Stock Price Trends

Apple Inc. (AAPL) 

Apple Inc. is an American multinational technology company headquartered in Cupertino, California. Apple is the worlds largest technology company by revenue, with US$394.3 billion in 2022 revenue. As of March 2023, Apple is the worlds biggest company by market capitalization.

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 12.90% per annum.
  • AAPL price at the close of March 1, 2024 was $179.66 and was inside the primary price channel.
  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 28.57% per annum.
  • AAPL price at the close of March 1, 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 AAPL 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: August 4, 2020
End date: March 1, 2024

a = 4.6306

b = 0.0003

s = 0.0875

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.90%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0875) – 1
= 41.88%

August 4, 2020 calculations

Top border of price channel:

Exp(Y359)
= Exp(a + b × X359 + 2 × s)
= Exp(a + b × 519 + 2 × s)
= Exp(4.6306 + 0.0003 × 519 + 2 × 0.0875)
= Exp(4.9781)
= $145.20

Bottom border of price channel:

Exp(Y359)
= Exp(a + b × X359 – 2 × s)
= Exp(a + b × 519 – 2 × s)
= Exp(4.6306 + 0.0003 × 519 – 2 × 0.0875)
= Exp(4.6283)
= $102.34

March 1, 2024 calculations

Top border of price channel:

Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.6306 + 0.0003 × 1,824 + 2 × 0.0875)
= Exp(5.4120)
= $224.08

Bottom border of price channel:

Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.6306 + 0.0003 × 1,824 – 2 × 0.0875)
= Exp(5.0622)
= $157.94

Description

  • The primary trend is increasing.
  • The growth rate of the primary trend is 12.90% per annum.
  • AAPL price at the close of March 1, 2024 was $179.66 and was inside the primary price channel.

Secondary Trend

Start date: September 29, 2022
End date: March 1, 2024

a = 4.0439

b = 0.0007

s = 0.0625

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.57%

Price channel spread:

Exp(4 × s) – 1
= Exp(4 × 0.0625) – 1
= 28.41%

September 29, 2022 calculations

Top border of price channel:

Exp(Y902)
= Exp(a + b × X902 + 2 × s)
= Exp(a + b × 1,305 + 2 × s)
= Exp(4.0439 + 0.0007 × 1,305 + 2 × 0.0625)
= Exp(5.0676)
= $158.79

Bottom border of price channel:

Exp(Y902)
= Exp(a + b × X902 – 2 × s)
= Exp(a + b × 1,305 – 2 × s)
= Exp(4.0439 + 0.0007 × 1,305 – 2 × 0.0625)
= Exp(4.8175)
= $123.65

March 1, 2024 calculations

Top border of price channel:

Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.0439 + 0.0007 × 1,824 + 2 × 0.0625)
= Exp(5.4249)
= $227.00

Bottom border of price channel:

Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.0439 + 0.0007 × 1,824 – 2 × 0.0625)
= Exp(5.1749)
= $176.77

Description

  • The secondary trend is increasing.
  • The growth rate of the secondary trend is 28.57% per annum.
  • AAPL price at the close of March 1, 2024 was inside the secondary price channel.