# 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:

Y_{i} = α + β × X_{i} + ε_{i}

Top border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} + 2 × s)

Bottom border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} – 2 × s)

where:

i - observation number

Y_{i} - natural logarithm of AAPL price

X_{i} - time index, 1 day interval

σ - standard deviation of ε_{i}

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(Y_{359})

= Exp(a + b × X_{359} + 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(Y_{359})

= Exp(a + b × X_{359} – 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(Y_{1,258})

= Exp(a + b × X_{1,258} + 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(Y_{1,258})

= Exp(a + b × X_{1,258} – 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(Y_{902})

= Exp(a + b × X_{902} + 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(Y_{902})

= Exp(a + b × X_{902} – 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(Y_{1,258})

= Exp(a + b × X_{1,258} + 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(Y_{1,258})

= Exp(a + b × X_{1,258} – 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.