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 51.31% per annum.
- MSFT price at the close of April 26, 2024 was $406.32 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 43.81% per annum.
- MSFT price at the close of April 26, 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 MSFT 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: September 21, 2022
End date: April 17, 2024
a = 4.0106
b = 0.0011
s = 0.0502
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 51.31%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0502) – 1
= 22.24%
September 21, 2022 calculations
Top border of price channel:
Exp(Y857)
= Exp(a + b × X857 + 2 × s)
= Exp(a + b × 1,241 + 2 × s)
= Exp(4.0106 + 0.0011 × 1,241 + 2 × 0.0502)
= Exp(5.5191)
= $249.42
Bottom border of price channel:
Exp(Y857)
= Exp(a + b × X857 – 2 × s)
= Exp(a + b × 1,241 – 2 × s)
= Exp(4.0106 + 0.0011 × 1,241 – 2 × 0.0502)
= Exp(5.3183)
= $204.03
April 17, 2024 calculations
Top border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 + 2 × s)
= Exp(a + b × 1,815 + 2 × s)
= Exp(4.0106 + 0.0011 × 1,815 + 2 × 0.0502)
= Exp(6.1704)
= $478.39
Bottom border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 – 2 × s)
= Exp(a + b × 1,815 – 2 × s)
= Exp(4.0106 + 0.0011 × 1,815 – 2 × 0.0502)
= Exp(5.9696)
= $391.34
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 51.31% per annum.
- MSFT price at the close of April 26, 2024 was $406.32 and was inside the primary price channel.
Secondary Trend
Start date: March 20, 2024
End date: April 26, 2024
a = 8.8864
b = -0.0016
s = 0.0138
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -43.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0138) – 1
= 5.68%
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,787 + 2 × s)
= Exp(8.8864 + -0.0016 × 1,787 + 2 × 0.0138)
= Exp(6.0918)
= $442.23
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,787 – 2 × s)
= Exp(8.8864 + -0.0016 × 1,787 – 2 × 0.0138)
= Exp(6.0366)
= $418.45
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(8.8864 + -0.0016 × 1,824 + 2 × 0.0138)
= Exp(6.0334)
= $417.13
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(8.8864 + -0.0016 × 1,824 – 2 × 0.0138)
= Exp(5.9781)
= $394.70
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 43.81% per annum.
- MSFT price at the close of April 26, 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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