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 2.98% per annum.
- PAYX price at the close of November 19, 2024 was $140.66 and was higher than the top border of the primary price channel by $7.24 (5.43%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 82.22% per annum.
- PAYX price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.73 (1.22%). 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 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: July 1, 2021
End date: August 21, 2024
a = 4.6323
b = 0.0001
s = 0.0571
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 2.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0571) – 1
= 25.66%
July 1, 2021 calculations
Top border of price channel:
Exp(Y405)
= Exp(a + b × X405 + 2 × s)
= Exp(a + b × 589 + 2 × s)
= Exp(4.6323 + 0.0001 × 589 + 2 × 0.0571)
= Exp(4.7939)
= $120.77
Bottom border of price channel:
Exp(Y405)
= Exp(a + b × X405 – 2 × s)
= Exp(a + b × 589 – 2 × s)
= Exp(4.6323 + 0.0001 × 589 – 2 × 0.0571)
= Exp(4.5655)
= $96.11
August 21, 2024 calculations
Top border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 + 2 × s)
= Exp(a + b × 1,736 + 2 × s)
= Exp(4.6323 + 0.0001 × 1,736 + 2 × 0.0571)
= Exp(4.8862)
= $132.45
Bottom border of price channel:
Exp(Y1,194)
= Exp(a + b × X1,194 – 2 × s)
= Exp(a + b × 1,736 – 2 × s)
= Exp(4.6323 + 0.0001 × 1,736 – 2 × 0.0571)
= Exp(4.6578)
= $105.40
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 2.98% per annum.
- PAYX price at the close of November 19, 2024 was $140.66 and was higher than the top border of the primary price channel by $7.24 (5.43%).
Secondary Trend
Start date: June 26, 2024
End date: November 15, 2024
a = 1.9898
b = 0.0016
s = 0.0166
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 82.22%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0166) – 1
= 6.86%
June 26, 2024 calculations
Top border of price channel:
Exp(Y1,155)
= Exp(a + b × X1,155 + 2 × s)
= Exp(a + b × 1,680 + 2 × s)
= Exp(1.9898 + 0.0016 × 1,680 + 2 × 0.0166)
= Exp(4.7849)
= $119.69
Bottom border of price channel:
Exp(Y1,155)
= Exp(a + b × X1,155 – 2 × s)
= Exp(a + b × 1,680 – 2 × s)
= Exp(1.9898 + 0.0016 × 1,680 – 2 × 0.0166)
= Exp(4.7186)
= $112.01
November 15, 2024 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(1.9898 + 0.0016 × 1,822 + 2 × 0.0166)
= Exp(5.0184)
= $151.17
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(1.9898 + 0.0016 × 1,822 – 2 × 0.0166)
= Exp(4.9520)
= $141.46
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 82.22% per annum.
- PAYX price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $1.73 (1.22%). This indicates a possible reversal in the secondary trend direction.