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 May 20, 2024 was $43.36 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 81.86% per annum.
- BMY price at the close of May 20, 2024 was higher than the top border of the secondary price channel by $0.08 (0.17%). This indicates a possible reversal in the secondary trend direction.
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 = 5.4906
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(Y866)
= Exp(a + b × X866 + 2 × s)
= Exp(a + b × 1,254 + 2 × s)
= Exp(5.4906 + -0.0009 × 1,254 + 2 × 0.0347)
= Exp(4.3958)
= $81.11
Bottom border of price channel:
Exp(Y866)
= Exp(a + b × X866 – 2 × s)
= Exp(a + b × 1,254 – 2 × s)
= Exp(5.4906 + -0.0009 × 1,254 – 2 × 0.0347)
= Exp(4.2570)
= $70.60
March 4, 2024 calculations
Top border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 + 2 × s)
= Exp(a + b × 1,749 + 2 × s)
= Exp(5.4906 + -0.0009 × 1,749 + 2 × 0.0347)
= Exp(3.9362)
= $51.23
Bottom border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 – 2 × s)
= Exp(a + b × 1,749 – 2 × s)
= Exp(5.4906 + -0.0009 × 1,749 – 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 May 20, 2024 was $43.36 and was inside the primary price channel.
Secondary Trend
Start date: March 25, 2024
End date: May 9, 2024
a = 12.2598
b = -0.0047
s = 0.0236
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0047) – 1
= -81.86%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0236) – 1
= 9.92%
March 25, 2024 calculations
Top border of price channel:
Exp(Y1,219)
= Exp(a + b × X1,219 + 2 × s)
= Exp(a + b × 1,770 + 2 × s)
= Exp(12.2598 + -0.0047 × 1,770 + 2 × 0.0236)
= Exp(4.0297)
= $56.24
Bottom border of price channel:
Exp(Y1,219)
= Exp(a + b × X1,219 – 2 × s)
= Exp(a + b × 1,770 – 2 × s)
= Exp(12.2598 + -0.0047 × 1,770 – 2 × 0.0236)
= Exp(3.9351)
= $51.17
May 9, 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(12.2598 + -0.0047 × 1,815 + 2 × 0.0236)
= Exp(3.8192)
= $45.57
Bottom border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 – 2 × s)
= Exp(a + b × 1,815 – 2 × s)
= Exp(12.2598 + -0.0047 × 1,815 – 2 × 0.0236)
= Exp(3.7247)
= $41.46
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 81.86% per annum.
- BMY price at the close of May 20, 2024 was higher than the top border of the secondary price channel by $0.08 (0.17%). 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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