# 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 48.66% per annum.
- MSFT price at the close of August 13, 2024 was $414.01 and was lower than the bottom border of the primary price channel by $18.65 (4.31%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 80.04% per annum.
- MSFT price at the close of August 13, 2024 was higher than the top border of the secondary price channel by $8.15 (2.01%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.

### 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 15, 2022

End date: July 23, 2024

a = 4.1879

b = 0.0011

s = 0.0507

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0011) – 1

= 48.66%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0507) – 1

= 22.50%

#### September 15, 2022 calculations

Top border of price channel:

Exp(Y_{778})

= Exp(a + b × X_{778} + 2 × s)

= Exp(a + b × 1,128 + 2 × s)

= Exp(4.1879 + 0.0011 × 1,128 + 2 × 0.0507)

= Exp(5.5147)

= $248.31

Bottom border of price channel:

Exp(Y_{778})

= Exp(a + b × X_{778} – 2 × s)

= Exp(a + b × 1,128 – 2 × s)

= Exp(4.1879 + 0.0011 × 1,128 – 2 × 0.0507)

= Exp(5.3117)

= $202.70

#### July 23, 2024 calculations

Top border of price channel:

Exp(Y_{1,242})

= Exp(a + b × X_{1,242} + 2 × s)

= Exp(a + b × 1,805 + 2 × s)

= Exp(4.1879 + 0.0011 × 1,805 + 2 × 0.0507)

= Exp(6.2501)

= $518.07

Bottom border of price channel:

Exp(Y_{1,242})

= Exp(a + b × X_{1,242} – 2 × s)

= Exp(a + b × 1,805 – 2 × s)

= Exp(4.1879 + 0.0011 × 1,805 – 2 × 0.0507)

= Exp(6.0471)

= $422.90

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 48.66% per annum.
- MSFT price at the close of August 13, 2024 was $414.01 and was lower than the bottom border of the primary price channel by $18.65 (4.31%). This indicates a possible reversal in the primary trend direction.

### Secondary Trend

Start date: July 2, 2024

End date: August 9, 2024

a = 14.0374

b = -0.0044

s = 0.0155

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0044) – 1

= -80.04%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0155) – 1

= 6.42%

#### July 2, 2024 calculations

Top border of price channel:

Exp(Y_{1,228})

= Exp(a + b × X_{1,228} + 2 × s)

= Exp(a + b × 1,784 + 2 × s)

= Exp(14.0374 + -0.0044 × 1,784 + 2 × 0.0155)

= Exp(6.1915)

= $488.56

Bottom border of price channel:

Exp(Y_{1,228})

= Exp(a + b × X_{1,228} – 2 × s)

= Exp(a + b × 1,784 – 2 × s)

= Exp(14.0374 + -0.0044 × 1,784 – 2 × 0.0155)

= Exp(6.1293)

= $459.10

#### August 9, 2024 calculations

Top border of price channel:

Exp(Y_{1,255})

= Exp(a + b × X_{1,255} + 2 × s)

= Exp(a + b × 1,822 + 2 × s)

= Exp(14.0374 + -0.0044 × 1,822 + 2 × 0.0155)

= Exp(6.0237)

= $413.09

Bottom border of price channel:

Exp(Y_{1,255})

= Exp(a + b × X_{1,255} – 2 × s)

= Exp(a + b × 1,822 – 2 × s)

= Exp(14.0374 + -0.0044 × 1,822 – 2 × 0.0155)

= Exp(5.9615)

= $388.19

#### Description

- The secondary trend is decreasing.
- The decline rate of the secondary trend is 80.04% per annum.
- MSFT price at the close of August 13, 2024 was higher than the top border of the secondary price channel by $8.15 (2.01%). This indicates a possible reversal in the secondary trend direction.