Conditional Correlations of Macro Variables and Implications for Asset Prices

1. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Conditional Correlations of Macro Variables and Implications for AssetPrices ApoorvaJavadekar1 JointWith RuiAlbuquerque2 March 10,2013 1 Boston University, Department of Economics 2 School of Management, BostonUniversity Albuquerque &Javadekar

2. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Broad Questions Understanding the structure of the Cross Country Correlation for MacroVariables: Do macro variables across countries co move more strongly during certain times than other? More precisely: Do cross country correlations are conditionally asymmetric? Asset Pricing and Risk SharingImplications How does regime switching or jumps in fundamental macro variables affect asset prices? In particular: Does asymmetric correlations in output translate in to asymmetric correlations for stock returns? What are the implications for Risk Sharing arrangements? Can current macro models explain these type of conditional asymmetries in MacroVariables? 1 2 3 Albuquerque &Javadekar

3. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Basics: ExceedenceCorrelation Consider a joint stochastic processes: {Xt, Yt} with E (Xt )= E (Yt ) =0 and unit variance. Exceedence Correlation at levelc: 1 2 .ρ(X,Y|X>c,Y>c) if c ≥0 ρ(X,Y|X<c,Y<c) if c ≤0 ρˆ(X,Y;c)= (1) For normal distribution ρ(X, Y |X > c, Y > c ) = ρ(X,Y|X<−c,Y<−c)foreveryc⇒Symmetric Exceedences 3 Albuquerque &Javadekar

4. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Output Growth: SimpleStatistics Table :Evidence on Asymmetries in Output Correlations 3 3 Source: Monthly Data from OECD Library for G7: Growth Rates are annualized and data is measured at Monthly frequencies Albuquerque &Javadekar

5. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Output Co movement: Drop at Zero! Figure :Exceedence Correlations - AgainstOECD Albuquerque &Javadekar

6. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Asymmetries in Output Correlations: Drop at Zero! Figure :Exceedence Correlations - AgainstGermany Albuquerque &Javadekar

7. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Asymmetries in Output Correlations: Drop at Zero! Figure :Exceedence Correlations - AgainstUSA Albuquerque &Javadekar

8. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Some RobustnessChecks Formal Hypothesis testing using Zhou, Tu and Hong Test of asymmetry(2007) Data filtering using growth and HP filter Time Aggregation: Quarterly vs Monthly Conditioning on single country being a threshold instead of both Justification for Industrial Production as a proxy for Output: (See Dumas et al.2003) GDP and IP highly correlated IP data available at monthly frequency: Trade off between low frequency movements vs having more observations for conditioning Behavior in recessions is similar (exception in2001) 1 2 3 4 5 Albuquerque &Javadekar

9. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Consumption Risk Sharing: QuickExercise Consider Brandt, Cochrane and Santa Clara Index of Risk Sharing 1 d σ2(lnmf −lnm) t+1 t+1 RSt = 1− (2) σ2(lnmf)+σ2(lnmd) t+1t+1 Interpretation: Numerator - volatility of the difference in consumption growth rate = Risk component notshared Denominator - Total volatility in consumption growth rates = total risk that can be shared Index = 1 - risk fraction not shared = fraction of risk shared Idea: Compute Risk Sharing index conditional on Output growth 2 3 Albuquerque &Javadekar

10. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing Consumption Risk Sharing: Upside vsDownside Figure :Cross Country Risk Sharing - Upside vs Downside Albuquerque &Javadekar

11. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing (ρ(y,y∗),ρ(c,c∗)) Figure :Output and Consumption Correlations -Downside Albuquerque &Javadekar

12. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Asymmetries in Output Implications for RiskSharing (ρ(y,y∗),ρ(c,c∗)) Figure :Output and Consumption Correlations -Upside Albuquerque &Javadekar

13. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Stocks: Vanishing Discontinuity atZero! Figure :Asymmetric Cross Country Correlations in Stock Returns Albuquerque &Javadekar

14. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Summarizing MainEvidence Cross country output growth follows regimes; highly correlated indownturns Stock returns correlations becoming symmetric: No major difference in correlations in upside vs downside Risk Sharing is state dependent: High international consumption risk sharing in downturns Asset Returns do not inherit the output growth distributionalproperties 1 2 3 4 Albuquerque &Javadekar

15. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Properties of PricingModel TwoFacts In EU area, discount rate shocks are highlycorrelated Stock returns correlations in EU area are becoming symmetric, while output growth correlation is becoming asymmetric. ⇒ We want a model where asset returns are driven by discount rate shocks more than cash flowshocks. Question: Can regime Switching correlation in output growth generate time variation in discountrates? First Steps: Take a regime switching process for output growth where correlations are different in different regimes and try to solve for optimalallocation. 1 2 3 4 Albuquerque &Javadekar

16. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Framework Recipe: Take output growth as a joint regime switching process, solve for consumption allocations, estimate the regime switching process and price the assets Framework: Two countries H and F, single good Output Growth Follows regime Switching (6y(st),6y∗(st))∼N.µ(st),Σ(st). Conjecture: Correlations higher in one regime that other. Preferences in both countries are simple CRRA Complete Markets ⇒ consumption growth rates are perfectlycorrelated 1 2 3 (3) 4 5 6 Ci ∗ Y +Y t+1 t+1 t+1 = (4) Ci Yt+Y∗ t t Albuquerque &Javadekar

17. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review PD Ratios: General IssuesInvolved State Variables: Relative Share of domestic tree (δ) and regime both act as a statevariables Cecchetti, Lam and Mark (1990) Method: Conjecture that PD ratio is constant within regime CLM method can not work: PD ratio is a regime dependent function of relative share. Essentially we need to find twofunctions. Note: Distribution of Output growth and relative share growth depends upon currentregime 1 2 3 4 Albuquerque &Javadekar

18. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Literature Review Models of Regime Switching: Hamilton (1989), Cecchetti, Lam and Mark (1990, 1993) Asset Pricing: Cochrane and Longstaff, Santa-Clara (2008), Dumas, Harvey and Ruiz (2003) Risk Sharing: Backus and Smith(1993) Asymmetries: Longin and Solnik (2001), Ang and Chen (2002), Ang (2011), Brandt, Cochrane, Santa Clara (2006) 1 2 3 4 Albuquerque &Javadekar

19. Broad ThemeofResearch EmpiricalEvidence Links to AssetPrices Asset PricingImplications Literature Review Thank You for Coming! Albuquerque &Javadekar