# Equity Residential (EQR)

Equity Residential is a publicly traded real estate investment trust that invests in apartments.

## 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 39.32% per annum.
- EQR price at the close of August 13, 2024 was $71.15 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 68.16% per annum.
- EQR price at the close of August 13, 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 EQR 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: October 20, 2023

End date: August 13, 2024

a = 2.5948

b = 0.0009

s = 0.0253

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0009) – 1

= 39.32%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0253) – 1

= 10.65%

#### October 20, 2023 calculations

Top border of price channel:

Exp(Y_{1,054})

= Exp(a + b × X_{1,054} + 2 × s)

= Exp(a + b × 1,528 + 2 × s)

= Exp(2.5948 + 0.0009 × 1,528 + 2 × 0.0253)

= Exp(4.0334)

= $56.45

Bottom border of price channel:

Exp(Y_{1,054})

= Exp(a + b × X_{1,054} – 2 × s)

= Exp(a + b × 1,528 – 2 × s)

= Exp(2.5948 + 0.0009 × 1,528 – 2 × 0.0253)

= Exp(3.9322)

= $51.02

#### August 13, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(2.5948 + 0.0009 × 1,826 + 2 × 0.0253)

= Exp(4.3041)

= $74.01

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(2.5948 + 0.0009 × 1,826 – 2 × 0.0253)

= Exp(4.2029)

= $66.88

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 39.32% per annum.
- EQR price at the close of August 13, 2024 was $71.15 and was inside the primary price channel.

### Secondary Trend

Start date: May 28, 2024

End date: August 13, 2024

a = 1.6729

b = 0.0014

s = 0.0121

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0014) – 1

= 68.16%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0121) – 1

= 4.95%

#### May 28, 2024 calculations

Top border of price channel:

Exp(Y_{1,204})

= Exp(a + b × X_{1,204} + 2 × s)

= Exp(a + b × 1,749 + 2 × s)

= Exp(1.6729 + 0.0014 × 1,749 + 2 × 0.0121)

= Exp(4.1874)

= $65.85

Bottom border of price channel:

Exp(Y_{1,204})

= Exp(a + b × X_{1,204} – 2 × s)

= Exp(a + b × 1,749 – 2 × s)

= Exp(1.6729 + 0.0014 × 1,749 – 2 × 0.0121)

= Exp(4.1392)

= $62.75

#### August 13, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,826 + 2 × s)

= Exp(1.6729 + 0.0014 × 1,826 + 2 × 0.0121)

= Exp(4.2971)

= $73.49

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,826 – 2 × s)

= Exp(1.6729 + 0.0014 × 1,826 – 2 × 0.0121)

= Exp(4.2488)

= $70.02

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 68.16% per annum.
- EQR price at the close of August 13, 2024 was inside the secondary price channel.