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 7.41% per annum.
- EMR price at the close of April 24, 2020 was $53.82 and was lower than the bottom border of the primary price channel by $0.35 (0.64%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 84.31% per annum.
- EMR price at the close of April 24, 2020 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 EMR 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 13, 2017
End date: October 16, 2019
a = 4.4944
b = -0.0002
s = 0.0589
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.41%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0589) – 1
= 26.57%
December 13, 2017 calculations
Top border of price channel:
Exp(Y665)
= Exp(a + b × X665 + 2 × s)
= Exp(a + b × 961 + 2 × s)
= Exp(4.4944 + -0.0002 × 961 + 2 × 0.0589)
= Exp(4.4096)
= $82.24
Bottom border of price channel:
Exp(Y665)
= Exp(a + b × X665 – 2 × s)
= Exp(a + b × 961 – 2 × s)
= Exp(4.4944 + -0.0002 × 961 – 2 × 0.0589)
= Exp(4.1740)
= $64.97
October 16, 2019 calculations
Top border of price channel:
Exp(Y1,127)
= Exp(a + b × X1,127 + 2 × s)
= Exp(a + b × 1,633 + 2 × s)
= Exp(4.4944 + -0.0002 × 1,633 + 2 × 0.0589)
= Exp(4.2680)
= $71.38
Bottom border of price channel:
Exp(Y1,127)
= Exp(a + b × X1,127 – 2 × s)
= Exp(a + b × 1,633 – 2 × s)
= Exp(4.4944 + -0.0002 × 1,633 – 2 × 0.0589)
= Exp(4.0323)
= $56.39
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 7.41% per annum.
- EMR price at the close of April 24, 2020 was $53.82 and was lower than the bottom border of the primary price channel by $0.35 (0.64%).
Secondary Trend
Start date: December 16, 2019
End date: April 21, 2020
a = 13.0633
b = -0.0051
s = 0.1072
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0051) – 1
= -84.31%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1072) – 1
= 53.52%
December 16, 2019 calculations
Top border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 + 2 × s)
= Exp(a + b × 1,694 + 2 × s)
= Exp(13.0633 + -0.0051 × 1,694 + 2 × 0.1072)
= Exp(4.6829)
= $108.09
Bottom border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 – 2 × s)
= Exp(a + b × 1,694 – 2 × s)
= Exp(13.0633 + -0.0051 × 1,694 – 2 × 0.1072)
= Exp(4.2543)
= $70.41
April 21, 2020 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(13.0633 + -0.0051 × 1,821 + 2 × 0.1072)
= Exp(4.0386)
= $56.75
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(13.0633 + -0.0051 × 1,821 – 2 × 0.1072)
= Exp(3.6100)
= $36.96
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 84.31% per annum.
- EMR price at the close of April 24, 2020 was inside the secondary price channel.
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