# 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 decreasing.
- The decline rate of the primary trend is 13.35% per annum.
- EQR price at the close of April 19, 2024 was $61.54 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.75% per annum.
- EQR price at the close of April 19, 2024 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:

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: July 8, 2021

End date: February 28, 2024

a = 4.6959

b = -0.0004

s = 0.0763

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × -0.0004) – 1

= -13.35%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0763) – 1

= 35.71%

#### July 8, 2021 calculations

Top border of price channel:

Exp(Y_{558})

= Exp(a + b × X_{558} + 2 × s)

= Exp(a + b × 808 + 2 × s)

= Exp(4.6959 + -0.0004 × 808 + 2 × 0.0763)

= Exp(4.5315)

= $92.89

Bottom border of price channel:

Exp(Y_{558})

= Exp(a + b × X_{558} – 2 × s)

= Exp(a + b × 808 – 2 × s)

= Exp(4.6959 + -0.0004 × 808 – 2 × 0.0763)

= Exp(4.2261)

= $68.45

#### February 28, 2024 calculations

Top border of price channel:

Exp(Y_{1,222})

= Exp(a + b × X_{1,222} + 2 × s)

= Exp(a + b × 1,773 + 2 × s)

= Exp(4.6959 + -0.0004 × 1,773 + 2 × 0.0763)

= Exp(4.1527)

= $63.61

Bottom border of price channel:

Exp(Y_{1,222})

= Exp(a + b × X_{1,222} – 2 × s)

= Exp(a + b × 1,773 – 2 × s)

= Exp(4.6959 + -0.0004 × 1,773 – 2 × 0.0763)

= Exp(3.8474)

= $46.87

#### Description

- The primary trend is decreasing.
- The decline rate of the primary trend is 13.35% per annum.
- EQR price at the close of April 19, 2024 was $61.54 and was inside the primary price channel.

### Secondary Trend

Start date: October 6, 2022

End date: April 19, 2024

a = 4.0100

b = 0.0000

s = 0.0485

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0000) – 1

= 1.75%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0485) – 1

= 21.40%

#### October 6, 2022 calculations

Top border of price channel:

Exp(Y_{873})

= Exp(a + b × X_{873} + 2 × s)

= Exp(a + b × 1,263 + 2 × s)

= Exp(4.0100 + 0.0000 × 1,263 + 2 × 0.0485)

= Exp(4.1671)

= $64.53

Bottom border of price channel:

Exp(Y_{873})

= Exp(a + b × X_{873} – 2 × s)

= Exp(a + b × 1,263 – 2 × s)

= Exp(4.0100 + 0.0000 × 1,263 – 2 × 0.0485)

= Exp(3.9731)

= $53.15

#### April 19, 2024 calculations

Top border of price channel:

Exp(Y_{1,258})

= Exp(a + b × X_{1,258} + 2 × s)

= Exp(a + b × 1,824 + 2 × s)

= Exp(4.0100 + 0.0000 × 1,824 + 2 × 0.0485)

= Exp(4.1938)

= $66.27

Bottom border of price channel:

Exp(Y_{1,258})

= Exp(a + b × X_{1,258} – 2 × s)

= Exp(a + b × 1,824 – 2 × s)

= Exp(4.0100 + 0.0000 × 1,824 – 2 × 0.0485)

= Exp(3.9998)

= $54.59

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.75% per annum.
- EQR price at the close of April 19, 2024 was inside the secondary price channel.