(Y666)
= Exp(a + b × X666 – 2 × s)
= Exp(a + b × 967 – 2 × s)
= Exp(5.4246 + 0.0002 × 967 – 2 × 0.1056)
= Exp(5.3938)
= $220.04
June 26, 2023 calculations
Top border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 + 2 × s)
= Exp(a + b × 1,785 + 2 × s)
= Exp(5.4246 + 0.0002 × 1,785 + 2 × 0.1056)
= Exp(5.9691)
= $391.14
Bottom border of price channel:
Exp(Y1,229)
= Exp(a + b × X1,229 – 2 × s)
= Exp(a + b × 1,785 – 2 × s)
= Exp(5.4246 + 0.0002 × 1,785 – 2 × 0.1056)
= Exp(5.5465)
= $256.35
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 7.05% per annum.
- ODFL price at the close of August 4, 2023 was $407.11 and was higher than the top border of the primary price channel by $13.11 (3.33%).
Secondary Trend
Start date: May 16, 2023
End date: August 4, 2023
a = -2.3045
b = 0.0046
s = 0.0313
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0046) – 1
= 430.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0313) – 1
= 13.33%
May 16, 2023 calculations
Top border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 + 2 × s)
= Exp(a + b × 1,744 + 2 × s)
= Exp(-2.3045 + 0.0046 × 1,744 + 2 × 0.0313)
= Exp(5.7332)
= $308.96
Bottom border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 – 2 × s)
= Exp(a + b × 1,744 – 2 × s)
= Exp(-2.3045 + 0.0046 × 1,744 – 2 × 0.0313)
= Exp(5.6081)
= $272.62
August 4, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-2.3045 + 0.0046 × 1,824 + 2 × 0.0313)
= Exp(6.0990)
= $445.43
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-2.3045 + 0.0046 × 1,824 – 2 × 0.0313)
= Exp(5.9739)
= $393.04
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 430.74% per annum.
- ODFL price at the close of August 4, 2023 was inside the secondary price channel.
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