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 56.94% per annum.
- ULTA price at the close of August 24, 2023 was $422.74 and was lower than the bottom border of the primary price channel by $340.66 (44.62%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.55% per annum.
- ULTA price at the close of August 24, 2023 was lower than the bottom border of the secondary price channel by $19.73 (4.46%). This indicates a possible reversal in the secondary trend direction.
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 ULTA 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: March 9, 2020
End date: January 7, 2022
a = 4.5448
b = 0.0012
s = 0.0790
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 56.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0790) – 1
= 37.18%
March 9, 2020 calculations
Top border of price channel:
Exp(Y384)
= Exp(a + b × X384 + 2 × s)
= Exp(a + b × 560 + 2 × s)
= Exp(4.5448 + 0.0012 × 560 + 2 × 0.0790)
= Exp(5.3943)
= $220.16
Bottom border of price channel:
Exp(Y384)
= Exp(a + b × X384 – 2 × s)
= Exp(a + b × 560 – 2 × s)
= Exp(4.5448 + 0.0012 × 560 – 2 × 0.0790)
= Exp(5.0782)
= $160.49
January 7, 2022 calculations
Top border of price channel:
Exp(Y848)
= Exp(a + b × X848 + 2 × s)
= Exp(a + b × 1,229 + 2 × s)
= Exp(4.5448 + 0.0012 × 1,229 + 2 × 0.0790)
= Exp(6.2204)
= $502.91
Bottom border of price channel:
Exp(Y848)
= Exp(a + b × X848 – 2 × s)
= Exp(a + b × 1,229 – 2 × s)
= Exp(4.5448 + 0.0012 × 1,229 – 2 × 0.0790)
= Exp(5.9043)
= $366.61
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 56.94% per annum.
- ULTA price at the close of August 24, 2023 was $422.74 and was lower than the bottom border of the primary price channel by $340.66 (44.62%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 16, 2020
End date: August 24, 2023
a = 5.2648
b = 0.0005
s = 0.0737
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 21.55%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0737) – 1
= 34.26%
November 16, 2020 calculations
Top border of price channel:
Exp(Y560)
= Exp(a + b × X560 + 2 × s)
= Exp(a + b × 812 + 2 × s)
= Exp(5.2648 + 0.0005 × 812 + 2 × 0.0737)
= Exp(5.8463)
= $345.96
Bottom border of price channel:
Exp(Y560)
= Exp(a + b × X560 – 2 × s)
= Exp(a + b × 812 – 2 × s)
= Exp(5.2648 + 0.0005 × 812 – 2 × 0.0737)
= Exp(5.5517)
= $257.68
August 24, 2023 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.2648 + 0.0005 × 1,823 + 2 × 0.0737)
= Exp(6.3870)
= $594.06
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.2648 + 0.0005 × 1,823 – 2 × 0.0737)
= Exp(6.0924)
= $442.47
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.55% per annum.
- ULTA price at the close of August 24, 2023 was lower than the bottom border of the secondary price channel by $19.73 (4.46%). This indicates a possible reversal in the secondary trend direction.
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