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 35.27% per annum.
- ESRX price at the close of October 31, 2018 was $96.97 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 75.95% per annum.
- ESRX price at the close of October 31, 2018 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 ESRX 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: April 25, 2017
End date: October 31, 2018
a = 2.9914
b = 0.0008
s = 0.0629
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 35.27%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0629) – 1
= 28.62%
April 25, 2017 calculations
Top border of price channel:
Exp(Y874)
= Exp(a + b × X874 + 2 × s)
= Exp(a + b × 1,271 + 2 × s)
= Exp(2.9914 + 0.0008 × 1,271 + 2 × 0.0629)
= Exp(4.1693)
= $64.67
Bottom border of price channel:
Exp(Y874)
= Exp(a + b × X874 – 2 × s)
= Exp(a + b × 1,271 – 2 × s)
= Exp(2.9914 + 0.0008 × 1,271 – 2 × 0.0629)
= Exp(3.9176)
= $50.28
October 31, 2018 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(2.9914 + 0.0008 × 1,825 + 2 × 0.0629)
= Exp(4.6278)
= $102.29
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(2.9914 + 0.0008 × 1,825 – 2 × 0.0629)
= Exp(4.3761)
= $79.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 35.27% per annum.
- ESRX price at the close of October 31, 2018 was $96.97 and was inside the primary price channel.
Secondary Trend
Start date: March 22, 2018
End date: October 31, 2018
a = 1.7465
b = 0.0015
s = 0.0335
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 75.95%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0335) – 1
= 14.35%
March 22, 2018 calculations
Top border of price channel:
Exp(Y1,102)
= Exp(a + b × X1,102 + 2 × s)
= Exp(a + b × 1,602 + 2 × s)
= Exp(1.7465 + 0.0015 × 1,602 + 2 × 0.0335)
= Exp(4.2934)
= $73.22
Bottom border of price channel:
Exp(Y1,102)
= Exp(a + b × X1,102 – 2 × s)
= Exp(a + b × 1,602 – 2 × s)
= Exp(1.7465 + 0.0015 × 1,602 – 2 × 0.0335)
= Exp(4.1593)
= $64.03
October 31, 2018 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(1.7465 + 0.0015 × 1,825 + 2 × 0.0335)
= Exp(4.6386)
= $103.40
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(1.7465 + 0.0015 × 1,825 – 2 × 0.0335)
= Exp(4.5046)
= $90.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 75.95% per annum.
- ESRX price at the close of October 31, 2018 was inside the secondary price channel.
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- Check the power of mathematical statistics.
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