Paychex Inc (PAYX)
Paychex, Inc. is an American provider of human resource, payroll, and benefits outsourcing services for small- to medium-sized businesses.
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 3.06% per annum.
- PAYX price at the close of March 31, 2025 was $154.28 and was higher than the top border of the primary price channel by $20.12 (14.99%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.94% per annum.
- PAYX price at the close of March 31, 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 PAYX 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 28, 2021
End date: August 21, 2024
a = 4.6339
b = 0.0001
s = 0.0573
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.06%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0573) – 1
= 25.77%
June 28, 2021 calculations
Top border of price channel:
Exp(Y312)
= Exp(a + b × X312 + 2 × s)
= Exp(a + b × 453 + 2 × s)
= Exp(4.6339 + 0.0001 × 453 + 2 × 0.0573)
= Exp(4.7859)
= $119.81
Bottom border of price channel:
Exp(Y312)
= Exp(a + b × X312 – 2 × s)
= Exp(a + b × 453 – 2 × s)
= Exp(4.6339 + 0.0001 × 453 – 2 × 0.0573)
= Exp(4.5566)
= $95.26
August 21, 2024 calculations
Top border of price channel:
Exp(Y1,104)
= Exp(a + b × X1,104 + 2 × s)
= Exp(a + b × 1,603 + 2 × s)
= Exp(4.6339 + 0.0001 × 1,603 + 2 × 0.0573)
= Exp(4.8808)
= $131.73
Bottom border of price channel:
Exp(Y1,104)
= Exp(a + b × X1,104 – 2 × s)
= Exp(a + b × 1,603 – 2 × s)
= Exp(4.6339 + 0.0001 × 1,603 – 2 × 0.0573)
= Exp(4.6515)
= $104.74
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 3.06% per annum.
- PAYX price at the close of March 31, 2025 was $154.28 and was higher than the top border of the primary price channel by $20.12 (14.99%).
Secondary Trend
Start date: February 21, 2023
End date: March 31, 2025
a = 4.1106
b = 0.0005
s = 0.0425
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 18.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0425) – 1
= 18.55%
February 21, 2023 calculations
Top border of price channel:
Exp(Y727)
= Exp(a + b × X727 + 2 × s)
= Exp(a + b × 1,056 + 2 × s)
= Exp(4.1106 + 0.0005 × 1,056 + 2 × 0.0425)
= Exp(4.6974)
= $109.66
Bottom border of price channel:
Exp(Y727)
= Exp(a + b × X727 – 2 × s)
= Exp(a + b × 1,056 – 2 × s)
= Exp(4.1106 + 0.0005 × 1,056 – 2 × 0.0425)
= Exp(4.5273)
= $92.50
March 31, 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(4.1106 + 0.0005 × 1,825 + 2 × 0.0425)
= Exp(5.0628)
= $158.03
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(4.1106 + 0.0005 × 1,825 – 2 × 0.0425)
= Exp(4.8926)
= $133.31
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.94% per annum.
- PAYX price at the close of March 31, 2025 was inside the secondary price channel.