Home ownership, equity and forecasting

Introduction to Financial Concepts in Python

Dakota Wixom

Quantitative Finance Analyst

Ownership

To calculate the percentage of the home you actually own (home equity):

$ \text{Percent Equity Owned}_t = P_{Down} + \frac{E_{Cumulative, t}}{V_{Home}} $

$ E_{Cumulative, t} = \sum_{t=1}^{T} P_{Principal, t} $

$ E_{Cumulative, t} $: Cumulative home equity at time $t$
$ P_{Principal, t} $: Principal payment at time $t$
$V_{Home}$: Total home value
$P_{Down}$: Initial down payment

Underwater mortgage

An underwater mortgage is when the remaining amount you owe on your mortgage is actually higher than the value of the house itself.

Cumulative operations in NumPy

Cumulative Sum

import numpy as np
np.cumsum(np.array([1, 2, 3]))

array([1, 3, 6])

Cumulative Product

import numpy as np
np.cumprod(np.array([1, 2, 3]))

array([1, 2, 6])

Forecasting cumulative growth

Example:

What is the cumulative value at each point in time of a $100 investment that grows by 3% in period 1, then 3% again in period 2, and then by 5% in period 3?

import numpy as np
np.cumprod(1 + np.array([0.03, 0.03, 0.05]))

array([ 1.03, 1.0609, 1.113945])

Let's practice!

Introduction to Financial Concepts in Python