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

Broad Theme of Research Empirical Evidence Links to Asset Prices

Asset Pricing ImplicationsLiterature Review

Conditional Correlations of Macro Variables and Implications for Asset

Prices

Apoorva Javadekar1

Joint With

Rui Albuquerque2

March 10, 2013

1 Boston University, Department of Economics 2 School of Management, Boston University

Albuquerque & Javadekar Asymmetries In Macro Variables



Broad Questions1

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Understanding the structure of the Cross Country Correlation for Macro Variables:

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 Sharing ImplicationsHow 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 Macro Variables?




Asymmetries in Output Implications for Risk Sharing

Basics: Exceedence Correlation

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Consider a joint stochastic processes: {Xt, Yt} with E (Xt ) =E (Yt ) = 0 and unit variance.Exceedence Correlation at level c:

ρ (̂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 ⇒ Symmetric Exceedences





Output Growth: Simple Statistics

Table :Evidence on Asymmetries in Output Correlations 3

Statistics 1980-2012 1980-1998 1999-2012Mean Growth % 1.008 1.65 .079

Mean Volatility % 15.77 14.89 16.59Mean Upside Vol % 9.03 9.39 8.30

Mean Downside Vol % 12.20 9.89 14.24Mean Correlation 0.23 0.14 0.33

Mean Positive Exceedence 0.08 0.102 0.12Mean Negative Exceedence 0.31 0.105 0.46

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





Output Co movement: Drop at Zero !

Figure :Exceedence Correlations - Against OECD





Asymmetries in Output Correlations: Drop at Zero !

Figure :Exceedence Correlations - Against Germany





Asymmetries in Output Correlations: Drop at Zero !

Figure :Exceedence Correlations - Against USA





Some Robustness Checks

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Formal Hypothesis testing using Zhou, Tu and Hong Test of asymmetry (2007)Data filtering using growth and HP filter Time Aggregation: Quarterly vs MonthlyConditioning on single country being a threshold instead of bothJustification for Industrial Production as a proxy for Output: (See Dumas et al. 2003)

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





Consumption Risk Sharing: Quick Exercise

1 Consider Brandt, Cochrane and Santa Clara Index of Risk Sharing

RSt = 1 −

σ2(ln mf

t+1dt+1− ln m )

t+1t+1

σ2(ln mf ) + σ2(ln md )(2)

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Interpretation:Numerator - volatility of the difference in consumption growth rate = 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

Idea: Compute Risk Sharing index conditional on Output growth





Consumption Risk Sharing: Upside vs Downside

Figure :Cross Country Risk Sharing - Upside vs Downside





(ρ(y, y∗), ρ(c, c∗))

Figure :Output and Consumption Correlations -Downside





(ρ(y, y∗), ρ(c, c∗))

Figure :Output and Consumption Correlations -Upside




Stocks: Vanishing Discontinuity at Zero!

Figure :Asymmetric Cross Country Correlations in Stock Returns




Summarizing Main Evidence

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Cross country output growth follows regimes; highly correlated in downturnsStock returns correlations becoming symmetric: No major difference in correlations in upside vs downsideRisk Sharing is state dependent: High international

consumption risk sharing in downturnsAsset Returns do not inherit the output growth

distributional properties




Properties of Pricing Model

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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.

⇒ We want a model where asset returns are driven by discount rate shocks more than cash flow shocks.Question: Can regime Switching correlation in output growth generate time variation in discount rates?First Steps: Take a regime switching process for output growth where correlations are different in different regimes and try to solve for optimal allocation.




Framework1

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(3)

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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

(6 y (st ), 6 y∗(st )) ∼ N .µ(st ), Σ(st ).

Conjecture: Correlations higher in one regime that other. Preferences in both countries are simple CRRAComplete Markets ⇒ consumption growth rates are perfectly correlated

C i t+1

C it= t+1Y +

Y∗

t+1Y t + Y ∗

t(4)




PD Ratios: General Issues Involved

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State Variables: Relative Share of domestic tree (δ) and regime both act as a state variablesCecchetti, Lam and Mark (1990) Method: Conjecture that PD ratio is constant within regimeCLM method can not work: PD ratio is a regime dependent function of relative share. Essentially we need to find two functions.Note: Distribution of Output growth and relative share growth depends upon current regime




Literature Review

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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)




Thank You for Coming !


Economy & Finance

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