Unsmoothing Real Estate Returns: A Regime Switching Approach

1. 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

2. 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)

3. The Index Issue … • FT Returns m 2.02% s 8.58% rt,t-1 0.014 • IPD Returns m 2.15% s 3.25% rt,t-1 0.813

4. Smoothing and Underlying Return Process • Basic Smoothing Model • Return Process • Note the Time Subscripts …

5. 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

6. 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

7. AR-TAR

8. AR-TAR: FT Returns Regimes

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

10. 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)

11. TAR-TAR Model • Focus on FT and LIBOR regimes • All bar LIBOR-FT models improve SSE • Best Model FT-FT • All Coefficients Save f1 significant

12. 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

13. TAR-TAR: FT Regimes Returns Regime: C1 = -1.2% Smoothing Regime: C2 = -13.2%

14. TAR-TAR: Model Fits

15. TAR-TAR versus a = 0.8

16. Descriptive Statistics

17. TAR-TAR versus a = 0.8 Correlation = 0.92

18. 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