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 26.28% per annum.
- AZN price at the close of March 10, 2015 was $32.29 and was lower than the bottom border of the primary price channel by $2.47 (7.11%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 10.11% per annum.
- AZN price at the close of March 10, 2015 was lower than the bottom border of the secondary price channel by $0.18 (0.56%).
- 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 AZN 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 26, 2012
End date: January 2, 2015
a = 2.5175
b = 0.0006
s = 0.0679
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 26.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0679) – 1
= 31.18%
April 26, 2012 calculations
Top border of price channel:
Exp(Y537)
= Exp(a + b × X537 + 2 × s)
= Exp(a + b × 777 + 2 × s)
= Exp(2.5175 + 0.0006 × 777 + 2 × 0.0679)
= Exp(3.1499)
= $23.33
Bottom border of price channel:
Exp(Y537)
= Exp(a + b × X537 – 2 × s)
= Exp(a + b × 777 – 2 × s)
= Exp(2.5175 + 0.0006 × 777 – 2 × 0.0679)
= Exp(2.8785)
= $17.79
January 2, 2015 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,758 + 2 × s)
= Exp(2.5175 + 0.0006 × 1,758 + 2 × 0.0679)
= Exp(3.7771)
= $43.69
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,758 – 2 × s)
= Exp(2.5175 + 0.0006 × 1,758 – 2 × 0.0679)
= Exp(3.5057)
= $33.30
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 26.28% per annum.
- AZN price at the close of March 10, 2015 was $32.29 and was lower than the bottom border of the primary price channel by $2.47 (7.11%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 28, 2014
End date: March 10, 2015
a = 4.0741
b = -0.0003
s = 0.0303
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0303) – 1
= 12.88%
April 28, 2014 calculations
Top border of price channel:
Exp(Y1,039)
= Exp(a + b × X1,039 + 2 × s)
= Exp(a + b × 1,509 + 2 × s)
= Exp(4.0741 + -0.0003 × 1,509 + 2 × 0.0303)
= Exp(3.6938)
= $40.20
Bottom border of price channel:
Exp(Y1,039)
= Exp(a + b × X1,039 – 2 × s)
= Exp(a + b × 1,509 – 2 × s)
= Exp(4.0741 + -0.0003 × 1,509 – 2 × 0.0303)
= Exp(3.5727)
= $35.61
March 10, 2015 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.0741 + -0.0003 × 1,825 + 2 × 0.0303)
= Exp(3.6015)
= $36.65
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.0741 + -0.0003 × 1,825 – 2 × 0.0303)
= Exp(3.4804)
= $32.47
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 10.11% per annum.
- AZN price at the close of March 10, 2015 was lower than the bottom border of the secondary price channel by $0.18 (0.56%).
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- Check the power of mathematical statistics.
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