Penske Automotive Group Inc (PAG)
Penske Automotive Group, Inc., a diversified transportation services company, operates commercial and automotive truck dealerships. The company is headquartered in Bloomfield Hills, Michigan.
Stock Price Trends
Stock price trends estimated using linear regression.
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.25% per annum.
- PAG price at the close of November 20, 2024 was $157.23 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.36% per annum.
- PAG price at the close of November 20, 2024 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 PAG 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: June 7, 2023
End date: November 20, 2024
a = 5.0438
b = 0.0000
s = 0.0461
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0461) – 1
= 20.24%
June 7, 2023 calculations
Top border of price channel:
Exp(Y890)
= Exp(a + b × X890 + 2 × s)
= Exp(a + b × 1,294 + 2 × s)
= Exp(5.0438 + 0.0000 × 1,294 + 2 × 0.0461)
= Exp(5.1272)
= $168.54
Bottom border of price channel:
Exp(Y890)
= Exp(a + b × X890 – 2 × s)
= Exp(a + b × 1,294 – 2 × s)
= Exp(5.0438 + 0.0000 × 1,294 – 2 × 0.0461)
= Exp(4.9429)
= $140.17
November 20, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.0438 + 0.0000 × 1,826 + 2 × 0.0461)
= Exp(5.1236)
= $167.94
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.0438 + 0.0000 × 1,826 – 2 × 0.0461)
= Exp(4.9392)
= $139.66
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.25% per annum.
- PAG price at the close of November 20, 2024 was $157.23 and was inside the primary price channel.
Secondary Trend
Start date: October 12, 2023
End date: November 20, 2024
a = 4.7063
b = 0.0002
s = 0.0346
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.36%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0346) – 1
= 14.85%
October 12, 2023 calculations
Top border of price channel:
Exp(Y978)
= Exp(a + b × X978 + 2 × s)
= Exp(a + b × 1,421 + 2 × s)
= Exp(4.7063 + 0.0002 × 1,421 + 2 × 0.0346)
= Exp(5.0518)
= $156.31
Bottom border of price channel:
Exp(Y978)
= Exp(a + b × X978 – 2 × s)
= Exp(a + b × 1,421 – 2 × s)
= Exp(4.7063 + 0.0002 × 1,421 – 2 × 0.0346)
= Exp(4.9134)
= $136.10
November 20, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.7063 + 0.0002 × 1,826 + 2 × 0.0346)
= Exp(5.1306)
= $169.11
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.7063 + 0.0002 × 1,826 – 2 × 0.0346)
= Exp(4.9921)
= $147.25
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 7.36% per annum.
- PAG price at the close of November 20, 2024 was inside the secondary price channel.