Papa John's International Inc (PZZA)
Papa John's International, Inc. operates and franchises pizza delivery and take-out restaurants under the Papa John's trademark in the United States and internationally. The company is headquartered in Louisville, Kentucky.
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 19.99% per annum.
- PZZA price at the close of May 9, 2024 was $53.22 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 10.52% per annum.
- PZZA price at the close of May 9, 2024 was lower than the bottom border of the secondary price channel by $4.47 (7.74%).
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 PZZA 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 8, 2021
End date: May 9, 2024
a = 5.2331
b = -0.0006
s = 0.1037
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0006) – 1
= -19.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1037) – 1
= 51.39%
July 8, 2021 calculations
Top border of price channel:
Exp(Y544)
= Exp(a + b × X544 + 2 × s)
= Exp(a + b × 790 + 2 × s)
= Exp(5.2331 + -0.0006 × 790 + 2 × 0.1037)
= Exp(4.9577)
= $142.27
Bottom border of price channel:
Exp(Y544)
= Exp(a + b × X544 – 2 × s)
= Exp(a + b × 790 – 2 × s)
= Exp(5.2331 + -0.0006 × 790 – 2 × 0.1037)
= Exp(4.5430)
= $93.98
May 9, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.2331 + -0.0006 × 1,826 + 2 × 0.1037)
= Exp(4.3247)
= $75.54
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.2331 + -0.0006 × 1,826 – 2 × 0.1037)
= Exp(3.9100)
= $49.90
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 19.99% per annum.
- PZZA price at the close of May 9, 2024 was $53.22 and was inside the primary price channel.
Secondary Trend
Start date: April 28, 2022
End date: May 9, 2024
a = 4.7597
b = -0.0003
s = 0.0742
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0742) – 1
= 34.57%
April 28, 2022 calculations
Top border of price channel:
Exp(Y748)
= Exp(a + b × X748 + 2 × s)
= Exp(a + b × 1,084 + 2 × s)
= Exp(4.7597 + -0.0003 × 1,084 + 2 × 0.0742)
= Exp(4.5779)
= $97.31
Bottom border of price channel:
Exp(Y748)
= Exp(a + b × X748 – 2 × s)
= Exp(a + b × 1,084 – 2 × s)
= Exp(4.7597 + -0.0003 × 1,084 – 2 × 0.0742)
= Exp(4.2810)
= $72.31
May 9, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.7597 + -0.0003 × 1,826 + 2 × 0.0742)
= Exp(4.3519)
= $77.63
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.7597 + -0.0003 × 1,826 – 2 × 0.0742)
= Exp(4.0550)
= $57.69
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 10.52% per annum.
- PZZA price at the close of May 9, 2024 was lower than the bottom border of the secondary price channel by $4.47 (7.74%).