# Microsoft Corporation (MSFT)

Microsoft Corporation is an American multinational technology corporation headquartered in Redmond, Washington. Microsofts best-known software products are the Windows line of operating systems, the Microsoft Office suite, and the Internet Explorer and Edge web browsers.

## Stock Price Trends

Stock price trends estimated using linear regression.

#### Key facts

- The primary trend is decreasing.
- The decline rate of the primary trend is 2.14% per annum.
- MSFT price at the close of November 28, 2023 was $382.70 and was higher than the top border of the primary price channel by $59.21 (18.30%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 51.62% per annum.
- MSFT price at the close of November 28, 2023 was inside the secondary price channel.
- 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: January 26, 2021

End date: April 26, 2023

a = 5.6723

b = -0.0001

s = 0.1076

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0001) – 1

= -2.14%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.1076) – 1

= 53.76%

#### January 26, 2021 calculations

Top border of price channel:

Exp(Y_{541})

= Exp(a + b × X_{541} + 2 × s)

= Exp(a + b × 789 + 2 × s)

= Exp(5.6723 + -0.0001 × 789 + 2 × 0.1076)

= Exp(5.8406)

= $344.00

Bottom border of price channel:

Exp(Y_{541})

= Exp(a + b × X_{541} – 2 × s)

= Exp(a + b × 789 – 2 × s)

= Exp(5.6723 + -0.0001 × 789 – 2 × 0.1076)

= Exp(5.4104)

= $223.73

#### April 26, 2023 calculations

Top border of price channel:

Exp(Y_{1,107})

= Exp(a + b × X_{1,107} + 2 × s)

= Exp(a + b × 1,609 + 2 × s)

= Exp(5.6723 + -0.0001 × 1,609 + 2 × 0.1076)

= Exp(5.7920)

= $327.66

Bottom border of price channel:

Exp(Y_{1,107})

= Exp(a + b × X_{1,107} – 2 × s)

= Exp(a + b × 1,609 – 2 × s)

= Exp(5.6723 + -0.0001 × 1,609 – 2 × 0.1076)

= Exp(5.3618)

= $213.10

### Secondary Trend

Start date: September 20, 2022

End date: November 28, 2023

a = 3.8308

b = 0.0011

s = 0.0567

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0011) – 1

= 51.62%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0567) – 1

= 25.45%

#### September 20, 2022 calculations

Top border of price channel:

Exp(Y_{957})

= Exp(a + b × X_{957} + 2 × s)

= Exp(a + b × 1,391 + 2 × s)

= Exp(3.8308 + 0.0011 × 1,391 + 2 × 0.0567)

= Exp(5.5304)

= $252.25

Bottom border of price channel:

Exp(Y_{957})

= Exp(a + b × X_{957} – 2 × s)

= Exp(a + b × 1,391 – 2 × s)

= Exp(3.8308 + 0.0011 × 1,391 – 2 × 0.0567)

= Exp(5.3037)

= $201.07

#### November 28, 2023 calculations

Top border of price channel:

Exp(Y_{1,256})

= Exp(a + b × X_{1,256} + 2 × s)

= Exp(a + b × 1,825 + 2 × s)

= Exp(3.8308 + 0.0011 × 1,825 + 2 × 0.0567)

= Exp(6.0253)

= $413.77

Bottom border of price channel:

Exp(Y_{1,256})

= Exp(a + b × X_{1,256} – 2 × s)

= Exp(a + b × 1,825 – 2 × s)

= Exp(3.8308 + 0.0011 × 1,825 – 2 × 0.0567)

= Exp(5.7986)

= $329.82