A Macro-Financial Analysis of the Euro Area Sovereign Bond Market (Redenomination Risk in the Euro Area Bond Market) Hans Dewachter a ; b Leonardo Iania a ; c Marco Lyrio d Maite de Sola Perea a a NBB, b KUL , c UCL, d Insper August 2013 1 / 52
Introduction The main goal of the paper is to identify and assess the relative importance of the "convertibility" or "redenomination" risk within euro area sovereign bond spreads. " These premia have to do, as I said, with default, with liquidity, but they also have to do more and more with convertibility, with the risk of convertibility. ” Mario Draghi July 2012 Identi…cation issue: redenomination risk is unobserved. We assume it incorporates: E¤ect of ‡ight-to-safety capital ‡ows across borders; and Dynamics of bond spreads not justi…ed by country-speci…c factors, euro-area economic fundamentals, and international in‡uences. 2 / 52
Disclaimer The views expressed are those of the authors and do not necessarily re‡ect those of the NBB. 3 / 52
Overview Introduction Multi-market a¢ne yield curve model Estimation methodology Empirical …ndings Application Conclusion 4 / 52
Introduction Identi…cation of redenomination risk Alternative approaches have been proposed in the academic literature. Market-based measures of implicit "devaluation" risk: di¤erence in CDS of euro area countries relative to Germany. Implied deviation of observed yield from a "fair" value : focus fair yield spreads on (macroeconomic) fundamental components (e.g. Di Cesare et al. (2012), De Grauwe and Li (2012)); standard (country-speci…c) regression approach for speci…c bond maturities. 5 / 52
Introduction Identi…cation of non-fundamental (redenomination) risk Example of fair yield model: ( Di Cesare et al (2012)). 6 / 52
Introduction Contribution of the paper Decompose of bond yield spreads based on canonical DTSM model . Introduce a no-arbitrage, multi-issuer, a¢ne term structure model: Limited number of spanned factors : parsimonious pricing function for the yield curve (as in Joslin, Singleton and Zhu (RFS 2011)); Large number of unspanned factors with predictive content for excess bond returns. This allows the identi…cation of speci…c shocks (as in Joslin, Priebsch and Singleton (2010)). Decompose EA sovereign yield spreads (relative to OIS) for …ve EA countries (BE, FR, GE, IT and SP): Economic risk : global/euro area environment and economic situation of the country; Idiosyncratic (country-speci…c) risk : additional non-economic risk; Non-fundamental (redenomination) risk : component not accounted for by macro-…nancial variables, i.e. that should not be present in a well-functioning monetary union. 7 / 52
Introduction Main results Fit of the yield curve In most cases, we obtain a good …t of the OIS and country-speci…c yield curves. Relative importance of bond spread components (IRFs and Var. Dec.) Redenomination shocks relatively important for shorter forecast horizons; Economic fundamentals remain important factor for EA bond spreads for longer forecast horizons. Historical decomposition of spread dynamics during crisis We observe an increase in bond yield spreads due to redenomination risk shocks after the intensi…cation of the debt crisis in September 2011 (in line with Di Cesare, Grande, Manna, and Taboga (2012) and De Grauwe and Ji (2012) ); Economic fundamentals remain an important driver of bond yield spreads. 8 / 52
A¢ne yield curve model 9 / 52
A¢ne yield curve models Basic set up Bond pricing equation (no-arbitrage condition): P t ; n = E t [ m t + 1 P t + 1 ; n � 1 ] ; Stochastic discount factor is a function of risks present in the economy: m t + 1 = exp [ � r t � 0 : 5 � 0 t � t � � 0 t " t + 1 ] " t � N ( 0 ; I K ) Prices of risks, � t ; and (risk-free) interest rate, r t ; are a function of state variables: � t = � 0 + � 1 X t ; r t = � 0 + � 1 X t Risk-neutral dynamics of the factors, X t ; follow a Gaussian VAR(I) process: X t = C Q + � Q X t � 1 + � " Q " Q � N ( 0 ; I K ) t ; 10 / 52
A¢ne yield curve models Obtaining the pricing function Given these assumptions bond prices can be expressed as exponential a¢ne functions of state variables (see Ang and Piazzesi, JME 2003): P t ; n = exp [ A n + B n X t ] ; where A n and B n satisfy DEs, imposing the no-arbitrage restrictions on bond prices: A n + 1 = A n + B n ( C P � �� 1 n (� P � �� 1 ) + 0 : 5 B 0 ) B n + A 1 | {z } | {z } C Q � Q B n + 1 = B n (� P � �� 1 ) + B 1 | {z } � Q The no-arbitrage a¢ne yield curve representation, for y t ; n = � ln P t ; n = n with n = 1 ; :::; L and � = f C Q ; � Q ; � ; � 0 ; � 1 ; � 0 ; � 1 g : y t ; n = a n (�) + b n (�) X t a n = � A n = n ; b n = � B n = n 11 / 52
A¢ne yield curve models Spanned and unspanned factors (Joslin, Singleton, and Zhu (RFS 2011)) JSZ propose the use of "spanned" factors by using bond portfolios ( P t = Wy t ) as pricing factors. Given a no-arbitrage, a¢ne yield curve representation in the original risk factors X t : y t = a (�) + b (�) X t De…ne the set (dim( X )) of yield portfolios P t : P t = Wy t An equivalent yield curve representation in function of the yield portfolios is given by: � � I � b (�)( Wb (�)) � 1 W + b (�)( Wb (�)) � 1 y t = a (�) P t | {z } | {z } b p (�) a p (�) The impact of macroeconomic variables on the yield curve can be assessed using the joint P � dynamics of Z t and P t � Z t � � C Z � � � ZZ � � Z t � 1 � � � ZZ � � " Z ; t � � Z P 0 = + + P t C P � PZ � PP P t � 1 � PZ � PP " P ; t 12 / 52
Multi-market a¢ne yield curve model 13 / 52
Multi-market a¢ne yield curve model Obtaining the pricing function Risk-neutral dynamics of the factors: " Q � N ( 0 ; I K ) X t = C Q X + � Q X X t � 1 + � X " Q t ; Instantaneous interest rate of market m depends on the pricing factors: r m ; t = � m X t ; m = 1 ; :::; M Multi-market framework ( m = 2 ) : Risk-free interest rate: r 0 ; t = � 0 X t ; � 0 = [ 1 ; 1 ; 0 ; 0 ] r 1 ; t = � 1 X t ; � 1 = [ 1 ; 1 ; 1 ; 1 ] Country-speci…c rate: r 1 ; t = � 0 X t + ( � 1 � � 0 ) X t |{z} | {z } risk-free spreads rel risk free 14 / 52
Multi-market a¢ne yield curve model Obtaining the multi-market yield curve representation Yield curve is as an a¢ne function of the latent factors y m ; t ( n ) = a n (� ; � m ) + b n (� ; � m ) X t Multi-market, no-arbitrage yield curve representation 2 3 2 3 2 3 y 0 ; t ( 1 ) a 1 (� ; � 0 ) b 1 (� ; � 0 ) 6 7 6 7 6 7 . . . . . . 6 7 6 7 6 7 . . . 6 7 6 7 6 7 6 7 6 7 6 7 y 0 ; t ( N ) a N (� ; � 0 ) b N (� ; � 0 ) 6 7 6 7 6 7 Y t = = + X t 6 7 6 7 6 7 y 1 ; t ( 1 ) a 1 (� ; � 1 ) b 1 (� ; � 1 ) 6 7 6 7 6 7 6 7 6 7 6 7 . . . . . . 4 5 4 5 4 5 . . . y 1 ; t ( N ) a N (� ; � 1 ) b N (� ; � 1 ) Re-express the fundamental a¢ne yield curve model in terms of the observable "yield portfolios", i.e. P t = WY t : Assuming zero measurement errors on the yield portfolios: � � I � b (�)( Wb (�)) � 1 W + b (�)( Wb (�)) � 1 Y t = a (�) P t | {z } | {z } b p (�) a p (�) 15 / 52
Multi-market a¢ne yield curve model Assessing the impact of macro-…nancial factors on the yield curve Multi-market, no-arbitrage yield curve representation Y t = a p (�) + b p (�) P t VAR(1) representation: assess the relative importance of macroeconomic, …nancial and redenomination variables through their impact on the yield portfolio factors ( P t ) � Z t � � C Z � � � ZZ � � Z t � 1 � � � ZZ � � " Z ; t � � Z P 0 = + + P t C P � PZ � PP P t � 1 � PZ � PP " P ; t Z t : set of (appropriately ordered) macroeconomic, …nancial and redenomination factors � ZZ and � PP are lower-triangular matrices implied by the Cholesky ordering and identi…cation of structural shocks. 16 / 52
Estimation methodology 17 / 52
Estimation methodology Likelihood function We use standard maximum likelihood techniques in two steps: We estimate the VAR system using standard OLS regressions; Conditional on VAR estimates, the remaining parameters to …t the OIS and country-speci…c yield curves are obtained by maximum likelihood . Model is estimated on data from Belgium, France, Germany, Italy, and Spain: August 2005 - March 2013 using bonds with maturities of 1, 2, 3, 4 and 5 years. 18 / 52
Estimation methodology The factors... � VIX t global tension and European economic situation ESI t 9 F 2 S t > > = PC Eur _ spr ; 1 t Z t = redenomination risk PC Eur _ spr ; 2 > > ; t POL t 9 GDP m = t CPI m ; economic condition/…scal sustainability of the country m t D m t = GDP m t � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � PC OIS ; 1 t …t OIS yield curve PC OIS ; 2 t P t = � PC spr ; 1 t …t country-speci…c yield curve PC spr ; 2 t 19 / 52
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