# Arch Capital Group Ltd (ACGL)

Arch Capital Group Ltd., offers insurance, reinsurance and mortgage products worldwide. The company is headquartered in Pembroke, Bermuda.

## Stock Price Trends

Stock price trends estimated using linear regression.

#### Key facts

- The primary trend is increasing.
- The growth rate of the primary trend is 35.48% per annum.
- ACGL price at the close of June 18, 2024 was $100.80 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 91.62% per annum.
- ACGL price at the close of June 18, 2024 was inside the secondary price channel.

### 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 ACGL 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: March 18, 2020

End date: June 18, 2024

a = 3.0356

b = 0.0008

s = 0.0789

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0008) – 1

= 35.48%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0789) – 1

= 37.08%

#### March 18, 2020 calculations

Top border of price channel:

Exp(Y_{187})

= Exp(a + b × X_{187} + 2 × s)

= Exp(a + b × 272 + 2 × s)

= Exp(3.0356 + 0.0008 × 272 + 2 × 0.0789)

= Exp(3.4196)

= $30.56

Bottom border of price channel:

Exp(Y_{187})

= Exp(a + b × X_{187} – 2 × s)

= Exp(a + b × 272 – 2 × s)

= Exp(3.0356 + 0.0008 × 272 – 2 × 0.0789)

= Exp(3.1042)

= $22.29

#### June 18, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,825 + 2 × s)

= Exp(3.0356 + 0.0008 × 1,825 + 2 × 0.0789)

= Exp(4.7116)

= $111.22

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,825 – 2 × s)

= Exp(3.0356 + 0.0008 × 1,825 – 2 × 0.0789)

= Exp(4.3961)

= $81.14

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 35.48% per annum.
- ACGL price at the close of June 18, 2024 was $100.80 and was inside the primary price channel.

### Secondary Trend

Start date: December 14, 2023

End date: June 18, 2024

a = 1.3961

b = 0.0018

s = 0.0229

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0018) – 1

= 91.62%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0229) – 1

= 9.57%

#### December 14, 2023 calculations

Top border of price channel:

Exp(Y_{1,130})

= Exp(a + b × X_{1,130} + 2 × s)

= Exp(a + b × 1,638 + 2 × s)

= Exp(1.3961 + 0.0018 × 1,638 + 2 × 0.0229)

= Exp(4.3603)

= $78.28

Bottom border of price channel:

Exp(Y_{1,130})

= Exp(a + b × X_{1,130} – 2 × s)

= Exp(a + b × 1,638 – 2 × s)

= Exp(1.3961 + 0.0018 × 1,638 – 2 × 0.0229)

= Exp(4.2689)

= $71.44

#### June 18, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,825 + 2 × s)

= Exp(1.3961 + 0.0018 × 1,825 + 2 × 0.0229)

= Exp(4.6935)

= $109.23

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,825 – 2 × s)

= Exp(1.3961 + 0.0018 × 1,825 – 2 × 0.0229)

= Exp(4.6021)

= $99.69

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 91.62% per annum.
- ACGL price at the close of June 18, 2024 was inside the secondary price channel.