Systemic and systematic risks SYstemic Risk TOmography: Signals, Measurements, Transmission Channels, and Policy Interventions Monica Billio, University Ca' Foscari Venezia (Italy) Massimiliano Caporin, University of Padova (Italy) Roberto Panzica, Goethe University Frankfurt (Germany) Loriana Pelizzon, University Ca' Foscari Venezia (Italy) and Goethe University Frankfurt (Germany) SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 2 2014 - Frankfurt (Bundesbank-ECB-ESRB)
SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO (Bundesbank-ECB-ESRB) Head Office of Deustche Bundesbank, Guest House Frankfurt am Main - July, 2 2014
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Systemic and
systematic risks
SYstemic Risk TOmography:
Signals, Measurements, Transmission Channels, and Policy Interventions
Monica Billio, University Ca' Foscari Venezia (Italy) Massimiliano Caporin, University of Padova (Italy) Roberto Panzica, Goethe University Frankfurt (Germany) Loriana Pelizzon, University Ca' Foscari Venezia (Italy) and Goethe University Frankfurt (Germany) SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 2 2014 - Frankfurt (Bundesbank-ECB-ESRB)
Research questions
Research questions
There is a general agreement on the traditional decomposition of an asset(portfolio) total risk into systematic and idiosyncratic components followingthe CAPM model
Systematic risks comes from the dependence of returns on common factors
Idiosyncratic risks are asset-specific
But...
There is also a recent consensus on the existence of systemic risks
Systemic risk definition: any set of circumstances that threatens the stabilityof, or public confidence in, the financial system
Systemic risk is a function of a system
Systemic risk arises endogenously from a system
Systemic risk is a function of connections between and the structure offinancial institutions or, more generally, between the companies and/oreconomic sectors
An increasing literature in economics investigates the role of interconnectionsbetween different firms and sectors, functioning as a potential propagationmechanism of idiosyncratic shocks throughout the economy.
Canonical idea: Lucas (1977), among others, that states that suchmicroeconomic shocks would average out and thus, would only havenegligible aggregate effects. Similarly, these shocks would have little impacton asset prices.
However:
Acemoglou et al. (2011) use network structure to show the possibility thataggregate fluctuations may originate from microeconomic shocks to firms.Such a possibility is discarded in standard macroeconomics models due to a“diversification argument”.
Shock propagation in static networks Horvath (1998, 2000), Dupor (1999),Shea (2002), and Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2011).
Role of idiosyncratic risk in asset pricing: The CAPM predicts that onlysystematic risk is priced and expected excess returns satisfy two-fundseparation. This prediction is contradicted by:
Ozsoylev and Walden (2009) study a static model of asset price formation inlarge information networks, mainly centred on the relation between pricevolatility and network connectedness.
Ang, Hodrick, Xing, and Zhang (2006), who show that idiosyncratic volatilityrisk is priced in the cross-section of expected stock returns, a regularity whichis not subsumed by size, book-to-market, momentum, or liquidity effects.
Buraschi and Porchia (2014): dynamic network connectivity has implicationson diversification and asset pricing
Traditional models consider several risk factors, one of them being the market
Standard decomposition of assets (and portfolios) total risk into a systematiccomponent (driven by the risk factors) and an idiosyncratic component(driven by asset-specific shocks)
Diversification acts on the idiosyncratic part and aims at reducing its impactin a portfolio
Recent literature on diversification and systemic risk:
Ozsoylev and Walden (2009), Ang, Hodrick, Xing, and Zhang (2006),Buraschi and Porchia (2014), Wagner (2011) and Battiston and Tasca(2013)
General multi-factor model for a k−dimensional vector of risky assets (m riskfactors) [avoiding for simplicity the introduction of the risk-free and assumingfactors have zero-mean]
A general framework with systemic and systematic risks
Systemic links represents relations across assets that co-exists with thedependence on common risk factors
Systemic links are relations across endogenous variables
ARt = BFt + εt (7)
The simultaneous equation system above is not identified unless we imposesome restriction; k number of assets is much larger than m the number offactors
Assumption 1: the idiosyncratic shocks are uncorrelated, that is Ω is adiagonal matrix
Assumption already taken into account in multi-factor models
A general framework with systemic and systematic risks
By means of spatial matrices we can impose a structure on matrix A andrewrite the simultaneous equation system
A = I − ρW (9)
Rt = ρWRt + BFt + εt (10)
The coefficient ρ represents the impact coming from neighbours and by nowwe assume it is a scalar
This simultaneous equation system corresponds to a Spatial Auto RegressionPanel model where the covariates (risk factors) are common across allsubjects (at least in a simplified representation)
A general framework with systemic and systematic risks
The model is similar to Spatial Econometric approaches, in particular theSpatial Auto Regression, see the books by Anselin (1988) and LeSage andKelley (2009), among others, and therein cited references
Being (potentially) applied on a large cross-section with repeatedobservations over time, the model is also related to the Spatial Panelliterature, see Elhorst (2003) and Anselin (2006)
The model might be also generalized to the spatio-temporal approacheswhere dynamic behaviours are introduced in the model structure
A general framework with systemic and systematic risks
If the reference (the true) model becomes
ARt = BFt + εt (11)
The parameters in B are the structural betas while standard linear factormodels would estimate reduced-form betas from the system
Rt = (A−1B)Ft + A−1εt (12)
= BFt + ηt (13)
Therefore, the model we propose might capture some of the observedcorrelation across idiosyncratic residuals observed in reduced form linearfactor models
A general framework with systemic and systematic risks
If the reference (the true) model becomes
ARt = BFt + εt (11)
The parameters in B are the structural betas while standard linear factormodels would estimate reduced-form betas from the system
Rt = (A−1B)Ft + A−1εt (12)
= BFt + ηt (13)
Therefore, the model we propose might capture some of the observedcorrelation across idiosyncratic residuals observed in reduced form linearfactor models
A general framework with systemic and systematic risks
If the reference (the true) model becomes
ARt = BFt + εt (11)
The parameters in B are the structural betas while standard linear factormodels would estimate reduced-form betas from the system
Rt = (A−1B)Ft + A−1εt (12)
= BFt + ηt (13)
Therefore, the model we propose might capture some of the observedcorrelation across idiosyncratic residuals observed in reduced form linearfactor models
A general framework with systemic and systematic risks
We can play around this decomposition to recover a more insightful one
ΣR = A−1BΣFB′ (A−1)′ + A−1Ω
(A−1
)′(16)
= BΣF B′ +AΩA′ (17)
= BΣF B′ +AΩA′ ± BΣFB
′ ± Ω (18)
= BΣFB′︸ ︷︷ ︸
i
+ Ω︸︷︷︸ii
+(BΣF B
′ − BΣFB′)︸ ︷︷ ︸
iii
+ (AΩA′ − Ω)︸ ︷︷ ︸iv
(19)
We have thus four terms in the risk decomposition
i The structural systematic componentii The structural idiosyncratic componentiii The systemic impact on the structural systematic componentiv The systemic impact on the idiosyncratic component
A general framework with systemic and systematic risks
Question: is the proposed framework providing insightful features?
Simulations: 100 assets, common factor volatility 15% yearly, betas to thecommon factor U ∼ (0.8, 1.2), idiosyncratic volatilities U ∼ (20%, 40%)
Spatial matrices W : ”market matrix”, all asset cross-dependent, 1k1′k − Ik ;”two-neighbours”, tri-diagonal matrix; ”random”, W elements followswi ∼ Bern (0.3)
A general framework with systemic and systematic risks
Relevant generalizations of the proposed framework
Evaluate alternative designs for common factorsSystemic links are time-dependent: deal with dynamics into parametermatricesSystemic impacts might be asset specific: make the ρ asset-specific
A general framework with systemic and systematic risks
Estimation of the spatial (or weight) matrices might be performed on arelatively low frequency or when extraordinary events take place
Estimates of the matrices W might be valid for sub-samples, or, say,before/during/after crises
The matrices Wt capture the dynamic in the links across assets, while thespatial coefficients R represents the impact on each asset of the neighbors,and are assumed to be time-independent
When the model is applied to high frequency data (weekly/daily)heteroskedasticity in the idiosyncratic component (and factors) must betaken into account
Note that the time-change in the Wt induces a form of heteroskedasticty onthe reduced-form model even when the underlying data have a low frequency(monthly/quarterly)
Granger causality model used to define the Spatial Matrix
Consider a set M of series on which we want to identify systemic links
Focus on two series of interest Xt and Yt taken from M
Xt =∑m
j=1 ajXt−j +∑m
j=1 bjYt−j +∑m
j=1 cjZt−j +∑m
j=1 djFt−j + εi
Yt =∑m
j=1 ejXt−j +∑m
j=1 rjYt−j +∑m
j=1 gjZt−j +∑m
j=1 hjFt−j + ηi
In addition to the causing series the equations include the effect of a commonfactor Ft and two additional background series included in Zt taken from M
The link between the Granger Causality and the Network analysis is theAdjacency Matrix A
In Network analysis, assuming that we have N series, the adjacency matrix isN × N with values determining the existence of links and their strength
The P-value matrix is recast into an Adjacency matrix
In out case, if the series i causes, in the sense of Granger, the series j , at agiven confidence level, then in A, the element aij = 1 otherwise aij = 0
Starting from adjacency matrix we are able to compute Network measures,but Adjacency matrices are also Spatial matrices W
We consider the industrial sector indices available from the Kenneth Frenchwebsite
We take the decomposition of the market into 48 economic sectors/industries
The market proxy (the common factor) is also recovered from the samesource (composite index of NYSE-AMEX-NASDAQ) and is used as theunique common factor
Data are considered at the daily and monthly frequencies
Networks, monitoring connections across economic sectors, have beenestimated by means of Granger Causality tests on daily data depurated byGarch(1,1)
Estimation of the networks is based on a daily date over yearly samples
We thus have a sequence of matrices Wt with time index evolving over years
On spatial returns models estimated on frequencies higher than the year thisinduces a time variation in the model coefficients and mild heteroskedasticityover reduced-form innovations