# Microsoft Corporation (MSFT)

Microsoft Corporation is an American multinational technology company which produces computer software, consumer electronics, personal computers, and related services. Its best known software products are the Microsoft Windows line of operating systems, the Microsoft Office suite, and the Internet Explorer and Edge web browsers. Its flagship hardware products are the Xbox video game consoles and the Microsoft Surface lineup of touchscreen personal computers. Microsoft ranked No. 21 in the 2020 Fortune 500 rankings of the largest United States corporations by total revenue; it was the world's largest software maker by revenue as of 2016. It is considered one of the Big Five companies in the U.S. information technology industry, along with Google, Apple, Amazon, 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 52.75% per annum.
- MSFT price at the close of April 16, 2024 was $414.58 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 40.30% per annum.
- MSFT price at the close of April 16, 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 MSFT 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: September 21, 2022

End date: April 16, 2024

a = 3.9511

b = 0.0012

s = 0.0503

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0012) – 1

= 52.75%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0503) – 1

= 22.27%

#### September 21, 2022 calculations

Top border of price channel:

Exp(Y_{864})

= Exp(a + b × X_{864} + 2 × s)

= Exp(a + b × 1,253 + 2 × s)

= Exp(3.9511 + 0.0012 × 1,253 + 2 × 0.0503)

= Exp(5.5058)

= $246.11

Bottom border of price channel:

Exp(Y_{864})

= Exp(a + b × X_{864} – 2 × s)

= Exp(a + b × 1,253 – 2 × s)

= Exp(3.9511 + 0.0012 × 1,253 – 2 × 0.0503)

= Exp(5.3047)

= $201.29

#### April 16, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(3.9511 + 0.0012 × 1,826 + 2 × 0.0503)

= Exp(6.1708)

= $478.55

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(3.9511 + 0.0012 × 1,826 – 2 × 0.0503)

= Exp(5.9697)

= $391.41

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 52.75% per annum.
- MSFT price at the close of April 16, 2024 was $414.58 and was inside the primary price channel.

### Secondary Trend

Start date: April 27, 2023

End date: April 16, 2024

a = 4.3452

b = 0.0009

s = 0.0434

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0009) – 1

= 40.30%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0434) – 1

= 18.96%

#### April 27, 2023 calculations

Top border of price channel:

Exp(Y_{1,014})

= Exp(a + b × X_{1,014} + 2 × s)

= Exp(a + b × 1,471 + 2 × s)

= Exp(4.3452 + 0.0009 × 1,471 + 2 × 0.0434)

= Exp(5.7967)

= $329.20

Bottom border of price channel:

Exp(Y_{1,014})

= Exp(a + b × X_{1,014} – 2 × s)

= Exp(a + b × 1,471 – 2 × s)

= Exp(4.3452 + 0.0009 × 1,471 – 2 × 0.0434)

= Exp(5.6230)

= $276.73

#### April 16, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(4.3452 + 0.0009 × 1,826 + 2 × 0.0434)

= Exp(6.1260)

= $457.61

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(4.3452 + 0.0009 × 1,826 – 2 × 0.0434)

= Exp(5.9524)

= $384.67

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 40.30% per annum.
- MSFT price at the close of April 16, 2024 was inside the secondary price channel.