Price Indices: What is Their Value?

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1 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

2 Overview I. Why indices? II. Construction Methods III. What is Their Value? Susan M. Wachter 2

3 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

4 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?

5 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

6 Susan M. Wachter 6

7 S&P/Case-Shiller Home Price Indices Name of Presenter 7

8 Major US Housing Indices Name of Presenter 8

9 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 Q from the Federal Housing Finance Agency (US and state) and National Association For Realtors (city) Name of Presenter 9

10 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

11 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

12 Comparing Methods Comparisons: Indices: Median Hedonic Case-Shiller repeat sales Autoregressive Predictive power: Hedonic Case-Shiller repeat sales Autoregressive Name of Presenter 12

13 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

14 Hedonic Price Analysis: An Application Example Median Philadelphia House Price $120,000 $100,000 $80,000 Median Price $60,000 $40,000 $20,000 $0

15 Hedonic Price Analysis: An Identification Example Median Philadelphia House Price v. Indexed Philadelphia House Price $120,000 $100,000 $80,000 Median Price Indexed Price* $60,000 $40,000 $20,000 $0

16 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

17 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

18 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

19 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

20 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.

21 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

22 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

23 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,

24 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 <.0001 oneh_story ln_lotsqft two_story ln_bsqft <.0001 twoh_story FAR <.0001 three_story ratio_frt_sqft threeplus_story one_fire apt_house two_fire detached threepl_fire row_house ln_dist_cbd <.0001 age <.0001 corner_dum abate_imprvd <.0001 cond_superior <.0001 abate_new cond_above_avg <.0001 spring cond_below_avg <.0001 summer <.0001 cond_inferior <.0001 repsale <.0001 central_air <.0001 repsale <.0001 rental <.0001 repsale <.0001 garage <.0001 repsale <.0001 frame Census Dummies? Yes masother <.0001 Time Dummies? Yes stone <.0001 N=5,516 home sales in Philadelphia in 2011 Q1,Q2 Dep. Var. = Ln(Price), R-Sq.= 78%

25 Hedonic Price Analysis: A Hypothesis Example Question: Do Green Amenities affect house values? Before After

26 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)

27 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

28 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

29 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

30 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

31 AUTOREGRESSIVE HOUSE PRICE INDEX METHODOLOGY Joint work with Chaitra H. Nagaraja (Fordham University) and Larry Brown (The Wharton School, University of Pennsylvania

32 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

33 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

34 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

35 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

36 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

37 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

38 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

39 Indices for Washington DC NAR series shows seasonality clearly here from Base period is March 31, Name of Presenter 39

40 Indices for Phoenix, Arizona Base period is March 31, Name of Presenter 40

41 Indices for Chicago, Illinois NAR is constructed from the median price: no smoothing across time periods. Base period is March 31, Name of Presenter 41

42 Index Results Name of Presenter 42

43 Index Results Name of Presenter 43

44 The Potential of Real Estate Price Indices Name of Presenter 44

45 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

46 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

47 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

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: Cell: wachter@wharton.upenn.edu Susan M. Wachter 48

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