Volatility Spillovers between U.S. Home Price Tiers. Tiers during the Housing Bubble

Transcription

1 Inroducion Daa The dynamic correlaion-coefficien model Volailiy Spillovers beween U.S. Home Price Tiers during he Housing Bubble Damian Damianov Deparmen of Economics and Finance The Universiy of Texas - Pan American Deparmen of Economics and Finance Durham Universiy Texas A&M Universiy Ocober, 2014 Volailiy Spillovers beween U.S. Home Price Tiers

2 Ouline Inroducion Daa The dynamic correlaion-coefficien model 1 Inroducion Conribuion and inuiion of he curren paper 2 Daa Daa 3 The dynamic correlaion-coefficien model Mean and Variance Equaions Dynamic Correlaion Esimaes 4 Dynamic Correlaions and he Bubble Burs Panel Esimaion of he Effec of he Bubble Burs Panel Esimaes 5 Volailiy Spillovers beween U.S. Home Price Tiers

3 Inroducion Daa The dynamic correlaion-coefficien model Conribuion and inuiion Conribuion and inuiion of he curren paper Analyze he volailiy ransmission beween hree S&P Case Shiller iered price indices for 12 MA. Use DCC-GARCH specificaion. Imporance: Volailiy of reurns in a major facor affecing porfolio performance of morgage lenders and morgage insurers. Heerogeneiy wihin MAs. Correlaion esimaes are major inpus in porfolio allocaion. Exisence of morgage backed securiies. Implicaions for Real Esae Invesmen Truss (REIT). Home owners. Findings: Dynamic correlaions across iers are posiive and persisen. The housing bubble burs increases he dynamic correlaions. There is a conagion effec afer he bubble burs as prices are driven by morgage defauls and increased supply. The burs limied he effeciveness of porfolio diversificaion. Volailiy Spillovers beween U.S. Home Price Tiers

4 Inroducion Daa The dynamic correlaion-coefficien model Conribuion and inuiion Conribuion and inuiion of he curren paper Figure: Bubble in Home Prices Low and High Price Tiers Miami 2007m m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1-3 Reurns Low Tier High Tier Bubble in housing prices. Dynamic correlaion beween reurns. Volailiy Spillovers beween U.S. Home Price Tiers

5 Daa Inroducion Daa The dynamic correlaion-coefficien model Daa Three iers (Low, Medium, and High). Twelve MAs (Cleveland, Denver, Las Vegas, Miami, Minneapolis, New York, Phoenix, Porland, San Francisco, Seale, Tampa, Washingon DC). From January 1987 hrough March S&P Case Shiller mehodology consrucs he indices as hree monh moving averages. Volailiy Spillovers beween U.S. Home Price Tiers

6 Inroducion Daa The dynamic correlaion-coefficien model Formulaion for he Price Tiers Mean and Variance Equaions Dynamic Correlaion Esimaes Mulivariae GARCH in Engle (2002) o esimae he DCC beween he reurns of differen price iers. Price Tier i for Tier = (Low, Mid, High). Three advanages: Robus o heeroscedasiciy. Mean equaion can include addiional regressors. Allows including muliple reurns wihou including oo many coefficiens. The mean equaion is modeled as: Re = δ 0 + δ 1 Re 1 + δ 2 Re S&P500 1 Where Re = (Re Low and ε Ω 1 N(0, H )., Re Mid, Re High + ε ), ε = (ε Low, ε Mid, ε High ), Volailiy Spillovers beween U.S. Home Price Tiers

7 Inroducion Daa The dynamic correlaion-coefficien model Condiional Variance Mean and Variance Equaions Dynamic Correlaion Esimaes The condiional variance is modeled as: H = D R D, R is he correlaion marix of ineres and D is a diagonal marix. The elemens in D are h Tier wih Tier = (Low, Mid, High). Two-sage approach o esimae he covariance H : 1 Ge esimaes of h Tier by fiing univariae volailiy models. 2 Transforms he residuals from sage (1) u Tier = ε Tier / h Tier, hen esimaes he parameers of he condiional correlaion using u Tier. The evoluion of he correlaion is modeled as: Q = (1 α β) Q + αu 1 u 1 + βq 1 Where α and β and (α + β) < 1. Q = E[u u ]: uncondiional variance-covariance marix of u. Q : ime-varying condiional variance-covariance marix of u. Volailiy Spillovers beween U.S. Home Price Tiers

8 Inroducion Daa The dynamic correlaion-coefficien model Condiional Variance Mean and Variance Equaions Dynamic Correlaion Esimaes Rescale Q o obain he correlaion marix: ( 1 R = diag, q Low 1 q Mid, 1 q High ) ( 1 Q diag q Low 1,, q Mid 1 q High Where q Tier are he main diagonal elemens of Q. The off-diagonal elemen of R will have he form (dropping High): ) ρ Low-Mid = (1 α β) q Low-Mid + αu Low 1 umid 1 + βqlow-mid 1 (1 α β) q Low + α(u 1 Low)2 + βq 1 Low (1 α β) q Mid + α(u Mid 1 )2 + βq Mid 1 Where q Low-Mid and Q. and q Low-Mid are he single off-diagonal elemens of Q Volailiy Spillovers beween U.S. Home Price Tiers

9 Inroducion Daa The dynamic correlaion-coefficien model Log-likelihood Funcion Mean and Variance Equaions Dynamic Correlaion Esimaes The log-likelihood funcion o be maximized: l (γ, δ) = T 1 T =1 ( 3 log(2π) + logd 2 + ε D 2 ε ) ( logr + u R 1 u u u ) γ and δ are he coefficiens o be esimaed in D and R. Volailiy Spillovers beween U.S. Home Price Tiers

10 Table: Esimaion Resuls for hree DCC-GARCH Models (1) (2) (3) (4) (5) (6) (7) (8) Mero Areas: Denver Miami Tiers: Low Mid High S&P500 Low Mid High S&P500 Mean Equaions: δ *** 0.241*** 0.211*** 0.571** 0.237*** 0.165*** 0.186*** 0.678*** (0.0483) (0.0353) (0.0330) (0.231) (0.0549) (0.0360) (0.0391) (0.229) δ *** 0.488*** 0.518*** *** 0.681*** 0.619*** (0.0439) (0.0446) (0.0421) (0.0669) (0.0548) (0.0457) (0.0491) (0.0669) δ ( ) ( ) ( ) ( ) ( ) ( ) Variance Equaions: c * ** ** ** ** ( ) ( ) ( ) (0.764) (0.0122) (0.0407) (0.0151) (1.093) a 0.131*** 0.125*** *** 0.141** 0.167*** 0.289*** 0.133*** 0.154** (0.0397) (0.0356) (0.0313) (0.0620) (0.0444) (0.0940) (0.0410) (0.0769) b 0.859*** 0.861*** 0.882*** 0.821*** 0.811*** 0.504*** 0.790*** 0.803*** (0.0394) (0.0333) (0.0383) (0.0674) (0.0439) (0.154) (0.0616) (0.0943) Mulivariae DCC Equaion: α *** *** (0.0162) (0.0249) β 0.836*** 0.639*** (0.0436) (0.103) Observaions χ χ 2 (p-value) 0 0 Noes: The figures in parenheses are sandard errors. * significan a 10%; ** significan a 5%; *** significan a 1%. For each meropolian area he reurn equaions are: Re = δ 0 + δ 1 Re 1 + δ 2 Re S&P ε, wih Re = (Re Low, Re Mid, Re High ), ε = (ε Low, ε Mid, ε High ), and ε Ω 1 N(0, H ). The variance equaions: h Tier = c Tier + a Tier h Tier 1 + btier (ε Tier 1 )2 for Tier = (Low, Mid, High).

11 Inroducion Daa The dynamic correlaion-coefficien model Mean and Variance Equaions Dynamic Correlaion Esimaes Dynamic Correlaions and he Bubble Burs Figure: Dynamic Correlaions for Cleveland and Washingon DC Cleveland Washingon DC Corr(High, Mid) Corr(High, Mid) m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 Corr(High, Low) Corr(High, Low) m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 Corr(Mid, Low) Corr(Mid, Low) m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 Volailiy Spillovers beween U.S. Home Price Tiers

12 Inroducion Daa The dynamic correlaion-coefficien model Dynamic Correlaions and he Bubble Burs Panel Esimaion of he Effec of he Bubble Burs Panel Esimaes Dynamic Correlaions and he Bubble Burs Figure: Dynamic Correlaions Panel Aggregaes (wih 95% C.I.) Dynamic Correlaion m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 Volailiy Spillovers beween U.S. Home Price Tiers

13 Inroducion Daa The dynamic correlaion-coefficien model Dynamic Correlaions and he Bubble Burs Panel Esimaion of he Effec of he Bubble Burs Panel Esimaes Panel Esimaion of he Effec of he Bubble Burs Model he effec of he bubble burs on he dynamic correlaion: i denoing he MA. ρ j -k i = γρ j -k i, 1 + θz i + η i + ν j -k i j and k denoe iers, (j, k) = (Low, Mid, High) for j k. We model he bubble burs Z i as poenially endogenous: } E(Z is ν j -k i ) = 0, s < E(Z is ν j -k i ) 0, s, i. Assume ν j-k i is serially uncorrelaed. Use momen condiions: E( ν j-k i W) and E[(η i + ν j-k i )M]. Tes he validiy of he insumen lis: W and M. Volailiy Spillovers beween U.S. Home Price Tiers

14 Regression Esimaes Table: Panel Daa Resuls. Wihin Tiers. Dep. Variable: (1) (2) (3) (4) (5) (6) (7) (8) ρ High-Low i ρ High-Mid i ρ Mid-Low i All VARIABLES Pooled FE Pooled FE Pooled FE Pooled FE Bubble Burs *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Cleveland 0.182*** 0.207*** 0.183*** 0.191*** ( ) ( ) ( ) ( ) Denver 0.411*** 0.466*** 0.516*** 0.464*** ( ) ( ) ( ) ( ) Las Vegas 0.185*** 0.395*** 0.282*** 0.287*** ( ) ( ) ( ) ( ) Miami 0.417*** 0.469*** 0.470*** 0.452*** ( ) ( ) ( ) ( ) Minneapolis 0.583*** 0.715*** 0.701*** 0.666*** ( ) ( ) ( ) ( ) New York 0.360*** 0.407*** 0.256*** 0.341*** ( ) ( ) ( ) ( ) Phoenix 0.402*** 0.488*** 0.549*** 0.480*** ( ) ( ) ( ) ( ) Porland 0.382*** 0.457*** 0.364*** 0.401*** ( ) ( ) ( ) ( ) San Francisco 0.422*** 0.524*** 0.490*** 0.479*** ( ) ( ) ( ) ( ) Seale 0.368*** 0.511*** 0.350*** 0.410*** ( ) ( ) ( ) ( ) Tampa 0.271*** 0.373*** 0.358*** 0.334*** ( ) ( ) ( ) ( ) Washingon DC 0.275*** 0.443*** 0.489*** 0.402*** ( ) ( ) ( ) ( ) Consan 0.358*** 0.454*** 0.418*** 0.410*** ( ) ( ) ( ) ( ) Observaions 7,206 7,206 7,206 7,206 7,206 7,206 21,618 21,618 R-squared Noes: The figures in parenheses are sandard errors. * significan a 10%; ** significan a 5%; *** significan a 1%.

15 Inroducion Daa The dynamic correlaion-coefficien model Dynamic Correlaions and he Bubble Burs Panel Esimaion of he Effec of he Bubble Burs Panel Esimaes Dynamic Panel Daa Resuls. Wihin Tiers. Table: Panel Daa Resuls. Wihin Tiers. Dep. Variable: (1) (2) (3) (4) ρ High-Low i ρ High-Mid i ρ Mid-Low i All Lagged Dep. Variable 0.792*** 0.784*** 0.787*** 0.775*** (0.0130) (0.0126) (0.0149) ( ) Bubble Burs *** *** *** *** ( ) ( ) ( ) ( ) Observaions Insrumens Serial Correlaion a Serial Correlaion (p-value) Hansen b Hansen (p-value) Noes: Figures in parenheses are he Windmeijer finie-sample correced sandard errors of he GMM wo-sep esimaes. * significan a 10%; ** significan a 5%; *** significan a 1%. a The null hypohesis is ha he errors in he firs-difference regression exhibi no second-order serial correlaion (valid specificaion). b The null hypohesis is ha he insrumens are no correlaed wih he residuals (valid specificaion). Passes he serial correlaion es. Hansen validaes he insrumen lis W and M. Volailiy Spillovers beween U.S. Home Price Tiers

16 Inroducion Daa The dynamic correlaion-coefficien model Mehods accoun for auocorrelaions, momenum, is parsimonious, allows including oher facors. Accoun for poenial endogeneiy in he burs. Higher dynamic correlaion afer he bubble burs. Lower opporuniies for diversificaion. Our findings are consisen wih oher markes (e.g., inernaional equiy markes) when we observe higher dynamic correlaions in (1) periods of high volailiy, (2) during bear markes, and (3) during financial crises. Sugges some direcions for fuure research. Asymmeric correlaions in bull and bear markes. VaR applicaion and examine correlaions in he ail of he disribuion. Volailiy Spillovers beween U.S. Home Price Tiers

17 Saa GARCH-DCC Example clear use hp:// mgarch dcc (oyoa nissan honda = L.oyoa L.nissan L.honda, noconsan), arch(1) garch(1) Calculaing saring values... Opimizing log likelihood (seing echnique o bhhh) Ieraion 0: log likelihood = Ieraion 17: log likelihood = Refining esimaes Ieraion 0: log likelihood = Ieraion 1: log likelihood =

18 Saa GARCH-DCC Example Dynamic condiional correlaion MGARCH model Sample: Number of obs = 2014 Disribuion: Gaussian Wald chi2(9) = Log likelihood = Prob > chi2 = Coef. Sd. Err. z P>z [95% Conf. Inerval] oyoa oyoa L nissan L honda L ARCH_oyoa arch L garch L _cons 4.47e e e e nissan oyoa L nissan L honda L ARCH_nissan arch L garch L _cons 7.21e e e honda oyoa L nissan L honda L ARCH_honda arch L garch L _cons 5.35e e e e corr(oyoa,nissan) corr(oyoa,honda) corr(nissan,honda) Adjusmen lambda lambda

19 Saa GARCH-DCC Example predic r2*, res predic h2*, variance gen pnissanoyoa = h2_nissan_oyoa/(sqr(h2_nissan_nissan)*sqr(h2_oyoa_oyoa)) gen phondaoyoa gen phondanissan = h2_honda_oyoa/(sqr(h2_honda_honda)*sqr(h2_oyoa_oyoa)) = h2_honda_nissan/(sqr(h2_honda_honda)*sqr(h2_nissan_nissan)) sline pnissanoyoa, scheme(sj) yile("corr(nissan,toyoa)") xile("") saving(nissanoyoa, replace) sline phondaoyoa, scheme(sj) yile("corr(honda,toyoa)") xile("") saving(hondaoyoa, replace) sline phondanissan, scheme(sj) yile("corr(honda,nissan)") xile("") saving(hondanissan, replace) sline pnissanoyoa phondaoyoa phondanissan, scheme(sj) yile("dynamic Correlaions") xile("") \\\ saving(dynamiccorrelaions, replace) gr combine nissanoyoa.gph hondaoyoa.gph hondanissan.gph dynamiccorrelaions.gph, scheme(sj) col(2) \\\ iscale (0.5) fysize(100) ile( "Dynamic Correlaions" )

20 Inroducion Daa The dynamic correlaion-coefficien model Saa GARCH-DCC Example Figure: Dynamic Correlaions Dynamic Correlaions Corr(Nissan,Toyoa) Corr(Honda,Toyoa) Corr(Honda,Nissan) Dynamic Correlaions pnissanoyoa phondaoyoa phondanissan Volailiy Spillovers beween U.S. Home Price Tiers