Unsmoothing Real Estate Returns: A Regime Switching Approach Colin Lizieri, Stephen Satchell and Warapong Wonwachara Department of Land Economy / Department of Economics University of Cambridge European Real Estate Society Conference Milano May 2010

Not Another Paper on Smoothing?  Many studies analysing impact of appraisal process on valuation-based real estate indices  Standard method assumes time-invariant process  Can we maintain this assumption?  Transaction-based indices and adjustment for liquidity  Tail dependence and behaviour in bubbles / crashes  Intuition here: may be a regime-based structure  For returns process (Lizieri et al., Brooks & Maitland-Smith)  For smoothing process (Chaplin, informal model)

The Index Issue …  FT Returns  2.02%  8.58%  t,t  IPD Returns  2.15%  3.25%  t,t

Smoothing and Underlying Return Process  Basic Smoothing Model  Return Process  Note the Time Subscripts …

Possible Models  AR Model  AR return process, single smoothing parameter  AR-TAR Model  Regime-based return, single smoothing process  TAR-AR  Regime-based smoothing, single return process  TAR-TAR  Regime-based smoothing and return processes

Defining Regimes and Modelling  Regime Variables Tested  Macro: GDP, Employment, Inflation, £/$  Asset & Cap Market: Equity Market, Interest Rate  Endogenous: Cap Rate  Analysis Quarterly, 1987Q1 – 2008Q4  Recursively Estimate and Minimise SSE  Best Regime Models: AR-TAR  FT Returns, LIBOR  Best Regime Model: TAR-TAR  FT Returns for Both Processes

AR-TAR

AR-TAR: FT Returns Regimes

AR-TAR versus AR: Fits  The AR model appears too volatile – particularly across 2008  The AR-TAR model generates more plausible results

AR-TAR versus AR: Fits  The AR model appears too volatile – particularly across 2008  The AR-TAR model generates more plausible results  Still seems rather smoothed …  Standard deviation compared to IPD 4.8% (3.1%)  Serial correlation 0.51 (0.81)

TAR-TAR Model  Focus on FT and LIBOR regimes  All bar LIBOR-FT models improve SSE  Best Model FT-FT  All Coefficients Save  1 significant

TAR-TAR (FT Model)  Return Processes Differ:  FT Returns > -1.2% steady growth  FT Returns < -1.2% negative, explosive autoreg.  Implies very sharply falling underlying returns  Low regime occurs 26% of time  Regime not persistent …  Smoothing Processes Differ:  FT Returns < -13% very strong smoothing  Information story?  This state occurs 7% of time  Smoothing parameter lower in other regime

TAR-TAR: FT Regimes Returns Regime: C 1 = -1.2% Smoothing Regime: C 2 = -13.2%

TAR-TAR: Model Fits

TAR-TAR versus  = 0.8

Descriptive Statistics IPD Returns TAR-TAR  = 0.8 Mean Mean Median Median Maximum Maximum Minimum Minimum Std. Dev. Std. Dev Skewness Skewness Kurtosis Kurtosis Serial Correlation Observations Observations

TAR-TAR versus  = 0.8 Correlation = 0.92

Summary and Conclusions  Aim: Extend Standard Desmoothing Model  Take account of underlying return process  Sensitive to asymmetries in return behaviour  Sensitive to time-varying smoothing behaviour  Approach Taken: TAR Models  Behaviour based on indicator variable(s)  Relatively simple to calculate and model  AR-TAR and TAR-TAR outperform AR  Best: TAR-TAR Model Based on FT  Implications for Understanding of Risk  Implications for Portfolio Strategy