Predictability of Downturns in Housing Markets: A Complex Systems Approach Maximilian Brauers Wiesbaden, 15 June 2012

Inflation-Adjusted Regional US House Price Indices 2 Introduction Is it possible to predict crashes in housing markets such as in 2007?

Is it possible to predict crashes in housing markets such as in 2007? A model originating in the field of statistical physics is claiming to be able to predict such downturns in financial markets (Johansen and Sornette, 2010). We test the model’s validity, predictive power and its success rate on 20 years of housing price data for nine regional sub-markets of the U.S. housing market. We propose a new model restriction to remedy estimation issues due to the low frequency of housing price data. This restriction constitutes a new test for exponential price growth against a power law growth in low frequency datasets. 3 Introduction

First proposal: for a connection between crashes in FTS and critical points was made by Sornette et al. (1996) applied to Oct Crash in Physika France. Confirmed independently: by Feigenbaum & Freund (1996) for 1929/1987 on arXiv.org (Cornell University), Sornette & Johansen (1997) Physika A, Johansen Sornette, (1999) Risk, Johansen, Ledoit, Sornette, (2000) Int J. of Theory and applied Finance rejected 2nd round RFS, Sornette & Zhou (2006), International Journal of Forecast (With a review on the link between herding and statistical physics models). Further independent tests on Stock Markets: : Vandewalle et al., (1998) Physica B; Feigenbaum and Freund, (1998), Intern. J. of Modern Ph.; Gluzman and Yukalov (1998) arXiv.org; Laloux et al., 1998, Euro Physics Letter; Bree (2010), DP. Noise and Estimation Issues: Feigenbaum (2001) QF; Bothmer et al. (2003) Physika A; Chang & Feigenbaum (2006) QF; Lin et al. (2009) WPS; Gazola et al. (2008) The European Physical Journal B, (Computational Issues: Liberatori, 2010 QF). Recent Summary on state of the art: Zhi, Sornette et al 2009 QF auf arXIV.org 4 Introduction

5 Foto- Fläche Exogen Endogen Downturns Introduction

6 Theoretical Background

7

Macro-Level: K ≡ strength of imitation, average over K i ’s K c ≡ critical size of K, i.e. point with highest probability for a crash K < K c ⟹ disorder rules on the market, i.e. agents do not agree with each other K ⟶ K c ⟹ order starts appearing, i.e. agents do agree with each other. At this point K c, the system is extremely unstable and sensitive to any new information. ⟹ THE HAZARD RATE OF A CRASH DEPENDS ON K 8

Theoretical Background 9

10

Theoretical Background 11

Theoretical Background Mathematical Formalization: Power Law Function Hierarchical Structures Discrete Scale Invariance 12 Economic Theory: Rational Expectations No Arbitrage Condition Herding Behavior Positive Feedback Synopsis / Intuitive summary of the Model: Imitation leads to herding and herding to positive feedback. The positive feedback can be detected as super-exponential growth in the price, i.e. a self reinforcing trend. This trend is corrected by log periodic oscillations due to the market structure. i.e. the way and strength of individual participants on each other.

Methodology 13

Methodology Behavior of Objective Function: 14

Methodology Original Parameter Restrictions 15

New Restriction Our restriction constitutes a null hypothesis for testing against the LPPL model in low frequency price series. We take the first log differences in the house price series and test with the KPSS test without trend for stationarity. If we cannot reject stationarity in the first log differences, we cannot reject the null hypothesis of exponential growth in the price trajectory and, therefore, we must reject the power law and LPPL fit. We choose the KPSS test as it offers the highest power for testing against I(0) within a time series. 16 Methodology

Data HPI provided by the Federal Housing Agency: Weighted repeat sales index in order to qualify as constant quality index. Purchase only. Obtained from repeat mortgage transaction securitized by Fannie Mae or Freddie Mac since January 1975 As of December 1995 there were over 6.9 million repeat transactions in the national sample Inflation-adjusted 17

Data 18 Housing Market Crashes in US Census Divisions

Results Windows of Best Fits 19

Results Out-of-Sample Predictions of Downturns 20

Results 21