# 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:
Yi = α + β × Xi + εi

Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)

Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)

where:

i - observation number
Yi - natural logarithm of MSFT price
Xi - time index, 1 day interval
σ - standard deviation of εi
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%

Exp(4 × s) – 1
= Exp(4 × 0.1076) – 1
= 53.76%

#### January 26, 2021 calculations

Top border of price channel:

Exp(Y541)
= Exp(a + b × X541 + 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(Y541)
= Exp(a + b × X541 – 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(Y1,107)
= Exp(a + b × X1,107 + 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(Y1,107)
= Exp(a + b × X1,107 – 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%

Exp(4 × s) – 1
= Exp(4 × 0.0567) – 1
= 25.45%

#### September 20, 2022 calculations

Top border of price channel:

Exp(Y957)
= Exp(a + b × X957 + 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(Y957)
= Exp(a + b × X957 – 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(Y1,256)
= Exp(a + b × X1,256 + 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(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(3.8308 + 0.0011 × 1,825 – 2 × 0.0567)
= Exp(5.7986)
= \$329.82