Apoorva Javadekar - Conditional Correlations of Macro Variables and Implications for Asset Prices

Broad Theme of ResearchEmpirical Evidence

Links to Asset PricesAsset Pricing Implications

Literature Review

Conditional Correlations of Macro Variables andImplications for Asset Prices

Apoorva Javadekar1

Joint With

Rui Albuquerque2

March 10, 2013

1Boston University, Department of Economics

2School of Management, Boston University

Albuquerque & Javadekar Asymmetries In Macro Variables



Literature Review

Broad Questions

1 Understanding the structure of the Cross CountryCorrelation for Macro Variables:

Do macro variables across countries co move more stronglyduring certain times than other?More precisely: Do cross country correlations are conditionallyasymmetric?

2 Asset Pricing and Risk Sharing ImplicationsHow does regime switching or jumps in fundamental macrovariables affect asset prices?In particular: Does asymmetric correlations in output translatein to asymmetric correlations for stock returns?What are the implications for Risk Sharing arrangements?

3 Can current macro models explain these type ofconditional asymmetries in Macro Variables?




Literature Review

Asymmetries in OutputImplications for Risk Sharing

Basics: Exceedence Correlation

1 Consider a joint stochastic processes: {Xt ,Yt} with E (Xt) =E (Yt) = 0 and unit variance.

2 Exceedence Correlation at level c:

ρ̂(X ,Y ; c) =

{ρ(X ,Y |X > c ,Y > c) if c ≥ 0

ρ(X ,Y |X < c ,Y < c) if c ≤ 0(1)

3 For normal distribution ρ(X ,Y |X > c ,Y > c) =ρ(X ,Y |X < −c ,Y < −c) for every c ⇒ SymmetricExceedences




Literature Review


Output Growth: Simple Statistics

Table : Evidence on Asymmetries in Output Correlations3

Statistics 1980-2012 1980-1998 1999-2012

Mean Growth % 1.008 1.65 .079Mean Volatility % 15.77 14.89 16.59

Mean Upside Vol % 9.03 9.39 8.30Mean Downside Vol % 12.20 9.89 14.24

Mean Correlation 0.23 0.14 0.33Mean Positive Exceedence 0.08 0.102 0.12Mean Negative Exceedence 0.31 0.105 0.46

3Source: Monthly Data from OECD Library for G7: Growth Rates areannualized and data is measured at Monthly frequencies




Literature Review


Output Co movement: Drop at Zero !

Figure : Exceedence Correlations - Against OECD




Literature Review


Asymmetries in Output Correlations: Drop at Zero !

Figure : Exceedence Correlations - Against Germany




Literature Review


Asymmetries in Output Correlations: Drop at Zero !

Figure : Exceedence Correlations - Against USA




Literature Review


Some Robustness Checks

1 Formal Hypothesis testing using Zhou, Tu and Hong Test ofasymmetry (2007)

2 Data filtering using growth and HP filter

3 Time Aggregation: Quarterly vs Monthly

4 Conditioning on single country being a threshold instead ofboth

5 Justification for Industrial Production as a proxy forOutput: (See Dumas et al. 2003)

GDP and IP highly correlatedIP data available at monthly frequency: Trade off between lowfrequency movements vs having more observations forconditioningBehavior in recessions is similar (exception in 2001)




Literature Review


Consumption Risk Sharing: Quick Exercise

1 Consider Brandt, Cochrane and Santa Clara Index of RiskSharing

RSt = 1−σ2(lnmf

t+1 − lnmdt+1)

σ2(lnmft+1) + σ2(lnmd

t+1)(2)

2 Interpretation:Numerator - volatility of the difference in consumption growthrate = Risk component not sharedDenominator - Total volatility in consumption growth rates =total risk that can be sharedIndex = 1 - risk fraction not shared = fraction of risk shared

3 Idea: Compute Risk Sharing index conditional on Outputgrowth




Literature Review


Consumption Risk Sharing: Upside vs Downside

Figure : Cross Country Risk Sharing - Upside vs Downside




Literature Review


(ρ(y , y ∗), ρ(c , c∗))

Figure : Output and Consumption Correlations -Downside




Literature Review


(ρ(y , y ∗), ρ(c , c∗))

Figure : Output and Consumption Correlations -Upside




Literature Review

Stocks: Vanishing Discontinuity at Zero!

Figure : Asymmetric Cross Country Correlations in Stock Returns




Literature Review

Summarizing Main Evidence

1 Cross country output growth follows regimes; highlycorrelated in downturns

2 Stock returns correlations becoming symmetric: Nomajor difference in correlations in upside vs downside

3 Risk Sharing is state dependent: High internationalconsumption risk sharing in downturns

4 Asset Returns do not inherit the output growthdistributional properties




Literature Review

Properties of Pricing Model

1 Two FactsIn EU area, discount rate shocks are highly correlatedStock returns correlations in EU area are becoming symmetric,while output growth correlation is becoming asymmetric.

2 ⇒ We want a model where asset returns are driven bydiscount rate shocks more than cash flow shocks.

3 Question: Can regime Switching correlation in output growthgenerate time variation in discount rates?

4 First Steps: Take a regime switching process for outputgrowth where correlations are different in different regimesand try to solve for optimal allocation.




Literature Review

Framework

1 Recipe: Take output growth as a joint regime switchingprocess, solve for consumption allocations, estimate theregime switching process and price the assets

2 Framework: Two countries H and F, single good3 Output Growth Follows regime Switching

(M y(st),M y∗(st)) ∼ N(µ(st),Σ(st)

)(3)

4 Conjecture: Correlations higher in one regime that other.5 Preferences in both countries are simple CRRA6 Complete Markets ⇒ consumption growth rates are

perfectly correlated

C it+1

C it

=Yt+1 + Y ∗

t+1

Yt + Y ∗t

(4)




Literature Review

PD Ratios: General Issues Involved

1 State Variables: Relative Share of domestic tree (δ) andregime both act as a state variables

2 Cecchetti, Lam and Mark (1990) Method: Conjecturethat PD ratio is constant within regime

3 CLM method can not work: PD ratio is a regimedependent function of relative share. Essentially we need tofind two functions.

4 Note: Distribution of Output growth and relative sharegrowth depends upon current regime




Literature Review

Literature Review

1 Models of Regime Switching: Hamilton (1989), Cecchetti,Lam and Mark (1990, 1993)

2 Asset Pricing: Cochrane and Longstaff, Santa-Clara (2008),Dumas, Harvey and Ruiz (2003)

3 Risk Sharing: Backus and Smith (1993)

4 Asymmetries: Longin and Solnik (2001), Ang and Chen(2002), Ang (2011), Brandt, Cochrane, Santa Clara (2006)




Literature Review

Thank You for Coming !


Apoorva Javadekar - Conditional Correlations of Macro Variables and Implications for Asset Prices

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