Financial volatility, currency diversication and banking stability

Transcription

1 Introduction Model An application to the US and EA nancial markets Conclusion Financial volatility, currency diversication and banking stability Justine Pedrono 1 1 CEPII, Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE August 25, 2017 International Workshop on Financial System Architecture and Stability

2 Introduction Model An application to the US and EA nancial markets Conclusion Motivation From the literature : Evans and McMillan [2009], Rey [2013], Miranda-Agrippino and Rey [2015], Ivashina et al. [2015], Pedrono and Violon [2017] European banks : a transatlantic asymmetry in international banking (Baba et al. [2009], McGuire and Von Peter [2012]) EA global banks exposed to the global nancial cycle : Co-movements between assets {C, C } Major inuence of US monetary policy on credit conditions worldwide {L, L } Regarding exchange rate, assets and liabilities : domestic currency appreciation with positive shock on domestic interest rate. Engel [1996], Kearns and Manners [2006], Ehrmann et al. [2011] {C, C, L, L, S} within EA banks' balance sheet are linked all together. Aim of this paper : Link the bank's exposure to the global nancial cycle to the banking volatility

3 Introduction Model An application to the US and EA nancial markets Conclusion Illustration (a) International stock market indices (b) Shadow short rates (SSR), daily returns (c) Exchange rate Figure: Financial markets. Sources : Bloomberg, The Reserve Bank of New Zealand.

4 Introduction Model An application to the US and EA nancial markets Conclusion Theoretical model : This paper Stochastic processes to dene assets, liabilities and foreign exchange rate marginal variation Equity returns : A residual of total asset and liability marginal variations Volatility of equity : Leverage and variance covariance matrix between {C, C, L, L, S} Data and empirical application : Daily data on : International stock market indices US and EA Shadow Short Rate Foreign exchange rate Bi-variate DCC GARCH : Conditional variances and correlations Estimation of ecient currency diversication Key ingredients : Dierentiating each source of risk within global bank's volatility Identication of the global nancial cycle : conditional correlations

5 Introduction Model An application to the US and EA nancial markets Conclusion Total assets : Total liabilities : A = C + SC D = L + SL with with Bank's equity is dened through E such that : Bank's leverage l : E = A D l = D/E Equity C SC = (1 ψ) ; A L SL = (1 λ) ; D A = ψ D = λ Following the Basel III framework, we assume that leverage is dened by authorities. Using denitions of l and E, we obtain the bank's equity SDE : dẽ = de E = (1 + l) da A l dd D ( = (1 + l) (1 ψ) d C + ψ(dc + d S) ) ( l (1 λ) d L + λ(dl + d S) )

6 Introduction Model An application to the US and EA nancial markets Conclusion Volatility of equity with currency diversication Introducing 10 covariances {σ CC, σ LL, σ LC, σ L C, σ L C, σ LC, σ SC, σ SC, σ SL, σ SL } Volatility of equity return : Var ( dẽ dt ) = Var of each component of the BS : σ 2 C σ2 C σ 2 L σ2 L σ 2 S + The exposure to the global nancial cycle : σ CC, σ LL The Asset-Debt hedging strategy : σ LC σ L C σ L C σ LC +/ The FX channel on converted returns and costs : σ SC, σ SC, σ SL, σ SL "Ecient" share of foreign asset ψ : min. of banking volatility (similarly for λ) ψ = + share of C in asset-side risk + risk reduction related to part of liability side being also in foreign currency + share of C risk that can be hedged with L + share of C risk that can be hedged with L Details FX channel

7 Introduction Model An application to the US and EA nancial markets Conclusion An application to the US and EA nancial markets Data C : log returns of the Eurostox50 index C : log returns of the S&P500 index L : EA SSR changes for EA monetary tightening L : US SSR changes for US monetary tightening S : the USD/EUR FX Identifying variances of {C, C, L, L, S} and correlations between the dierent components : 10 bivariate DCC GARCH(1,1) using daily data from 2000 to 2015 Compared to cointegration analysis : Details Capture the potential change in nancial integration as mentioned by Evans and McMillan [2009].

8 Introduction Model An application to the US and EA nancial markets Conclusion Main results from DCC GARCH Identication of nancial distress : - bursting of the Dotcom bubble ( ) - the subprime crisis ( ) - global volatility surge in 2008 Assets are more volatile {σ C, σ C } > {σ S } > {σ L, σ L } US Vs EA volatility σ C > σ C except for 2008 σ L > σ L for 2000, 2003, 2009 and since 2011 Conrm the global nancial cycle : {ρ CC, ρ LL }, all positive with some dynamics {ρ LC ρ L C ρ L C ρ LC }, all positive with dynamics Correlations regarding FX : {ρ SC, ρ SC, ρ SL, ρ SL } : positive to negative dynamic depending on sub-period Vol. DCC

9 Introduction Model An application to the US and EA nancial markets Conclusion Ecient diversication 2008 : peak in vol. but large ρ LC and ρ L C, and FX compensation with ρ SC = ρ SC and ρ SL = ρ SL : Currency diver. still stabilizing : large compensation eect with ρ SC < 0, plus ρ LC > ρ L C : Currency mismatch is optimal Figure: Ecient currency diversication of bank's balance sheet ( ) : ψ and λ are dened as to minimize the volatility of bank's equity. After 2012, ρ LC < ρ L C and ρ SC increases and becomes positive : Currency mismatch is absorbed

10 Introduction Model An application to the US and EA nancial markets Conclusion Conclusion Link the bank's exposure to the global nancial cycle to the banking stability. An application to the US and EA nancial markets Identication of the global nancial cycle Diversication reduces equity volatility even during large nancial distresses such as The currency dimension of banks' balance sheet then oers an interesting potential regulatory tool to improve the resilience of banks : Possible to hedge FX risk completely. Possible to understand the consequences of banks' external positions : currency mismatch may improve banking stability. Possible to improve stress test exercises by including FX adjustments. Extension : Compared ecient diversication and observed diversication Explain dierences in currency diversication Explain conditional correlations.

11 Equity return volatility Var( dẽ dt ) = Σ ortho + 2(1 + l) 2 ψ(1 ψ)σ CC + }{{} l 2 λ(1 λ)σ LL }{{} global financial cycle risk global financial cycle risk 2(1 + l)l [(1 ψ) ((1 λ)σ LC + λσ L C ) + ψ (λσ L C + (1 λ)σ LC )] }{{} A D hedging strategies + 2(ψ + l(ψ λ)) (1 + l) [(1 ψ)σ SC + ψσ SC ] }{{} FX channel, asset 2(ψ + l(ψ λ)) l [(1 λ)σ SL + λσ SL ] }{{} FX channel, liability where : Σ ortho = ((1 + l)(1 ψ)) 2 σ 2 C + ((1 + l)ψ)2 σ 2 C + (ψ + l(ψ λ)) 2 σ 2 S + (l(1 λ))2 σ 2 L + (l λ)) 2 σ 2 L Return (1)

12 Ecient asset diversication Σ 2 global ψ = 0 λ constant σ ψ 2 C global = σ CC σ SC σ 2 C + σ2 C + σ 2 S 2 (σ CC + σ SC σ SC ) ( ) l σ 2 S + λ + σ SC σ SC 1 + l σ 2 C + σ2 C + σ 2 S 2 (σ CC + σ SC σ SC ) ( ) l σ SL + σ L + λ C σ L C 1 + l σ 2 C + σ2 C + σ 2 S 2 (σ CC + σ SC σ SC ) }{{} share of C risk that can be hedged with L ( ) l σ SL + σ LC σ LC + (1 λ) 1 + l σ 2 C + σ2 C + σ 2 S 2 (σ CC + σ SC σ SC ) }{{} share of C risk that can be hedged with L (2) Return

13 Ecient liability diversication Similarly for the "Ecient" share of foreign liability λ : Σ 2 global = 0 ψ constant λ σ λ 2 L global = σ LL σ SL σ 2 L + σ2 L + σ 2 S 2(σ LL + σ SL σ SL ) ( ) 1 + l σ 2 S + ψ + σ SL σ SL l σ 2 L + σ2 L + σ 2 S 2(σ LL + σ SL σ SL ) ( ) 1 + l σ L + ψ C + σ SC σ LC l σ 2 L + σ2 L + σ 2 S 2(σ LL + σ SL σ SL ) }{{} share of L risk that can be hedged with L ( ) 1 + l σ SC + σ L + (1 ψ) C σ LC l σ 2 L + σ2 L + σ 2 S 2(σ LL + σ SL σ SL ) }{{} share of L risk that can be hedged with C (3) Return

14 The FX channel On the asset side Following empirical literature (Ehrmann et al. [2011]) : σ SC > 0 and σ SC < 0 Assuming that σ SC = σ SC and : ψ = 0.5 : FX channel=0 ψ > 0.5 : a positive shock on {r, r } goes with a foreign currency appreciation Converted asset returns increase, thus : - A relatively low λ increases Σ 2 (i.e when ψ λ > l ) : no compensation 1+l - A relatively large λ decreases Σ 2 (i.e when ψ λ < l 1+l ) : compensation ψ < 0.5 : a positive shock on {r, r } goes with a foreign currency depreciation Converted asset returns decrease, thus : - A relatively low λ decreases Σ 2 (i.e when ψ λ > l 1+l ) : compensation - A relatively large λ increases Σ 2 (i.e when ψ λ < l ) : no compensation 1+l When ψ = λ = 0, or when ψ λ = Return l, FX channel=0 1+l

15 DCC GARCH Two steps : 1) estimate the conditional volatility of each one of the two series {i, j} from univariate GARCH(1,1) ; 2) capture from the rst step the dynamic correlation between the two series. Suppose r t a 2x1 vector of returns of 2 assets at time t, H t a 2x2 matrix of conditional variances of r t at time t and z t a 2x1 vector of iid errors such that E[z t ] = 0 and E[z t zt T ] = I. Then, univariate GARCH is such that : r t = H 1/2 t z t (4) Decomposing the covariance matrix H t into conditional standard deviation D t from univariate GARCH, and a correlation matrix R t capturing the dynamic correlation {i, j}, the DCC GARCH introduces the following extension : Where the varying conditional correlation matrix R t is dened as : H t = D t R t D t (5) R t = (I Q t ) 1/2 Q t (I Q t ) 1/2 (6) Q t = (1 a b) Q + aɛ t 1 ɛ T t 1 + bq t 1 (7) Therefore, the dynamic matrix process Q t is a function of Q, the unconditional correlation matrix of the standardized errors ɛ t. Our results suggest that all correlations are mean-reverting process where (a + b) < 1. Additionally, all Wald tests reject the null hypothesis where a = b = 0 : conditional correlations are dynamic. Return

16 Conditional variance e e e US SSR EA SSR Identication of nancial distress : : the bursting of the dotcom bubble : the subprime crisis 2008 : peak in volatility Assets are more volatile : {σ C, σ C } > {σ S } > {σ L, σ L } S&P500 Eurostoxx50 US Vs EA volatility : σ C > σ C except for 2008 σ L > σ L for 2000, 2003, 2009 and since 2011 FX Return

17 Conditional variance σ 2 C σ 2 C σ 2 S σ 2 L σ 2 L e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-08 Table: Conditional variances. S, C, C, L and L refer to the exchange rate, the eurostoxx 50 index, the S&P500 index, the euro Shadow Short Rate and the US Shadow Short Rate respectively. Return

18 Conditional correlations : assets and liabilities Corr(Eurostoxx50, SP500) Corr(EA SSR, Eurostoxx50) Corr(US SSR, Eurostoxx50) Corr(US SSR, EA SSR) Corr(US SSR, S&P500) Corr(EA SSR, SP500) Return

19 Conditional correlations : foreign exchange rate Corr(Eurostoxx50, FX) Corr(SP500, FX) Corr(US SSR, FX) Corr(EA SSR, FX)

20 Conditional correlations : ρ LL ρ CC ρ LC ρ L C ρ LC ρ L C ρ SL ρ SL ρ SC ρ SC Table: Conditional correlations. S, C, C, L and L refer to the exchange rate, the eurostoxx 50 index, the S&P500 index, the euro Shadow Short Rate and the US Shadow Short Rate respectively. Return

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