KAR Auction Services Inc (KAR)
KAR Auction Services, Inc. provides used vehicle auctions and related vehicle remarketing services for the automotive industry in the United States, Europe, Canada, Mexico, and the United Kingdom. The company is headquartered in Carmel, Indiana.
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 14.98% per annum.
- KAR price at the close of July 26, 2024 was $17.86 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.90% per annum.
- KAR price at the close of July 26, 2024 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 KAR 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 6, 2022
End date: July 26, 2024
a = 2.1293
b = 0.0004
s = 0.0598
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 14.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0598) – 1
= 27.03%
September 6, 2022 calculations
Top border of price channel:
Exp(Y783)
= Exp(a + b × X783 + 2 × s)
= Exp(a + b × 1,135 + 2 × s)
= Exp(2.1293 + 0.0004 × 1,135 + 2 × 0.0598)
= Exp(2.6830)
= $14.63
Bottom border of price channel:
Exp(Y783)
= Exp(a + b × X783 – 2 × s)
= Exp(a + b × 1,135 – 2 × s)
= Exp(2.1293 + 0.0004 × 1,135 – 2 × 0.0598)
= Exp(2.4438)
= $11.52
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.1293 + 0.0004 × 1,824 + 2 × 0.0598)
= Exp(2.9465)
= $19.04
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.1293 + 0.0004 × 1,824 – 2 × 0.0598)
= Exp(2.7072)
= $14.99
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 14.98% per annum.
- KAR price at the close of July 26, 2024 was $17.86 and was inside the primary price channel.
Secondary Trend
Start date: October 12, 2023
End date: July 26, 2024
a = 1.2091
b = 0.0009
s = 0.0469
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0009) – 1
= 39.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0469) – 1
= 20.64%
October 12, 2023 calculations
Top border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 + 2 × s)
= Exp(a + b × 1,536 + 2 × s)
= Exp(1.2091 + 0.0009 × 1,536 + 2 × 0.0469)
= Exp(2.7160)
= $15.12
Bottom border of price channel:
Exp(Y1,060)
= Exp(a + b × X1,060 – 2 × s)
= Exp(a + b × 1,536 – 2 × s)
= Exp(1.2091 + 0.0009 × 1,536 – 2 × 0.0469)
= Exp(2.5284)
= $12.53
July 26, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(1.2091 + 0.0009 × 1,824 + 2 × 0.0469)
= Exp(2.9809)
= $19.71
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(1.2091 + 0.0009 × 1,824 – 2 × 0.0469)
= Exp(2.7933)
= $16.33
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 39.90% per annum.
- KAR price at the close of July 26, 2024 was inside the secondary price channel.