# Apple Inc (AAPL)

Apple Inc. is an American multinational technology company that specializes in consumer electronics, computer software, and online services. Apple is the world's largest technology company by revenue (totalling $274.5 billion in 2020) and, since January 2021, the world's most valuable company. As of 2021, Apple is the world's fourth-largest PC vendor by unit sales, and fourth-largest smartphone manufacturer. It is one of the Big Five American information technology companies, along with Amazon, Google, Microsoft, and Facebook.

## 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 12.68% per annum.
- AAPL price at the close of July 23, 2024 was $225.01 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 289.82% per annum.
- AAPL price at the close of July 23, 2024 was lower than the bottom border of the secondary price channel by $3.39 (1.49%). This indicates a possible reversal in the secondary trend direction.

### 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 6, 2020

End date: June 11, 2024

a = 4.6676

b = 0.0003

s = 0.0869

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0003) – 1

= 12.68%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0869) – 1

= 41.56%

#### August 6, 2020 calculations

Top border of price channel:

Exp(Y_{262})

= Exp(a + b × X_{262} + 2 × s)

= Exp(a + b × 379 + 2 × s)

= Exp(4.6676 + 0.0003 × 379 + 2 × 0.0869)

= Exp(4.9654)

= $143.36

Bottom border of price channel:

Exp(Y_{262})

= Exp(a + b × X_{262} – 2 × s)

= Exp(a + b × 379 – 2 × s)

= Exp(4.6676 + 0.0003 × 379 – 2 × 0.0869)

= Exp(4.6178)

= $101.27

#### June 11, 2024 calculations

Top border of price channel:

Exp(Y_{1,229})

= Exp(a + b × X_{1,229} + 2 × s)

= Exp(a + b × 1,784 + 2 × s)

= Exp(4.6676 + 0.0003 × 1,784 + 2 × 0.0869)

= Exp(5.4250)

= $227.01

Bottom border of price channel:

Exp(Y_{1,229})

= Exp(a + b × X_{1,229} – 2 × s)

= Exp(a + b × 1,784 – 2 × s)

= Exp(4.6676 + 0.0003 × 1,784 – 2 × 0.0869)

= Exp(5.0774)

= $160.36

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 12.68% per annum.
- AAPL price at the close of July 23, 2024 was $225.01 and was inside the primary price channel.

### Secondary Trend

Start date: April 16, 2024

End date: July 17, 2024

a = -1.3321

b = 0.0037

s = 0.0216

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0037) – 1

= 289.82%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0216) – 1

= 9.01%

#### April 16, 2024 calculations

Top border of price channel:

Exp(Y_{1,190})

= Exp(a + b × X_{1,190} + 2 × s)

= Exp(a + b × 1,728 + 2 × s)

= Exp(-1.3321 + 0.0037 × 1,728 + 2 × 0.0216)

= Exp(5.1521)

= $172.79

Bottom border of price channel:

Exp(Y_{1,190})

= Exp(a + b × X_{1,190} – 2 × s)

= Exp(a + b × 1,728 – 2 × s)

= Exp(-1.3321 + 0.0037 × 1,728 – 2 × 0.0216)

= Exp(5.0658)

= $158.51

#### July 17, 2024 calculations

Top border of price channel:

Exp(Y_{1,253})

= Exp(a + b × X_{1,253} + 2 × s)

= Exp(a + b × 1,820 + 2 × s)

= Exp(-1.3321 + 0.0037 × 1,820 + 2 × 0.0216)

= Exp(5.4950)

= $243.48

Bottom border of price channel:

Exp(Y_{1,253})

= Exp(a + b × X_{1,253} – 2 × s)

= Exp(a + b × 1,820 – 2 × s)

= Exp(-1.3321 + 0.0037 × 1,820 – 2 × 0.0216)

= Exp(5.4088)

= $223.35

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 289.82% per annum.
- AAPL price at the close of July 23, 2024 was lower than the bottom border of the secondary price channel by $3.39 (1.49%). This indicates a possible reversal in the secondary trend direction.