Price Indices: What is Their Value? - Real Estate...

KNOWLEDGE FOR ACTION

SKBI Annual Conferece

May 7, 2013

Susan M. Wachter Richard B. Worley Professor of Financial Management

Professor of Real Estate and Finance

Price Indices: What is

Their Value?


Overview

Susan M. Wachter 2

I. Why indices?

II. Construction Methods

III. What is Their Value?


Why the Need for Indices?

Name of Presenter 3

• How have housing prices changed over time?

–Heterogeneous asset class that does not transact

continuously

–Can extract from, but not the average transaction

price, due to quality and composition issues

• What is the national housing price over time?

• This is the question

–What is the value of real estate/re derivatives in

bank portfolios?

• What is the value of a individual home, what is the

value of a location and locational attributes?


Housing Price Indices: Goals

Dichotomy of goals

Macroeconomic Housing comprises an integral part of the national economy.

Tracking housing indices can paint global picture of the current status and

evolution of the economy, important for bank capital, macro-prudential issues

and for consumer spending and overall economic activity

Microeconomic Paint a local portrait of “affordability” in specific metropolitan areas

Predict price of individual home

Predict neighborhood and locational values

Complete the real estate market?


Real Estate Indices

Susan M. Wachter 5

• Real estate indices aim to provide information about

the overall state of a given market

• In U.S., S&P/Case-Shiller Composite index based on

repeat sales methodology widely used for home prices

– In addition, FHFA produces a similar repeat sales

House Price Index based on GSEs portfolio

• There are a variety of U.S. commercial real estate

indices, commonly cited ones include:

• Green Street’s Commercial Property Price Index

• NCREIF Property Index

KNOWLEDGE FOR ACTION Susan M. Wachter 6


S&P/Case-Shiller Home Price Indices

Name of Presenter 7


Major US Housing Indices

Name of Presenter 8


National vs. Local Indices

Name of Presenter 9

• National index:

– Often a composite of regional indices.

– Does not capture local variation

– Example: Median US house price: $180,176

• highest area is Washington DC: $404,380

• lowest state is Michigan: $96,398

• Local indices:

– Region/state/metropolitan area/neighborhood level

– Need enough data for area to construct a stable index.

– Example: Median house price in state of California: $330,037 Metro

areas within California:

• San Francisco: $550,500

• Sacramento: $192,200

• Los Angeles: $305,500 Data for Q2 2010 from the Federal Housing Finance Agency (US and state) and National Association

For Realtors (city)


Construction Methods: Index Types

Name of Presenter 10

• 3 primary types of real estate valuation methods:

–Mean –Subject to selection bias, conflates quality

–Hedonic – Controls characteristics of a home:

heterogeneity does not disappear

–Repeat sales – Leaves out new buildings

• Emerging tools:

–AR models – make it possible to incorporate first

time sales

– Individual point estimates – provides information

to buyers/sellers/collateral lenders


Issues


• When large enough sample all indexes move

similarly

• In growing markets it is crucial to be able to include

first time sales.

• The major issue remains the lack of transactions in

market segments

• Magnifying the signal


Comparing Methods


Comparisons:

• Indices:

– Median

– Hedonic

– Case-Shiller repeat sales

– Autoregressive

• Predictive power:

– Hedonic

– Case-Shiller repeat sales

– Autoregressive

•


Disadvantages of Unadjusted Price Indices


Composition problems:

• Seasonal effects

• No control over types of houses sold each period

• No quality adjustment


Hedonic Price Analysis: An Application Example

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Median Philadelphia House Price1980-2011

Median Price


Hedonic Price Analysis: An Identification Example

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Median Philadelphia House Price v. Indexed Philadelphia House Price1980-2011

Median Price

Indexed Price*


Hedonic Indices


• General form:

• i represents house

• t represents time period

• εit denotes random variation

• Can use price or log price.

• Generally fit using regression techniques.

• Error often modeled as: εit ∼ N(0,σ2)


Disadvantages of Hedonic Indices


• Data requirements very high, characteristics vary.

• Effect of hedonic characteristics hard to model without rich data.

• Thus do not incorporate changes in hedonic effects over time.


What is Hedonic Price Analysis?

Two (Complementary) Views:

A way of breaking down the total price of a product into the value of its

individual attributes

Total Price = ∑(Prices of individual components)

Useful for developing valuation models

A method of identifying the price of something that is not directly

observable

Breakdown total price into individual prices, in order to isolate the

price of the component you are interested in.

Useful for hypothesis testing


What is Hedonic Price Analysis? Etymology

“Hedonic” is from the Greek word for “pleasure”

“Hedonist”, “Hedonism”

Unpack the total value of something to find the value of the individual

components

Different components give different levels of utility (or pleasure), and hence

consumers have a different willingness-to-pay for different levels of utility.

Consumers place different values on different levels of pleasure


Hedonic Price Analysis: Summary

Hedonic Analysis is a means of “unpacking” the single price of a product into

the market value of its components

Method: Regression of price on characteristics

Uses:

Pricing model of implicit prices;

e.g. house value

Hypothesis testing and isolation of attribute values;

e.g. green amenities

Identification of underlying movements in value;

e.g. removal of “noise” imparted by seasonality, heterogeneity, sample

selection, etc.


Advantages of Hedonic Price Analysis

Useful in building pricing models

Price=f(characteristics)

Allows you to remove heterogeneity , “noise” or other interfering factors that

affect prices and/or price movements; e.g. seasonality, non-standardized

products

When total price is observable, allows you to impute implicit prices of individual

components

Useful when subject good is a “bundled good”

Allows you to isolate and measure the value of the specific component of

interest and facilitates hypothesis testing


How much have house values changed during a

particular period of time?

Challenge: Just examining median (or average) prices over time is problematic,

because house prices are subject to:

Seasonality: house prices (and sales volume) rise in warm weather months

and fall in cold weather months

Heterogeneity: house prices differ due to the fact that housing

characteristics differ

Sample selection bias: homes that do transact may not be representative of

the underlying housing stock


Hedonic Price Analysis: An Application Example

Method: Estimate a hybrid hedonic

Ln(Pi) =α+∑(βi×Ci )+ ∑(φi×ti )

Where:

ti = 1 if house i transacted in time period t, 0 otherwise

t=1,2,…,T time periods that the data spans

Basically, it’s a regression of the log price of a home on its characteristics

and location (control vars), and a vector of dummy variables denoting

when each home sold.

Data: Home sales in Philadelphia, 2009-2011


Hedonic Price Analysis: A Modeling Example Variable Est. Coeff. Std. Error t Value Pr > |t| Variable

Est. Coeff.

Std. Error t Value Pr > |t|

Intercept 7.95352 0.30358 26.2 <.0001 oneh_story -0.00626 0.04026 -0.16 0.8765 ln_lotsqft -0.01187 0.0392 -0.3 0.762 two_story -0.03475 0.02213 -1.57 0.1165 ln_bsqft 0.59666 0.05054 11.81 <.0001 twoh_story -0.08904 0.05349 -1.66 0.096 FAR -0.28545 0.05818 -4.91 <.0001 three_story 0.02983 0.04309 0.69 0.4888 ratio_frt_sqft -4.24259 2.88234 -1.47 0.1411 threeplus_story 0.16843 0.12007 1.4 0.1608 one_fire 0.03551 0.03616 0.98 0.3262 apt_house 0.10195 0.03678 2.77 0.0056 two_fire 0.18997 0.1114 1.71 0.0882 detached 0.32581 0.04943 7.52 0.6016 threepl_fire 0.16137 0.21616 0.75 0.4554 row_house -0.07013 0.04285 -1.64 0.1018 ln_dist_cbd 0.0713 0.01758 4.06 <.0001 age -0.00403 0.00107 -3.76 <.0001 corner_dum 0.023 0.02111 1.09 0.276 abate_imprvd 0.27471 0.02404 11.35 <.0001 cond_superior 0.20979 0.04344 4.83 <.0001 abate_new 0.09075 0.09654 0.94 0.3472 cond_above_avg 0.15394 0.03742 4.11 <.0001 spring 0.03563 0.01101 3.23 0.0012 cond_below_avg -0.20709 0.04628 -4.47 <.0001 summer 0.06043 0.01297 4.66 <.0001 cond_inferior -0.28615 0.06774 -4.22 <.0001 repsale1 0.25156 0.01714 14.68 <.0001 central_air 0.06891 0.01744 3.95 <.0001 repsale2 0.09562 0.01378 6.94 <.0001 rental -0.07672 0.01347 -5.7 <.0001 repsale3 0.08425 0.01391 6.06 <.0001 garage 0.08735 0.01608 5.43 <.0001 repsale4 0.05293 0.013 4.07 <.0001 frame 0.00951 0.03408 0.28 0.7803 Census Dummies? Yes

masother 0.11355 0.01899 5.98 <.0001 Time Dummies? Yes stone 0.474562 0.0467 10.16 <.0001

N=5,516 home sales in Philadelphia in 2011 Q1,Q2 Dep. Var. = Ln(Price), R-Sq.= 78%


Hedonic Price Analysis: A Hypothesis Example

Question: Do “Green” Amenities affect house values?

Before After


Hedonic Price Analysis: A Hypothesis Example

Source: Susan M. Wachter, Kevin C. Gillen, and Carolyn R. Brown, "Green Investment Strategies: How They Help Urban Neighborhoods" in Susan Wachter and Genie Birch, eds., Growing Greener Cities (Philadelphia: University of Pennsylvania Press). 2008.


Repeat Sale Indices


• Compare prices of two sales of the same house.

• Directly measure change in prices.

• Previous price proxy for hedonic effects.


Basic Repeat Sale Index Setup


• i is house

• t' and t are time periods, t’ > t

• (log priceit, log priceit’) is a sale pair.

• ε denotes random variation.

• Assumptions about error terms vary across methods.


Disadvantages of Repeat Sale Indices


• Over a period of time, housing sales falls into one of four

categories:

• Repeat sales indices should use only the last type of house.

• Result: most home sales ignored.


Summary


Each index has advantages and disadvantages:

• Mean: data skewed, composition problems (as does median)

• Hedonic: data requirement high, functional form

• Repeat sales: large amount of data ignored (bias)


AUTOREGRESSIVE HOUSE PRICE

INDEX METHODOLOGY

Joint work with Chaitra H. Nagaraja

(Fordham University) and Larry Brown (The

Wharton School, University of Pennsylvania


Autoregressive Method


• Repeat sales methods organize data in sale pairs.

• Autoregressive model considers all sales of the same house

as components of one series

– in theory, house has a price at each time period

– price observed only when sold


Notation for Autoregressive Method


• Define an adjusted price:

𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 = log 𝑝𝑟𝑖𝑐𝑒𝑖𝑡 − log 𝑡𝑖𝑚𝑒 𝑒𝑓𝑓𝑒𝑐𝑡𝑡 −𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 ℎ𝑒𝑑𝑜𝑛𝑖𝑐

𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐𝑠𝑖

• AR(1): autoregressive process of order 1 where current value

depends on previous value through parameter φ

• Adjusted price follows an underlying, stationary AR(1) process

• Method is a version of this process which accounts for the gap

time between sales.


Autoregressive Models Applied to Data


• Additional hedonic variables modeled but did not result in

improvements in predictions.

• ZIP code as a proxy for location along with previous sale price may

be sufficient for this model.

• Autoregressive model with hedonics is similar in spirit to a repeat

sales hybrid method (Case and Quigley 1991)

• We examine results for the autoregressive model with ZIP code

here.


Assessing the Quality of the Index Methods


• Investigate accuracy of the methods’ price predictions

• Divide data into two parts:

– training data: fit model on these sales

– validation data: apply model to these sales to obtain predicted

prices.

• Validation data assembled from a selection of final sales from

repeat sales homes.

• Examining results on unused validation data allows for a fairer

comparison of methods and avoids overfitting of data.


RMSE = Root Mean Squared Error


• Measure the quality of a model by:

• m: number of sale prices predicted

• predicted price = exp(predicted log price)

• Compute RMSE on the validation data

• Compare values across index methods


Prediction Results


• A lower RMSE implies a better fitting model.

• RMSE for each method:

• Autoregressive method has the lowest RMSE value.


Prediction: RMSE Results for 20 Metropolitan Areas


• Study of 20 US

metropolitan areas

• Lower RMSE value

in red

• Autoregressive

method has lower

RMSE for all areas


Indices for Washington DC


• NAR series shows seasonality clearly here from 1990-2000.

Base period is March 31, 2000.


Indices for Phoenix, Arizona




Indices for Chicago, Illinois


• NAR is constructed from the median price: no smoothing across

time periods.



Index Results



The Potential of Real Estate Price Indices



Publicly Traded Indices and Hedging Ownership

Susan M. Wachter 45

• Publicly traded indicesto allow hedging of real estate

positions

– can create “shorting” and hedging options

• The only index that can be publicly traded in the U.S. is

the Case-Shiller index on the CME

• Sub-indices exist for a handful of cities

• On April 30th total trading volume in all real estate

related futures was 8 (for all 11 contracts combined)


Use of Indices for Macro Prudential Policy


• Basel III: Compliance of financial sector to capital

requirement

• Real Estate bubbles matter because it is not just

optimists who will go away in the bust but the entire

financial system since large exposure to real estate and

underwriting based on estimated market value

• Appraisal use market values , which ratifies the optimist

values.

• Also as showed with Herring and Wachter (2002), banks

tend to increase their portfolio exposure because they

suffer of the same expectation biases


Valuing Real Estate and Real Estate Collateralized

Portfolios over the Cycle for Liquidity


• Accurate information about real estate value in

theory could prevent liquidity episodes

• Market prices used by financial institutions in

providing credit for real estate transactions

• But indexes reflect these, need additional

information on capital market pricing and real

estate fundamentals (Pavlov/Wachter, 2013)

KNOWLEDGE FOR ACTION Susan M. Wachter 48

Thank you

Susan M. Wachter

Richard B. Worley Professor of Financial Management

Professor of Real Estate and Finance

Co-Director - Institute for Urban Research

The Wharton School, University of Pennsylvania

Tel: 215-898-6355

Cell: 610-299-9714

[email protected]

tel:215-898-6355

tel:215-898-6355

tel:215-898-6355

tel:215-898-6355

tel:215-898-6355

tel:610-299-9714

tel:610-299-9714

tel:610-299-9714

tel:610-299-9714

tel:610-299-9714

http://[email protected]/

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