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## Stock Price Trends

Stock price trends estimated using linear regression.

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Amazon.com Inc. pages available for free this week:

- Statement of Comprehensive Income
- Balance Sheet: Assets
- Cash Flow Statement
- Common-Size Income Statement
- DuPont Analysis: Disaggregation of ROE, ROA, and Net Profit Margin
- Enterprise Value to FCFF (EV/FCFF)
- Price to FCFE (P/FCFE)
- Total Asset Turnover since 2005
- Price to Operating Profit (P/OP) since 2005
- Analysis of Debt

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#### Key facts

- The primary trend is decreasing.
- The decline rate of the primary trend is 29.91% per annum.
- AMZN price at the close of June 8, 2023 was $124.25 and was higher than the top border of the primary trend channel by $13.28 (11.97%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 173.73% per annum.
- AMZN price at the close of June 8, 2023 was inside the secondary trend 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 trend channel:

Exp(Y_{i}) = Exp(a + b × X_{i} + 2 × s)

Bottom border of trend channel:

Exp(Y_{i}) = Exp(a + b × X_{i} – 2 × s)

where:

i - observation number

Y_{i} - natural logarithm of AMZN 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:

End date:

a =

b =

s =

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × ) – 1

=

Trend channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### April 7, 2021 calculations

Top border of trend channeld:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### May 9, 2023 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

### Secondary Trend

Start date:

End date:

a =

b =

s =

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × ) – 1

=

Trend channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### February 24, 2023 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### June 8, 2023 calculations

Top border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of trend channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $