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 5.04% per annum.
- DEO price at the close of August 12, 2014 was $117.25 and was lower than the bottom border of the primary price channel by $3.86 (3.19%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 63.85% per annum.
- DEO price at the close of August 12, 2014 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 DEO 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 27, 2012
End date: August 6, 2014
a = 4.6113
b = 0.0001
s = 0.0302
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.04%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0302) – 1
= 12.83%
September 27, 2012 calculations
Top border of price channel:
Exp(Y788)
= Exp(a + b × X788 + 2 × s)
= Exp(a + b × 1,141 + 2 × s)
= Exp(4.6113 + 0.0001 × 1,141 + 2 × 0.0302)
= Exp(4.8253)
= $124.62
Bottom border of price channel:
Exp(Y788)
= Exp(a + b × X788 – 2 × s)
= Exp(a + b × 1,141 – 2 × s)
= Exp(4.6113 + 0.0001 × 1,141 – 2 × 0.0302)
= Exp(4.7046)
= $110.45
August 6, 2014 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,819 + 2 × s)
= Exp(4.6113 + 0.0001 × 1,819 + 2 × 0.0302)
= Exp(4.9166)
= $136.54
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,819 – 2 × s)
= Exp(4.6113 + 0.0001 × 1,819 – 2 × 0.0302)
= Exp(4.7959)
= $121.01
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.04% per annum.
- DEO price at the close of August 12, 2014 was $117.25 and was lower than the bottom border of the primary price channel by $3.86 (3.19%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: July 1, 2014
End date: August 12, 2014
a = 9.8462
b = -0.0028
s = 0.0058
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0028) – 1
= -63.85%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0058) – 1
= 2.34%
July 1, 2014 calculations
Top border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 + 2 × s)
= Exp(a + b × 1,783 + 2 × s)
= Exp(9.8462 + -0.0028 × 1,783 + 2 × 0.0058)
= Exp(4.8867)
= $132.52
Bottom border of price channel:
Exp(Y1,228)
= Exp(a + b × X1,228 – 2 × s)
= Exp(a + b × 1,783 – 2 × s)
= Exp(9.8462 + -0.0028 × 1,783 – 2 × 0.0058)
= Exp(4.8636)
= $129.49
August 12, 2014 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(9.8462 + -0.0028 × 1,825 + 2 × 0.0058)
= Exp(4.7696)
= $117.88
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(9.8462 + -0.0028 × 1,825 – 2 × 0.0058)
= Exp(4.7465)
= $115.18
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 63.85% per annum.
- DEO price at the close of August 12, 2014 was inside the secondary price channel.
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