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 34.30% per annum.
- YUM price at the close of October 11, 2016 was $63.44 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 3.30% per annum.
- YUM price at the close of October 11, 2016 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 YUM 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 7, 2015
End date: October 11, 2016
a = 2.7136
b = 0.0008
s = 0.0377
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 34.30%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0377) – 1
= 16.30%
October 7, 2015 calculations
Top border of price channel:
Exp(Y1,002)
= Exp(a + b × X1,002 + 2 × s)
= Exp(a + b × 1,456 + 2 × s)
= Exp(2.7136 + 0.0008 × 1,456 + 2 × 0.0377)
= Exp(3.9654)
= $52.74
Bottom border of price channel:
Exp(Y1,002)
= Exp(a + b × X1,002 – 2 × s)
= Exp(a + b × 1,456 – 2 × s)
= Exp(2.7136 + 0.0008 × 1,456 – 2 × 0.0377)
= Exp(3.8144)
= $45.35
October 11, 2016 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.7136 + 0.0008 × 1,826 + 2 × 0.0377)
= Exp(4.2643)
= $71.12
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.7136 + 0.0008 × 1,826 – 2 × 0.0377)
= Exp(4.1134)
= $61.15
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 34.30% per annum.
- YUM price at the close of October 11, 2016 was $63.44 and was inside the primary price channel.
Secondary Trend
Start date: July 22, 2016
End date: October 11, 2016
a = 4.3273
b = -0.0001
s = 0.0129
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -3.30%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0129) – 1
= 5.29%
July 22, 2016 calculations
Top border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 + 2 × s)
= Exp(a + b × 1,745 + 2 × s)
= Exp(4.3273 + -0.0001 × 1,745 + 2 × 0.0129)
= Exp(4.1927)
= $66.20
Bottom border of price channel:
Exp(Y1,201)
= Exp(a + b × X1,201 – 2 × s)
= Exp(a + b × 1,745 – 2 × s)
= Exp(4.3273 + -0.0001 × 1,745 – 2 × 0.0129)
= Exp(4.1412)
= $62.88
October 11, 2016 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.3273 + -0.0001 × 1,826 + 2 × 0.0129)
= Exp(4.1853)
= $65.71
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.3273 + -0.0001 × 1,826 – 2 × 0.0129)
= Exp(4.1337)
= $62.41
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 3.30% per annum.
- YUM price at the close of October 11, 2016 was inside the secondary price channel.
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