## Thursday, September 8, 2016

### House Price Index - HPI

House Price Index (HPI) measures the price changes of residential housing. Methodologies commonly used to calculate HPI are the hedonic regression (HR), simple moving average (SMA) and repeat-sales regression (RSR).

The HPI was developed in conjunction with OFHEO's (now FHFA) responsibilities as a regulator of Fannie Mae and Freddie Mac. It is used to measure the adequacy of their capital against the value of their assets, which are primarily home mortgages.
In Canada, the New Housing Price Index is calculated monthly by Statistics Canada. Additionally, a resale house price index is also maintained by the Canadian Real Estate Association, based on reported sale prices submitted by real estate agents, and averaged by region. In December 2008, the private National Bank and the information technology firm Teranet began a separate monthly house price index based on resale prices of individual single-family houses in selected metropolitan areas, using a methodology similar to the Case-Shiller index and based on actual sale prices taken from government land registry databases. This allows Teranet and the National Bank to track prices without allowing periods of high sales in one city to push up the national average. The National Bank also operates a forward market on Canadian housing prices.

## Hedonic Regression(HR)

In economics, hedonic regression or hedonic demand theory is a revealed preference method of estimating demand or value. It decomposes the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic.
In real estate economics, hedonic pricing is used to adjust for the problems associated with researching a good that is as heterogeneous as buildings. Because buildings are so different, it is difficult to estimate the demand for buildings generically. Instead, it is assumed that a house can be decomposed into characteristics such as number of bedrooms, size of lot, or distance to the city center.
A hedonic regression equation treats these attributes (or bundles of attributes) separately, and estimates prices (in the case of an additive model) or elasticity (in the case of a log model) for each of them. This information can be used to construct a price index that can be used to compare the price of housing in different cities, or to do time series analysis.
As with CPI calculations, hedonic pricing can be used to correct for quality changes in constructing a housing price index. It can also be used to assess the value of a property, in the absence of specific market transaction data. It can also be used to analyze the demand for various housing characteristics, and housing demand in general. It has also been used to test assumptions in spatial economics.

Hedonic models are commonly used in tax assessment, litigation, academic studies, and other mass appraisal projects

## Simple Moving Average (SMA)

In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms
In financial applications a simple moving average (SMA) is the unweighted mean of the previous n data. However, in science and engineering the mean is normally taken from an equal number of data on either side of a central value.

If those prices are ${\displaystyle p_{M},p_{M-1},\dots ,p_{M-(n-1)}}$ then the formula is
{\displaystyle {\begin{aligned}SMA&={\frac {p_{M}+p_{M-1}+\cdots +p_{M-(n-1)}}{n}}\\&={\frac {1}{n}}\sum _{i=0}^{n-1}p_{M-i}\end{aligned}}}
When calculating successive values, a new value comes into the sum and an old value drops out, meaning a full summation each time is unnecessary for this simple case,

${\displaystyle {\textit {SMA}}_{\mathrm {today} }={\textit {SMA}}_{\mathrm {yesterday} }+{p_{M} \over n}-{p_{M-n} \over n}}$

## Repeat Sales Regression (RSR)

Perhaps the most well-known housing index that uses the repeat-sales method is the Case-Shiller Index, which measures changes in house prices. It excludes new construction, condos and co-ops. It also excludes non-arms-length transactions, such as home sales between family members at below-market prices. It does include foreclosure sales.

Other indexes that use the repeat-sales method are the Federal Housing Finance Agency’s monthly House Price Index, which is based on Fannie Mae and Freddie Mac’s data on single-family home sale prices and refinance appraisals; and Core Logic’s Loan Performance

Home Price Index, which covers a broader geographic area than the Case-Shiller or FHFA indexes. Canada’s major home price index, the National Composite House Price Index, uses the repeat-sales method, too. Indexes such as these typically report changes in home prices from the previous month, quarter and year. Increasing home prices indicate increasing demand, while decreasing prices indicate decreasing demand.

An advantage of repeat-sales methods is that they calculate changes in home prices based on sales of the same property, so they avoid the problem of trying to account for price differences in homes with varying characteristics. Repeat-sales methods also offer a more accurate alternative to regression analysis or to calculating average sales price by geographic area. A shortcoming of repeat-sales methods is that they don’t account for homes that were sold only once during the reported time period.

## Office of Federal Housing Enterprise Oversight (OFHEO)

The Office of Federal Housing Enterprise Oversight (OFHEO) was an agency within the Department of Housing and Urban Development of the United States of America. It was charged with ensuring the capital adequacy and financial safety and soundness of two government sponsored enterprises—the Federal National Mortgage Association (Fannie Mae) and the Federal Home Loan Mortgage Corporation (Freddie Mac). It was established by the Federal Housing Enterprises Financial Safety and Soundness Act of 1992.

OFHEO was managed by a Director, appointed by the President and ratified by the Senate.

## FHFA/OFHEO

The US Federal Housing Finance Agency (formerly Office of Federal Housing Enterprise Oversight a.k.a. OFHEO) publishes the HPI inx, a quarterly broad measure of the movement of single-family house prices.

## Federal Housing Finance Agency (FHFA)

The Federal Housing Finance Agency (FHFA) is an independent federal agency created as the successor regulatory agency resulting from the statutory merger of the Federal Housing Finance Board (FHFB), the Office of Federal Housing Enterprise Oversight (OFHEO), and the U.S. Department of Housing and Urban Development government-sponsored enterprise mission team, absorbing the powers and regulatory authority of both entities, with expanded legal and regulatory authority, including the ability to place government sponsored enterprises (GSEs) into receivership or conservatorship.

In its role as regulator, it regulates Fannie Mae, Freddie Mac, and the 11 Federal Home Loan Banks (FHLBanks, or FHLBank System). It is wholly separate from the Federal Housing Administration, which largely provides mortgage insurance.