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 increasing.
- The growth rate of the primary trend is 1.74% per annum.
- PAG price at the close of April 28, 2025 was $157.86 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 6.16% per annum.
- PAG price at the close of April 28, 2025 was inside the secondary price channel.
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 6, 2023
End date: April 28, 2025
a = 4.9640
b = 0.0000
s = 0.0488
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0488) – 1
= 21.56%
June 6, 2023 calculations
Top border of price channel:
Exp(Y781)
= Exp(a + b × X781 + 2 × s)
= Exp(a + b × 1,133 + 2 × s)
= Exp(4.9640 + 0.0000 × 1,133 + 2 × 0.0488)
= Exp(5.1151)
= $166.51
Bottom border of price channel:
Exp(Y781)
= Exp(a + b × X781 – 2 × s)
= Exp(a + b × 1,133 – 2 × s)
= Exp(4.9640 + 0.0000 × 1,133 – 2 × 0.0488)
= Exp(4.9198)
= $136.98
April 28, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.9640 + 0.0000 × 1,825 + 2 × 0.0488)
= Exp(5.1477)
= $172.04
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.9640 + 0.0000 × 1,825 – 2 × 0.0488)
= Exp(4.9525)
= $141.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.74% per annum.
- PAG price at the close of April 28, 2025 was $157.86 and was inside the primary price channel.
Secondary Trend
Start date: October 12, 2023
End date: April 28, 2025
a = 4.7752
b = 0.0002
s = 0.0412
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0412) – 1
= 17.93%
October 12, 2023 calculations
Top border of price channel:
Exp(Y870)
= Exp(a + b × X870 + 2 × s)
= Exp(a + b × 1,261 + 2 × s)
= Exp(4.7752 + 0.0002 × 1,261 + 2 × 0.0412)
= Exp(5.0642)
= $158.25
Bottom border of price channel:
Exp(Y870)
= Exp(a + b × X870 – 2 × s)
= Exp(a + b × 1,261 – 2 × s)
= Exp(4.7752 + 0.0002 × 1,261 – 2 × 0.0412)
= Exp(4.8993)
= $134.19
April 28, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(4.7752 + 0.0002 × 1,825 + 2 × 0.0412)
= Exp(5.1566)
= $173.57
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.7752 + 0.0002 × 1,825 – 2 × 0.0412)
= Exp(4.9916)
= $147.18
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 6.16% per annum.
- PAG price at the close of April 28, 2025 was inside the secondary price channel.