Stock Price Trends

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%

Price channel spread:

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%

Price channel spread:

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