# International Business Machines (IBM)

International Business Machines Corporation (IBM) is an American multinational technology company headquartered in Armonk, New York, with operations in over 170 countries. The company began in 1911, founded in Endicott, New York, as the Computing-Tabulating-Recording Company (CTR) and was renamed International Business Machines in 1924. IBM is incorporated in New York. IBM produces and sells computer hardware, middleware and software, and provides hosting and consulting services in areas ranging from mainframe computers to nanotechnology. IBM is also a major research organization, holding the record for most annual U.S. patents generated by a business (as of 2020) for 28 consecutive years. Inventions by IBM include the automated teller machine (ATM), the floppy disk, the hard disk drive, the magnetic stripe card, the relational database, the SQL programming language, the UPC barcode, and dynamic random-access memory (DRAM). The IBM mainframe, exemplified by the System/360, was the dominant computing platform during the 1960s and 1970s.

## Stock Price Trends

Stock price trends estimated using linear regression.

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#### Key facts

- The primary trend is increasing.
- The growth rate of the primary trend is 45.89% per annum.
- IBM price at the close of November 5, 2024 was $207.57 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 107.11% per annum.
- IBM price at the close of November 5, 2024 was lower than the bottom border of the secondary price channel by $6.29 (2.94%). This indicates a possible reversal in the secondary trend direction.

### 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 IBM 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

=

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### February 23, 2023 calculations

Top border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### November 5, 2024 calculations

Top border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 45.89% per annum.
- IBM price at the close of November 5, 2024 was $207.57 and was inside the primary price channel.

### Secondary Trend

Start date:

End date:

a =

b =

s =

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × ) – 1

=

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × ) – 1

=

#### April 30, 2024 calculations

Top border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### November 5, 2024 calculations

Top border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} + 2 × s)

= Exp(a + b × + 2 × s)

= Exp( + × + 2 × )

= Exp()

= $

Bottom border of price channel:

Exp(Y_{})

= Exp(a + b × X_{} – 2 × s)

= Exp(a + b × – 2 × s)

= Exp( + × – 2 × )

= Exp()

= $

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 107.11% per annum.
- IBM price at the close of November 5, 2024 was lower than the bottom border of the secondary price channel by $6.29 (2.94%). This indicates a possible reversal in the secondary trend direction.