# FactSet Research Systems Inc. (FDS)

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## 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 0.79% per annum.
• FDS price at the close of December 8, 2023 was \$443.89 and was inside the primary price channel.
• The secondary trend is increasing.
• The growth rate of the secondary trend is 29.70% per annum.
• FDS price at the close of December 8, 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 FDS 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: September 29, 2021
End date: November 3, 2023

a = 6.0703

b = 0.0000

s = 0.0602

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.79%

Exp(4 × s) – 1
= Exp(4 × 0.0602) – 1
= 27.22%

#### September 29, 2021 calculations

Top border of price channel:

Exp(Y706)
= Exp(a + b × X706 + 2 × s)
= Exp(a + b × 1,024 + 2 × s)
= Exp(6.0703 + 0.0000 × 1,024 + 2 × 0.0602)
= Exp(6.1686)
= \$477.50

Bottom border of price channel:

Exp(Y706)
= Exp(a + b × X706 – 2 × s)
= Exp(a + b × 1,024 – 2 × s)
= Exp(6.0703 + 0.0000 × 1,024 – 2 × 0.0602)
= Exp(5.9278)
= \$375.32

#### November 3, 2023 calculations

Top border of price channel:

Exp(Y1,234)
= Exp(a + b × X1,234 + 2 × s)
= Exp(a + b × 1,789 + 2 × s)
= Exp(6.0703 + 0.0000 × 1,789 + 2 × 0.0602)
= Exp(6.1520)
= \$469.66

Bottom border of price channel:

Exp(Y1,234)
= Exp(a + b × X1,234 – 2 × s)
= Exp(a + b × 1,789 – 2 × s)
= Exp(6.0703 + 0.0000 × 1,789 – 2 × 0.0602)
= Exp(5.9112)
= \$369.16

### Secondary Trend

Start date: May 2, 2023
End date: December 5, 2023

a = 4.8301

b = 0.0007

s = 0.0238

Annual growth rate:

Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 29.70%

Exp(4 × s) – 1
= Exp(4 × 0.0238) – 1
= 10.00%

#### May 2, 2023 calculations

Top border of price channel:

Exp(Y1,105)
= Exp(a + b × X1,105 + 2 × s)
= Exp(a + b × 1,604 + 2 × s)
= Exp(4.8301 + 0.0007 × 1,604 + 2 × 0.0238)
= Exp(6.0207)
= \$411.85

Bottom border of price channel:

Exp(Y1,105)
= Exp(a + b × X1,105 – 2 × s)
= Exp(a + b × 1,604 – 2 × s)
= Exp(4.8301 + 0.0007 × 1,604 – 2 × 0.0238)
= Exp(5.9253)
= \$374.39

#### December 5, 2023 calculations

Top border of price channel:

Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(4.8301 + 0.0007 × 1,821 + 2 × 0.0238)
= Exp(6.1753)
= \$480.71

Bottom border of price channel:

Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(4.8301 + 0.0007 × 1,821 – 2 × 0.0238)
= Exp(6.0799)
= \$437.00