SKBI Annual Conferece May 7, 2013 Price Indices: What is Their Value? Susan M. Wachter Richard B. Worley Professor of Financial Management Professor of Real Estate and Finance
Overview I. Why indices? II. Construction Methods III. What is Their Value? Susan M. Wachter 2
Why the Need for Indices? 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? Name of Presenter 3
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 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 Susan M. Wachter 5
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 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) Name of Presenter 9
Construction Methods: Index Types 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 Name of Presenter 10
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 Name of Presenter 11
Comparing Methods Comparisons: Indices: Median Hedonic Case-Shiller repeat sales Autoregressive Predictive power: Hedonic Case-Shiller repeat sales Autoregressive Name of Presenter 12
Disadvantages of Unadjusted Price Indices Composition problems: Seasonal effects No control over types of houses sold each period No quality adjustment Name of Presenter 13
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Hedonic Price Analysis: An Application Example Median Philadelphia House Price 1980-2011 $120,000 $100,000 $80,000 Median Price $60,000 $40,000 $20,000 $0
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Hedonic Price Analysis: An Identification Example Median Philadelphia House Price v. Indexed Philadelphia House Price 1980-2011 $120,000 $100,000 $80,000 Median Price Indexed Price* $60,000 $40,000 $20,000 $0
Hedonic Indices General form: i represents house t represents time period ε it denotes random variation Can use price or log price. Generally fit using regression techniques. Error often modeled as: ε it N(0,σ 2 ) Name of Presenter 16
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. Name of Presenter 17
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 Neighb 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. Name of Presenter 27
Basic Repeat Sale Index Setup i is house t' and t are time periods, t > t (log price it, log price it ) is a sale pair. ε denotes random variation. Assumptions about error terms vary across methods. Name of Presenter 28
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. Name of Presenter 29
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) Name of Presenter 30
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 Name of Presenter 32
Notation for Autoregressive Method Define an adjusted price: effect of hedonic adjusted price it = log price it log time effect t characteristics 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. i Name of Presenter 33
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. Name of Presenter 34
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. Name of Presenter 35
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 Name of Presenter 36
Prediction Results A lower RMSE implies a better fitting model. RMSE for each method: Autoregressive method has the lowest RMSE value. Name of Presenter 37
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 Name of Presenter 38
Indices for Washington DC NAR series shows seasonality clearly here from 1990-2000. Base period is March 31, 2000. Name of Presenter 39
Indices for Phoenix, Arizona Base period is March 31, 2000. Name of Presenter 40
Indices for Chicago, Illinois NAR is constructed from the median price: no smoothing across time periods. Base period is March 31, 2000. Name of Presenter 41
Index Results Name of Presenter 42
Index Results Name of Presenter 43
The Potential of Real Estate Price Indices Name of Presenter 44
Publicly Traded Indices and Hedging Ownership 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 30 th total trading volume in all real estate related futures was 8 (for all 11 contracts combined) Susan M. Wachter 45
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 Name of Presenter 46
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) Name of Presenter 47
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 wachter@wharton.upenn.edu Susan M. Wachter 48