Network Connectivity and Systematic Risk

Size: px
Start display at page:

Download "Network Connectivity and Systematic Risk"

Transcription

1 Network Connectivity and Systematic Risk Monica Billio 1 Massimiliano Caporin 2 Roberto Panzica 3 Loriana Pelizzon 1,3 1 University Ca Foscari Venezia (Italy) 2 University of Padova (Italy) 3 Goethe University Frankfurt (Germany) March, 2015 Billio, Caporin, Panzica and Pelizzon N&S March, / 47

2 Research questions Introduction There is a general agreement on the traditional decomposition of an asset (portfolio) total risk into systematic and idiosyncratic components following the 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 network interconnections/systemic risks that affect asset pricing Billio, Caporin, Panzica and Pelizzon N&S March, / 47

3 Research questions (Challenging) Research questions What is the impact of network interconnections on the asset return loading to common factors? How does network interconncetions affect asset pricing in a factor model? Does network interconnections endanger the power of diversification? Billio, Caporin, Panzica and Pelizzon N&S March, / 47

4 Literature review - Part I Literature review An increasing literature investigates the role of interconnections between different firms and sectors, functioning as a potential propagation mechanism of idiosyncratic shocks throughout the economy. Canonical idea: microeconomic shocks average out and thus, only have negligible aggregate effects (Lucas, 1977, among others). Similarly, these shocks have little impact on asset prices. However: Acemoglou et al. (2011) use network structure to show the possibility that aggregate 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). Billio, Caporin, Panzica and Pelizzon N&S March, / 47

5 Literature review - Part I Measuring systemic links Role of idiosyncratic risk in asset pricing: The CAPM predicts that only systematic risk is priced and expected excess returns satisfy two-fund separation. This prediction is contradicted by: Ozsoylev and Walden (2011): study a static model of asset price formation in large information networks, mainly centred on the relation between price volatility and network connectedness. Ang, Hodrick, Xing, and Zhang (2006): who show that idiosyncratic volatility risk is priced in the cross-section of expected stock returns, a regularity which is not subsumed by size, book-to-market, momentum, or liquidity effects. Buraschi and Porchia (2014) and Branger et al. (2014): dynamic network connectivity has implications on diversification and asset pricing Billio, Caporin, Panzica and Pelizzon N&S March, / 47

6 Literature review - Part I Measuring systematic risk Traditional models consider several risk factors, one of them being the market Expected returns depend on risk premiums of common factors and betas (loadings) to the factors Standard decomposition of assets (and portfolios) total risk into a systematic component (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 impact in a portfolio Billio, Caporin, Panzica and Pelizzon N&S March, / 47

7 Literature review - Part I Pricing and diversification in multifactor models General multi-factor model for a k dimensional vector of risky assets (m risk factors) R t = E [R t ] + BF t + ɛ t (1) Expected returns depend on the factor risk premiums Λ E [R t ] = r f + BΛ (2) Standard total risk decomposition VAR [R t ] = BVAR [F t ] B + VAR [ɛ t ] (3) Σ R = BΣ F B + Ω (4) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

8 Literature review - Part I Pricing and diversification in multifactor models Portfolio risk decomposition (ω being a k dimensional vector of portfolio weights) VAR [ω R t ] = ω BVAR [F t ] B ω + ω VAR [ɛ t ] ω (5) ω Σ R ω = ω BΣ F B ω + ω Ωω (6) Diversification benefit lim k ω Ωω = ν (7) Special case: uncorrelated idiosyncratic shocks with average variance σ 2 lim k ω Ωω = 1 k σ2 = 0 (8) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

9 Systemic and systematic risks Adding network connections in multifactor models Network connections represent contemporaneous relations across assets that co-exists with the dependence on common risk factors Network connections (A) are contemporaneous relations across endogenous variables A (R t E [R t ]) = BF t + ɛ t (9) The simultaneous equation system above is not identified unless we impose some restriction; k number of assets is much larger than m the number of factors Assumption 1: the idiosyncratic shocks are uncorrelated, that is Ω is a diagonal matrix Assumption already taken into account in multi-factor models Billio, Caporin, Panzica and Pelizzon N&S March, / 47

10 Systemic and systematic risks Adding Network connections in multifactor models Assumption 2: In networks, nodes are connected (in general) to a subset of the network total number of nodes, where connections represent links across assets; shocks are transmitted through the network Intuition: connected assets are neighbours assets Spatial Econometrics tools introduced to capture the spatial dependence across subjects Billio, Caporin, Panzica and Pelizzon N&S March, / 47

11 Systemic and systematic risks Adding Network connections in multifactor models Networks can be used to define spatial matrices An example of a spatial matrix (10) Spatial matrices can be row normalized Spatial matrices might be generalized in such a way values are associated with the intensity of the link across assets Billio, Caporin, Panzica and Pelizzon N&S March, / 47

12 Systemic and systematic risks Adding Network connections in multifactor models An example of a network Networks provide information on the existence of links across assets and on the strength/intensity of the link Networks can be represented as spatial matrices Billio, Caporin, Panzica and Pelizzon N&S March, / 47

13 Systemic and systematic risks A general framework with Network connections and systematic risks By means of spatial matrices we can impose a structure on matrix A and rewrite the simultaneous equation system A = I ρw (11) (R t E [R t ]) = ρw (R t E [R t ]) + BF t + ɛ t (12) The coefficient ρ represents the impact coming from neighbours and by now we assume it is a scalar This simultaneous equation system corresponds to a Spatial Auto Regression Panel model where the covariates (risk factors) are common across all subjects (at least in a simplified representation) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

14 Systemic and systematic risks Literature review - Part II Few works with similar intuition Fernandez (2011) adds a spatial term to the CAPM for Value-at-Risk estimation and recovers the W from correlations Fernandez-Aviles et al. (2012) show that asset proximity should be measured by financial quantities and not geographical locations Arnold et al. (2013) combine different financial closeness measures within a risk management framework Asgharian et al. (2013) use countries economic relations to analyse stock markets co-movements Wied (2013) risk management and parameter stability testing in spatial models for stock market data Keiler and Eder (2013) attach a systemic risk interpretation to the ρ with W coming from correlations Blasques et al. (2014) make the ρ time-varying with W coming from bank s cross-border exposures Billio, Caporin, Panzica and Pelizzon N&S March, / 47

15 Systemic and systematic risks Our contributions Consider a multifactor model and focus on both pricing and diversification effects Measure links starting from a network that capture causality relations Show that network connections act as an inflating factor on the asset loadings to the common factors Show that network elements impact on both the systematic and idiosyncratic risk components Generalize the model in two directions First by adding heterogeneity to the asset reaction to the network links A = I RW (13) R = diag (ρ 1, ρ 2,..., ρ N ) (14) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

16 Systemic and systematic risks Our contributions Then, by allowing for a time-variation in the W matrix A A t = I RW t (15) In this way the matrices W t capture the dynamic in the links across assets (the evolution of the newtork), while the spatial coefficients included in R represent the impact on each asset of the neighbours, and are assumed to be time-independent The W t matrices are also assumed to be known at time t and thus we condition the model estimation and the analysis to their availability We assume the evolution of W t is smooth or acts at a time scale much lower than that affecting the evolution of asset returns (i.e. for monthly returns the W change with, say, a yearly frequency) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

17 Systemic and systematic risks Network links impact on model structure From the simultaneous equation system A t (R t E [R t ]) = BF t + ɛ t (16) The parameters in B are the structural betas; recast the model into the reduced form R t = E [R t ] + (A 1 t B)F t + A 1 t ɛ t (17) = E [R t ] + B t F t + η t (18) Two relevant consequences: the presence of Network links lead to a reduced form model (standard linear factor model) with dynamic betas and whose idiosyncratic shocks are contemporaneously correlated due to the interaction between the W t matrices and the spatial coefficients in R mildly heteroskedastic due to the smooth evolution of W t Billio, Caporin, Panzica and Pelizzon N&S March, / 47

18 Systemic and systematic risks Network links impact on expected returns For simplicity focus on the scalar case ρ with time invariant W (I ρw ) (R t E [R t ]) = BF t + ɛ t (19) It holds that (I ρw ) 1 = I + ρw + ρ 2 W 2 + ρ 3 W 3... (20) Therefore the model corresponds to R t = E [R t ] + BF t + ρ j W j BF t + η t (21) j=1 Billio, Caporin, Panzica and Pelizzon N&S March, / 47

19 Systemic and systematic risks Network links impact on expected returns The expected returns equal E [R t ] = r f + BΛ + ρ j W j BΛ (22) Therefore, as ρ > 0 and elements in W are positive, the presence of systemic links inflates the loading to the factors with an impact on the asset expected returns In addition, if W (or even ρ) change over time we have a dynamic in the expected returns driven by the network links Expected returns increase as a consequence to an increase in ρ or a change in W with subsequent effects on prices The use of asset-specific ρ allows for an heterogeneous reaction of the assets to changes in W j=1 Billio, Caporin, Panzica and Pelizzon N&S March, / 47

20 Systemic and systematic risks Network links impact on risk A risk decomposition applies also in our case, starting from the reduced form model VAR [R t ] = A 1 BVAR [F t ] B ( A 1) + A 1 VAR [ɛ t ] ( A 1) Σ R = A 1 BΣ F B ( A 1) + A 1 Ω ( A 1) (23) (24) In this case, the systematic and idiosyncratic contributions to total risk are also influenced by the existence of Network connections Obviously, if network links are absent, that is ρ = 0 we get back to the traditional risk decomposition Billio, Caporin, Panzica and Pelizzon N&S March, / 47

21 Systemic and systematic risks Network links impact on risk We can play around this decomposition to recover a more insightful one Σ R = A 1 BΣ F B ( A 1) + A 1 Ω ( A 1) (25) = BΣ F B + AΩA (26) = BΣ B F + AΩA ± BΣ F B ± Ω (27) = BΣ F B }{{} + }{{} Ω + ( BΣ F B BΣ F B ) + (AΩA Ω) (28) }{{}}{{} i ii iii iv We have thus four terms in the risk decomposition i The systematic component ii The idiosyncratic component iii The network impact on the systematic component iv The network impact on the idiosyncratic component Billio, Caporin, Panzica and Pelizzon N&S March, / 47

22 Systemic and systematic risks Network links impact on risk This has effects on the diversification benefits which can be analytically derived in a special case Consider K uncorrelated idiosyncratic shocks with average variance σ 2 and a W matrix where all assets are linked to each other, we have lim K ω AΩ η A ω = K + ρ 2 (K + ρ) 2 (ρ 1) 2 σ2 = 0 (29) Diversification benefits still present but the decrease of the idiosyncratic component of the portfolio variance is much slower Billio, Caporin, Panzica and Pelizzon N&S March, / 47

23 Systemic and systematic risks Network links impact on risk Portfolio idiosyncratic risk across different ρ levels and increasing number of assets. The case ρ = 0 corresponds to the absence of spatial links and is the standard result for diversification benefits. Billio, Caporin, Panzica and Pelizzon N&S March, / 47

24 Systemic and systematic risks Simulated examples Question: is the proposed framework providing insightful features? Simulations: 100 assets, common factor volatility 15% yearly, betas to the common factor U (0.8, 1.2), idiosyncratic volatilities U (20%, 40%) Spatial matrices W : market matrix, all asset cross-dependent, 1 k 1 k I k; two-neighbours, tri-diagonal matrix; random, W elements follows w i Bern (0.3) Evaluate the effects of different ρ values Billio, Caporin, Panzica and Pelizzon N&S March, / 47

25 Systemic and systematic risks Simulated examples Beta values across assets: structural betas (in blue) and augmented betas (in red) across different spatial matrices W. Billio, Caporin, Panzica and Pelizzon N&S March, / 47

26 Systemic and systematic risks Simulated examples Beta values across assets: structural betas (in blue) and augmented betas (in red) across different values for ρ with the random matrix W. Billio, Caporin, Panzica and Pelizzon N&S March, / 47

27 Systemic and systematic risks Simulated examples Relative variance decomposition without network links (ρ = 0) across the 100 simulated assets Billio, Caporin, Panzica and Pelizzon N&S March, / 47

28 Systemic and systematic risks Simulated examples Relative variance decomposition with network links (ρ = 0.25) and market matrix W across the 100 simulated assets Billio, Caporin, Panzica and Pelizzon N&S March, / 47

29 Systemic and systematic risks Simulated examples Relative variance decomposition with systemic links (ρ = 0.5) and random matrix W across the 100 simulated assets Billio, Caporin, Panzica and Pelizzon N&S March, / 47

30 Systemic and systematic risks Simulated examples 1/N portfolio variance decomposition across different values of ρ with the same random matrix W (relative decomposition) Billio, Caporin, Panzica and Pelizzon N&S March, / 47

31 Systemic and systematic risks Simulated examples 1/N portfolio idiosyncratic component variance - relative contraction with increasing N and across ρ values Billio, Caporin, Panzica and Pelizzon N&S March, / 47

32 Systemic and systematic risks Model estimation We do not impose a method for estimating the network links, those can come from any approach or measurement framework; we do impose that the W is known before estimating the other model parameters In this work we estimate W by means of Granger causality, see Billio et al. (2012) Estimation of the factor loadings, spatial coefficients, and idiosyncratic shocks by Full Information Maximum Likelihood; computational advantages come from the possibility of concentrating out the factor loadings (and the error variances) If needed impose technical assumptions guaranteeing the non singularity of A t and the identification of the parameters in R Billio, Caporin, Panzica and Pelizzon N&S March, / 47

33 Empirical example Data description We consider the industrial sector indexes available from the Kenneth French website over the range , thus allowing for pre-crisis ( ) and crisis + post-crisis ( ) samples of the same length (7 years) We take the decomposition of the market into 48 economic sectors/industries We recover the common factors from the same source: the market index (composite index of NYSE-AMEX-NASDAQ); the three additional factors of Fama-French and Carhart, SMB, HML and MOM We make use of daily data to estimate the networks and monthly data to estimate the full model Billio, Caporin, Panzica and Pelizzon N&S March, / 47

34 Empirical example Estimating networks We estimate networks, monitoring connections across economic sectors, by means of Granger Causality tests on daily data depurated by Garch(1,1) Estimation of the networks is based on a daily date over yearly samples We thus have a sequence of matrices W t with time index evolving over years We stress we thus have a reduced form model with heteroskedastic innovations Billio, Caporin, Panzica and Pelizzon N&S March, / 47

35 Empirical example Estimating networks 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 X t and Y t taken from M X t = m j=1 a jx t j + m j=1 b jy t j + m j=1 c jz t j + m j=1 d jf t j + ɛ i Y t = m j=1 e jx t j + m j=1 r jy t j + m j=1 g jz t j + m j=1 h jf t j + η i In addition to the causing series the equations include the effect of a common factor F t and two additional background series included in Z t taken from M Billio, Caporin, Panzica and Pelizzon N&S March, / 47

36 Empirical example Estimating networks For each pair of causing-caused series X t and Y t we run a Granger Causality test for each of possible pair of background series Z t Y G X if b j is different from 0 X G Y if e j is different from 0 If both b j and e j are different from 0, feedback relation We pick then the worst case, the higher p-value on causality tests, and consider it as our reference quantity obtaining a P-Value Matrix Billio, Caporin, Panzica and Pelizzon N&S March, / 47

37 Empirical example Estimating networks The link between the Granger Causality and the Network analysis is the Adjacency Matrix A In Network analysis, assuming that we have N series, the adjacency matrix is N 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 a given confidence level, then in A, the element a ij = 1 otherwise a ij = 0 Starting from adjacency matrix we are able to compute Network measures, but Adjacency matrices are also Spatial matrices W Billio, Caporin, Panzica and Pelizzon N&S March, / 47

38 Empirical example Estimated networks Estimated network for the year 2002 Billio, Caporin, Panzica and Pelizzon N&S March, / 47

39 Empirical example Estimated networks Estimated network for the year 2008 Billio, Caporin, Panzica and Pelizzon N&S March, / 47

40 Empirical example Model output Estimated ρ for selected sectors and over the two samples Billio, Caporin, Panzica and Pelizzon N&S March, / 47

41 Empirical example Model output The estimated reduced form beta parameters B t = (I RW t ) 1 B are time-varying given that the W matrix is time-varying To summarize findings, we take averages of the reduced form betas over years and recover the average impact of network links on the reduced form betas Focus mostly on market impact Billio, Caporin, Panzica and Pelizzon N&S March, / 47

42 Empirical example Model output Estimated β for selected sectors and over different periods Billio, Caporin, Panzica and Pelizzon N&S March, / 47

43 Empirical example Model output Estimated Sector volatility decomposition Billio, Caporin, Panzica and Pelizzon N&S March, / 47

44 Empirical example Model output Estimated Sector volatility decomposition Billio, Caporin, Panzica and Pelizzon N&S March, / 47

45 Empirical example Model output Estimated equally weighted portfolio variance Billio, Caporin, Panzica and Pelizzon N&S March, / 47

46 Empirical example Model output Main findings Network impact coefficients ρ i increase during the crisis period leading to a larger impact of connections on stock returns Total exposure to factor shocks increases for most sectors Billio, Caporin, Panzica and Pelizzon N&S March, / 47

47 Empirical example Future developments Deeper evaluation of risk factor exposure and pricing implications; analysis of diversification impact of network exposure Time-variation in the ρ coefficients Different design of the W matrices taking into account the strength of the relation across subjects Comparison between US and Europe Billio, Caporin, Panzica and Pelizzon N&S March, / 47

Network Connectivity, Systematic Risk and Diversification

Network Connectivity, Systematic Risk and Diversification Network Connectivity, Systematic Risk and Diversification Monica Billio 1 Massimiliano Caporin 2 Roberto Panzica 3 Loriana Pelizzon 1,3 1 University Ca Foscari Venezia (Italy) 2 University of Padova (Italy)

More information

Estimation and model-based combination of causality networks

Estimation and model-based combination of causality networks Estimation and model-based combination of causality networks Giovani Bonaccolto Massimiliano Caporin Roberto Panzica This version: November 26, 2016 Abstract Causality is a widely-used concept in theoretical

More information

Multivariate GARCH models.

Multivariate GARCH models. Multivariate GARCH models. Financial market volatility moves together over time across assets and markets. Recognizing this commonality through a multivariate modeling framework leads to obvious gains

More information

Estimating Global Bank Network Connectedness

Estimating Global Bank Network Connectedness Estimating Global Bank Network Connectedness Mert Demirer (MIT) Francis X. Diebold (Penn) Laura Liu (Penn) Kamil Yılmaz (Koç) September 22, 2016 1 / 27 Financial and Macroeconomic Connectedness Market

More information

Econ671 Factor Models: Principal Components

Econ671 Factor Models: Principal Components Econ671 Factor Models: Principal Components Jun YU April 8, 2016 Jun YU () Econ671 Factor Models: Principal Components April 8, 2016 1 / 59 Factor Models: Principal Components Learning Objectives 1. Show

More information

Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions

Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions Mikhail Anufriev a b a Economics, University of Technology, Sydney b Business

More information

R = µ + Bf Arbitrage Pricing Model, APM

R = µ + Bf Arbitrage Pricing Model, APM 4.2 Arbitrage Pricing Model, APM Empirical evidence indicates that the CAPM beta does not completely explain the cross section of expected asset returns. This suggests that additional factors may be required.

More information

Ross (1976) introduced the Arbitrage Pricing Theory (APT) as an alternative to the CAPM.

Ross (1976) introduced the Arbitrage Pricing Theory (APT) as an alternative to the CAPM. 4.2 Arbitrage Pricing Model, APM Empirical evidence indicates that the CAPM beta does not completely explain the cross section of expected asset returns. This suggests that additional factors may be required.

More information

Financial Econometrics Short Course Lecture 3 Multifactor Pricing Model

Financial Econometrics Short Course Lecture 3 Multifactor Pricing Model Financial Econometrics Short Course Lecture 3 Multifactor Pricing Model Oliver Linton obl20@cam.ac.uk Renmin University Financial Econometrics Short Course Lecture 3 MultifactorRenmin Pricing University

More information

Identifying Aggregate Liquidity Shocks with Monetary Policy Shocks: An Application using UK Data

Identifying Aggregate Liquidity Shocks with Monetary Policy Shocks: An Application using UK Data Identifying Aggregate Liquidity Shocks with Monetary Policy Shocks: An Application using UK Data Michael Ellington and Costas Milas Financial Services, Liquidity and Economic Activity Bank of England May

More information

Measuring interconnectedness between financial institutions with Bayesian time-varying VARs

Measuring interconnectedness between financial institutions with Bayesian time-varying VARs Measuring interconnectedness between financial institutions with Bayesian time-varying VARs Financial Risk & Network Theory Marco Valerio Geraci 1,2 Jean-Yves Gnabo 2 1 ECARES, Université libre de Bruxelles

More information

Regression: Ordinary Least Squares

Regression: Ordinary Least Squares Regression: Ordinary Least Squares Mark Hendricks Autumn 2017 FINM Intro: Regression Outline Regression OLS Mathematics Linear Projection Hendricks, Autumn 2017 FINM Intro: Regression: Lecture 2/32 Regression

More information

MFE Financial Econometrics 2018 Final Exam Model Solutions

MFE Financial Econometrics 2018 Final Exam Model Solutions MFE Financial Econometrics 2018 Final Exam Model Solutions Tuesday 12 th March, 2019 1. If (X, ε) N (0, I 2 ) what is the distribution of Y = µ + β X + ε? Y N ( µ, β 2 + 1 ) 2. What is the Cramer-Rao lower

More information

Factor Models for Asset Returns. Prof. Daniel P. Palomar

Factor Models for Asset Returns. Prof. Daniel P. Palomar Factor Models for Asset Returns Prof. Daniel P. Palomar The Hong Kong University of Science and Technology (HKUST) MAFS6010R- Portfolio Optimization with R MSc in Financial Mathematics Fall 2018-19, HKUST,

More information

The Slow Convergence of OLS Estimators of α, β and Portfolio. β and Portfolio Weights under Long Memory Stochastic Volatility

The Slow Convergence of OLS Estimators of α, β and Portfolio. β and Portfolio Weights under Long Memory Stochastic Volatility The Slow Convergence of OLS Estimators of α, β and Portfolio Weights under Long Memory Stochastic Volatility New York University Stern School of Business June 21, 2018 Introduction Bivariate long memory

More information

Commodity Connectedness

Commodity Connectedness Commodity Connectedness Francis X. Diebold (Penn) Laura Liu (Penn) Kamil Yılmaz (Koç) November 9, 2016 1 / 29 Financial and Macroeconomic Connectedness Portfolio concentration risk Credit risk Counterparty

More information

A primer on Structural VARs

A primer on Structural VARs A primer on Structural VARs Claudia Foroni Norges Bank 10 November 2014 Structural VARs 1/ 26 Refresh: what is a VAR? VAR (p) : where y t K 1 y t = ν + B 1 y t 1 +... + B p y t p + u t, (1) = ( y 1t...

More information

Model Mis-specification

Model Mis-specification Model Mis-specification Carlo Favero Favero () Model Mis-specification 1 / 28 Model Mis-specification Each specification can be interpreted of the result of a reduction process, what happens if the reduction

More information

Inference in VARs with Conditional Heteroskedasticity of Unknown Form

Inference in VARs with Conditional Heteroskedasticity of Unknown Form Inference in VARs with Conditional Heteroskedasticity of Unknown Form Ralf Brüggemann a Carsten Jentsch b Carsten Trenkler c University of Konstanz University of Mannheim University of Mannheim IAB Nuremberg

More information

Financial Econometrics Return Predictability

Financial Econometrics Return Predictability Financial Econometrics Return Predictability Eric Zivot March 30, 2011 Lecture Outline Market Efficiency The Forms of the Random Walk Hypothesis Testing the Random Walk Hypothesis Reading FMUND, chapter

More information

Applications of Random Matrix Theory to Economics, Finance and Political Science

Applications of Random Matrix Theory to Economics, Finance and Political Science Outline Applications of Random Matrix Theory to Economics, Finance and Political Science Matthew C. 1 1 Department of Economics, MIT Institute for Quantitative Social Science, Harvard University SEA 06

More information

Structural VAR Models and Applications

Structural VAR Models and Applications Structural VAR Models and Applications Laurent Ferrara 1 1 University of Paris Nanterre M2 Oct. 2018 SVAR: Objectives Whereas the VAR model is able to capture efficiently the interactions between the different

More information

ASSET PRICING MODELS

ASSET PRICING MODELS ASSE PRICING MODELS [1] CAPM (1) Some notation: R it = (gross) return on asset i at time t. R mt = (gross) return on the market portfolio at time t. R ft = return on risk-free asset at time t. X it = R

More information

Bayesian Graphical Models for Structural Vector AutoregressiveMarch Processes 21, / 1

Bayesian Graphical Models for Structural Vector AutoregressiveMarch Processes 21, / 1 Bayesian Graphical Models for Structural Vector Autoregressive Processes Daniel Ahelegbey, Monica Billio, and Roberto Cassin (2014) March 21, 2015 Bayesian Graphical Models for Structural Vector AutoregressiveMarch

More information

Nominal Rigidity and the Idiosyncratic Origin of Aggregate. Fluctuations

Nominal Rigidity and the Idiosyncratic Origin of Aggregate. Fluctuations Nominal Rigidity and the Idiosyncratic Origin of Aggregate Fluctuations Ernesto Pasten, Raphael Schoenle, Michael Weber Februay 2016 PRELIMINARY AND INCOMPLETE PLEASE DO NOT CITE Abstract We study the

More information

Identifying Financial Risk Factors

Identifying Financial Risk Factors Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition Lisa Goldberg Alex Shkolnik Berkeley Columbia Meeting in Engineering and Statistics 24 March 2016 Outline 1 A Brief History of Factor

More information

Generalized Autoregressive Score Models

Generalized Autoregressive Score Models Generalized Autoregressive Score Models by: Drew Creal, Siem Jan Koopman, André Lucas To capture the dynamic behavior of univariate and multivariate time series processes, we can allow parameters to be

More information

Equity risk factors and the Intertemporal CAPM

Equity risk factors and the Intertemporal CAPM Equity risk factors and the Intertemporal CAPM Ilan Cooper 1 Paulo Maio 2 1 Norwegian Business School (BI) 2 Hanken School of Economics BEROC Conference, Minsk Outline 1 Motivation 2 Cross-sectional tests

More information

Financial Econometrics Lecture 6: Testing the CAPM model

Financial Econometrics Lecture 6: Testing the CAPM model Financial Econometrics Lecture 6: Testing the CAPM model Richard G. Pierse 1 Introduction The capital asset pricing model has some strong implications which are testable. The restrictions that can be tested

More information

Identifying SVARs with Sign Restrictions and Heteroskedasticity

Identifying SVARs with Sign Restrictions and Heteroskedasticity Identifying SVARs with Sign Restrictions and Heteroskedasticity Srečko Zimic VERY PRELIMINARY AND INCOMPLETE NOT FOR DISTRIBUTION February 13, 217 Abstract This paper introduces a new method to identify

More information

Supply Chain Network Structure and Risk Propagation

Supply Chain Network Structure and Risk Propagation Supply Chain Network Structure and Risk Propagation John R. Birge 1 1 University of Chicago Booth School of Business (joint work with Jing Wu, Chicago Booth) IESE Business School Birge (Chicago Booth)

More information

A Guide to Modern Econometric:

A Guide to Modern Econometric: A Guide to Modern Econometric: 4th edition Marno Verbeek Rotterdam School of Management, Erasmus University, Rotterdam B 379887 )WILEY A John Wiley & Sons, Ltd., Publication Contents Preface xiii 1 Introduction

More information

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology

FE670 Algorithmic Trading Strategies. Stevens Institute of Technology FE670 Algorithmic Trading Strategies Lecture 8. Robust Portfolio Optimization Steve Yang Stevens Institute of Technology 10/17/2013 Outline 1 Robust Mean-Variance Formulations 2 Uncertain in Expected Return

More information

Financial Econometrics

Financial Econometrics Financial Econometrics Multivariate Time Series Analysis: VAR Gerald P. Dwyer Trinity College, Dublin January 2013 GPD (TCD) VAR 01/13 1 / 25 Structural equations Suppose have simultaneous system for supply

More information

Empirical properties of large covariance matrices in finance

Empirical properties of large covariance matrices in finance Empirical properties of large covariance matrices in finance Ex: RiskMetrics Group, Geneva Since 2010: Swissquote, Gland December 2009 Covariance and large random matrices Many problems in finance require

More information

The Conditional Pricing of Systematic and Idiosyncratic Risk in the UK Equity Market. Niall O Sullivan b Francesco Rossi c. This version: July 2014

The Conditional Pricing of Systematic and Idiosyncratic Risk in the UK Equity Market. Niall O Sullivan b Francesco Rossi c. This version: July 2014 The Conditional Pricing of Systematic and Idiosyncratic Risk in the UK Equity Market John Cotter a Niall O Sullivan b Francesco Rossi c This version: July 2014 Abstract We test whether firm idiosyncratic

More information

A Non-Parametric Approach of Heteroskedasticity Robust Estimation of Vector-Autoregressive (VAR) Models

A Non-Parametric Approach of Heteroskedasticity Robust Estimation of Vector-Autoregressive (VAR) Models Journal of Finance and Investment Analysis, vol.1, no.1, 2012, 55-67 ISSN: 2241-0988 (print version), 2241-0996 (online) International Scientific Press, 2012 A Non-Parametric Approach of Heteroskedasticity

More information

Introduction to Macroeconomics

Introduction to Macroeconomics Introduction to Macroeconomics Martin Ellison Nuffi eld College Michaelmas Term 2018 Martin Ellison (Nuffi eld) Introduction Michaelmas Term 2018 1 / 39 Macroeconomics is Dynamic Decisions are taken over

More information

LECTURE 3 The Effects of Monetary Changes: Statistical Identification. September 5, 2018

LECTURE 3 The Effects of Monetary Changes: Statistical Identification. September 5, 2018 Economics 210c/236a Fall 2018 Christina Romer David Romer LECTURE 3 The Effects of Monetary Changes: Statistical Identification September 5, 2018 I. SOME BACKGROUND ON VARS A Two-Variable VAR Suppose the

More information

News Shocks, Information Flows and SVARs

News Shocks, Information Flows and SVARs 12-286 Research Group: Macroeconomics March, 2012 News Shocks, Information Flows and SVARs PATRICK FEVE AND AHMAT JIDOUD News Shocks, Information Flows and SVARs Patrick Feve Toulouse School of Economics

More information

Identifying the Monetary Policy Shock Christiano et al. (1999)

Identifying the Monetary Policy Shock Christiano et al. (1999) Identifying the Monetary Policy Shock Christiano et al. (1999) The question we are asking is: What are the consequences of a monetary policy shock a shock which is purely related to monetary conditions

More information

APT looking for the factors

APT looking for the factors APT looking for the factors February 5, 2018 Contents 1 the Arbitrage Pricing Theory 2 1.1 One factor models............................................... 2 1.2 2 factor models.................................................

More information

A Bootstrap Test for Causality with Endogenous Lag Length Choice. - theory and application in finance

A Bootstrap Test for Causality with Endogenous Lag Length Choice. - theory and application in finance CESIS Electronic Working Paper Series Paper No. 223 A Bootstrap Test for Causality with Endogenous Lag Length Choice - theory and application in finance R. Scott Hacker and Abdulnasser Hatemi-J April 200

More information

1. Shocks. This version: February 15, Nr. 1

1. Shocks. This version: February 15, Nr. 1 1. Shocks This version: February 15, 2006 Nr. 1 1.3. Factor models What if there are more shocks than variables in the VAR? What if there are only a few underlying shocks, explaining most of fluctuations?

More information

Time-Varying Vector Autoregressive Models with Structural Dynamic Factors

Time-Varying Vector Autoregressive Models with Structural Dynamic Factors Time-Varying Vector Autoregressive Models with Structural Dynamic Factors Paolo Gorgi, Siem Jan Koopman, Julia Schaumburg http://sjkoopman.net Vrije Universiteit Amsterdam School of Business and Economics

More information

Macroeconomics Theory II

Macroeconomics Theory II Macroeconomics Theory II Francesco Franco FEUNL February 2016 Francesco Franco Macroeconomics Theory II 1/23 Housekeeping. Class organization. Website with notes and papers as no "Mas-Collel" in macro

More information

Evaluating Latent and Observed Factors in Macroeconomics and Finance. September 15, Preliminary: Comments Welcome

Evaluating Latent and Observed Factors in Macroeconomics and Finance. September 15, Preliminary: Comments Welcome Evaluating Latent and Observed Factors in Macroeconomics and Finance Jushan Bai Serena Ng September 15, 2003 Preliminary: Comments Welcome Abstract Common factors play an important role in many disciplines

More information

Portfolio Optimization Using a Block Structure for the Covariance Matrix

Portfolio Optimization Using a Block Structure for the Covariance Matrix Journal of Business Finance & Accounting Journal of Business Finance & Accounting, 39(5) & (6), 806 843, June/July 202, 0306-686X doi: 0/j468-595720202279x Portfolio Optimization Using a Block Structure

More information

Beta Is Alive, Well and Healthy

Beta Is Alive, Well and Healthy Beta Is Alive, Well and Healthy Soosung Hwang * Cass Business School, UK Abstract In this study I suggest some evidence that the popular cross-sectional asset pricing test proposed by Black, Jensen, and

More information

Factor models. March 13, 2017

Factor models. March 13, 2017 Factor models March 13, 2017 Factor Models Macro economists have a peculiar data situation: Many data series, but usually short samples How can we utilize all this information without running into degrees

More information

Lecture 2. (1) Permanent Income Hypothesis (2) Precautionary Savings. Erick Sager. February 6, 2018

Lecture 2. (1) Permanent Income Hypothesis (2) Precautionary Savings. Erick Sager. February 6, 2018 Lecture 2 (1) Permanent Income Hypothesis (2) Precautionary Savings Erick Sager February 6, 2018 Econ 606: Adv. Topics in Macroeconomics Johns Hopkins University, Spring 2018 Erick Sager Lecture 2 (2/6/18)

More information

17 Factor Models and Principal Components

17 Factor Models and Principal Components 17 Factor Models and Principal Components 17.1 Dimension Reduction High-dimensional data can be challenging to analyze. They are difficult to visualize, need extensive computer resources, and often require

More information

The Bond Pricing Implications of Rating-Based Capital Requirements. Internet Appendix. This Version: December Abstract

The Bond Pricing Implications of Rating-Based Capital Requirements. Internet Appendix. This Version: December Abstract The Bond Pricing Implications of Rating-Based Capital Requirements Internet Appendix This Version: December 2017 Abstract This Internet Appendix examines the robustness of our main results and presents

More information

Intro VEC and BEKK Example Factor Models Cond Var and Cor Application Ref 4. MGARCH

Intro VEC and BEKK Example Factor Models Cond Var and Cor Application Ref 4. MGARCH ntro VEC and BEKK Example Factor Models Cond Var and Cor Application Ref 4. MGARCH JEM 140: Quantitative Multivariate Finance ES, Charles University, Prague Summer 2018 JEM 140 () 4. MGARCH Summer 2018

More information

Measuring interconnectedness between financial institutions with Bayesian time-varying vector autoregressions

Measuring interconnectedness between financial institutions with Bayesian time-varying vector autoregressions Introduction Previous Studies Empirical methodology Empirical analysis Conclusion References Appendix Measuring interconnectedness between financial institutions with Bayesian time-varying vector autoregressions

More information

Vector Auto-Regressive Models

Vector Auto-Regressive Models Vector Auto-Regressive Models Laurent Ferrara 1 1 University of Paris Nanterre M2 Oct. 2018 Overview of the presentation 1. Vector Auto-Regressions Definition Estimation Testing 2. Impulse responses functions

More information

Notes on empirical methods

Notes on empirical methods Notes on empirical methods Statistics of time series and cross sectional regressions 1. Time Series Regression (Fama-French). (a) Method: Run and interpret (b) Estimates: 1. ˆα, ˆβ : OLS TS regression.

More information

VAR Models and Applications

VAR Models and Applications VAR Models and Applications Laurent Ferrara 1 1 University of Paris West M2 EIPMC Oct. 2016 Overview of the presentation 1. Vector Auto-Regressions Definition Estimation Testing 2. Impulse responses functions

More information

ECON3327: Financial Econometrics, Spring 2016

ECON3327: Financial Econometrics, Spring 2016 ECON3327: Financial Econometrics, Spring 2016 Wooldridge, Introductory Econometrics (5th ed, 2012) Chapter 11: OLS with time series data Stationary and weakly dependent time series The notion of a stationary

More information

Endogenous Information Choice

Endogenous Information Choice Endogenous Information Choice Lecture 7 February 11, 2015 An optimizing trader will process those prices of most importance to his decision problem most frequently and carefully, those of less importance

More information

Econometría 2: Análisis de series de Tiempo

Econometría 2: Análisis de series de Tiempo Econometría 2: Análisis de series de Tiempo Karoll GOMEZ kgomezp@unal.edu.co http://karollgomez.wordpress.com Segundo semestre 2016 IX. Vector Time Series Models VARMA Models A. 1. Motivation: The vector

More information

The Econometric Analysis of Mixed Frequency Data with Macro/Finance Applications

The Econometric Analysis of Mixed Frequency Data with Macro/Finance Applications The Econometric Analysis of Mixed Frequency Data with Macro/Finance Applications Instructor: Eric Ghysels Structure of Course It is easy to collect and store large data sets, particularly of financial

More information

ECONOMICS 210C / ECONOMICS 236A MONETARY HISTORY

ECONOMICS 210C / ECONOMICS 236A MONETARY HISTORY Fall 018 University of California, Berkeley Christina Romer David Romer ECONOMICS 10C / ECONOMICS 36A MONETARY HISTORY A Little about GLS, Heteroskedasticity-Consistent Standard Errors, Clustering, and

More information

Linear Factor Models and the Estimation of Expected Returns

Linear Factor Models and the Estimation of Expected Returns Linear Factor Models and the Estimation of Expected Returns Cisil Sarisoy a,, Peter de Goeij b, Bas J.M. Werker c a Department of Finance, CentER, Tilburg University b Department of Finance, Tilburg University

More information

Linear Factor Models and the Estimation of Expected Returns

Linear Factor Models and the Estimation of Expected Returns Linear Factor Models and the Estimation of Expected Returns Cisil Sarisoy, Peter de Goeij and Bas Werker DP 03/2016-020 Linear Factor Models and the Estimation of Expected Returns Cisil Sarisoy a,, Peter

More information

Visualizing VAR s: Regularization and Network Tools for High-Dimensional Financial Econometrics

Visualizing VAR s: Regularization and Network Tools for High-Dimensional Financial Econometrics Visualizing VAR s: Regularization and Network Tools for High-Dimensional Financial Econometrics Francis X. Diebold University of Pennsylvania March 7, 2015 1 / 32 DGP: N-Variable VAR(p), t = 1,..., T Φ(L)x

More information

Financial Times Series. Lecture 12

Financial Times Series. Lecture 12 Financial Times Series Lecture 12 Multivariate Volatility Models Here our aim is to generalize the previously presented univariate volatility models to their multivariate counterparts We assume that returns

More information

DATABASE AND METHODOLOGY

DATABASE AND METHODOLOGY CHAPTER 3 DATABASE AND METHODOLOGY In the present chapter, sources of database used and methodology applied for the empirical analysis has been presented The whole chapter has been divided into three sections

More information

ECON4515 Finance theory 1 Diderik Lund, 5 May Perold: The CAPM

ECON4515 Finance theory 1 Diderik Lund, 5 May Perold: The CAPM Perold: The CAPM Perold starts with a historical background, the development of portfolio theory and the CAPM. Points out that until 1950 there was no theory to describe the equilibrium determination of

More information

University of Pretoria Department of Economics Working Paper Series

University of Pretoria Department of Economics Working Paper Series University of Pretoria Department of Economics Working Paper Series Predicting Stock Returns and Volatility Using Consumption-Aggregate Wealth Ratios: A Nonlinear Approach Stelios Bekiros IPAG Business

More information

Lecture 6: Univariate Volatility Modelling: ARCH and GARCH Models

Lecture 6: Univariate Volatility Modelling: ARCH and GARCH Models Lecture 6: Univariate Volatility Modelling: ARCH and GARCH Models Prof. Massimo Guidolin 019 Financial Econometrics Winter/Spring 018 Overview ARCH models and their limitations Generalized ARCH models

More information

Testing the APT with the Maximum Sharpe. Ratio of Extracted Factors

Testing the APT with the Maximum Sharpe. Ratio of Extracted Factors Testing the APT with the Maximum Sharpe Ratio of Extracted Factors Chu Zhang This version: April, 2008 Abstract. This paper develops a test of the asymptotic arbitrage pricing theory (APT) via the maximum

More information

In modern portfolio theory, which started with the seminal work of Markowitz (1952),

In modern portfolio theory, which started with the seminal work of Markowitz (1952), 1 Introduction In modern portfolio theory, which started with the seminal work of Markowitz (1952), many academic researchers have examined the relationships between the return and risk, or volatility,

More information

The Instability of Correlations: Measurement and the Implications for Market Risk

The Instability of Correlations: Measurement and the Implications for Market Risk The Instability of Correlations: Measurement and the Implications for Market Risk Prof. Massimo Guidolin 20254 Advanced Quantitative Methods for Asset Pricing and Structuring Winter/Spring 2018 Threshold

More information

1 Teaching notes on structural VARs.

1 Teaching notes on structural VARs. Bent E. Sørensen February 22, 2007 1 Teaching notes on structural VARs. 1.1 Vector MA models: 1.1.1 Probability theory The simplest (to analyze, estimation is a different matter) time series models are

More information

This paper develops a test of the asymptotic arbitrage pricing theory (APT) via the maximum squared Sharpe

This paper develops a test of the asymptotic arbitrage pricing theory (APT) via the maximum squared Sharpe MANAGEMENT SCIENCE Vol. 55, No. 7, July 2009, pp. 1255 1266 issn 0025-1909 eissn 1526-5501 09 5507 1255 informs doi 10.1287/mnsc.1090.1004 2009 INFORMS Testing the APT with the Maximum Sharpe Ratio of

More information

Motivation Non-linear Rational Expectations The Permanent Income Hypothesis The Log of Gravity Non-linear IV Estimation Summary.

Motivation Non-linear Rational Expectations The Permanent Income Hypothesis The Log of Gravity Non-linear IV Estimation Summary. Econometrics I Department of Economics Universidad Carlos III de Madrid Master in Industrial Economics and Markets Outline Motivation 1 Motivation 2 3 4 5 Motivation Hansen's contributions GMM was developed

More information

Cascades in Networks and Aggregate Volatility

Cascades in Networks and Aggregate Volatility Cascades in Networks and Aggregate Volatility Daron Acemoglu, Asuman Ozdaglar, and Alireza Tahbaz Salehi First version: August 2010 This version: October 2010 Abstract We provide a general framework for

More information

Is there a flight to quality due to inflation uncertainty?

Is there a flight to quality due to inflation uncertainty? MPRA Munich Personal RePEc Archive Is there a flight to quality due to inflation uncertainty? Bulent Guler and Umit Ozlale Bilkent University, Bilkent University 18. August 2004 Online at http://mpra.ub.uni-muenchen.de/7929/

More information

Sample Exam Questions for Econometrics

Sample Exam Questions for Econometrics Sample Exam Questions for Econometrics 1 a) What is meant by marginalisation and conditioning in the process of model reduction within the dynamic modelling tradition? (30%) b) Having derived a model for

More information

Principal Component Analysis (PCA) Our starting point consists of T observations from N variables, which will be arranged in an T N matrix R,

Principal Component Analysis (PCA) Our starting point consists of T observations from N variables, which will be arranged in an T N matrix R, Principal Component Analysis (PCA) PCA is a widely used statistical tool for dimension reduction. The objective of PCA is to find common factors, the so called principal components, in form of linear combinations

More information

A new test on the conditional capital asset pricing model

A new test on the conditional capital asset pricing model Appl. Math. J. Chinese Univ. 2015, 30(2): 163-186 A new test on the conditional capital asset pricing model LI Xia-fei 1 CAI Zong-wu 2,1 REN Yu 1, Abstract. Testing the validity of the conditional capital

More information

Consumption Risk Sharing over the Business Cycle: the Role of Small Firms Access to Credit Markets

Consumption Risk Sharing over the Business Cycle: the Role of Small Firms Access to Credit Markets 1 Consumption Risk Sharing over the Business Cycle: the Role of Small Firms Access to Credit Markets Mathias Hoffmann & Iryna Shcherbakova-Stewen University of Zurich PhD Topics Lecture, 22 Sep 2014 www.econ.uzh.ch/itf

More information

Volatility. Gerald P. Dwyer. February Clemson University

Volatility. Gerald P. Dwyer. February Clemson University Volatility Gerald P. Dwyer Clemson University February 2016 Outline 1 Volatility Characteristics of Time Series Heteroskedasticity Simpler Estimation Strategies Exponentially Weighted Moving Average Use

More information

Econ 423 Lecture Notes: Additional Topics in Time Series 1

Econ 423 Lecture Notes: Additional Topics in Time Series 1 Econ 423 Lecture Notes: Additional Topics in Time Series 1 John C. Chao April 25, 2017 1 These notes are based in large part on Chapter 16 of Stock and Watson (2011). They are for instructional purposes

More information

Cross-regional Spillover Effects in the Korean Housing Market

Cross-regional Spillover Effects in the Korean Housing Market 1) Cross-regional Spillover Effects in the Korean Housing Market Hahn Shik Lee * and Woo Suk Lee < Abstract > In this paper, we examine cross-regional spillover effects in the Korean housing market, using

More information

Animal Spirits, Fundamental Factors and Business Cycle Fluctuations

Animal Spirits, Fundamental Factors and Business Cycle Fluctuations Animal Spirits, Fundamental Factors and Business Cycle Fluctuations Stephane Dées Srečko Zimic Banque de France European Central Bank January 6, 218 Disclaimer Any views expressed represent those of the

More information

Nonlinear Bivariate Comovements of Asset Prices: Theory and Tests

Nonlinear Bivariate Comovements of Asset Prices: Theory and Tests Nonlinear Bivariate Comovements of Asset Prices: Theory and Tests M. Corazza, A.G. Malliaris, E. Scalco Department of Applied Mathematics University Ca Foscari of Venice (Italy) Department of Economics

More information

International Monetary Policy Spillovers

International Monetary Policy Spillovers International Monetary Policy Spillovers Dennis Nsafoah Department of Economics University of Calgary Canada November 1, 2017 1 Abstract This paper uses monthly data (from January 1997 to April 2017) to

More information

Specification Test Based on the Hansen-Jagannathan Distance with Good Small Sample Properties

Specification Test Based on the Hansen-Jagannathan Distance with Good Small Sample Properties Specification Test Based on the Hansen-Jagannathan Distance with Good Small Sample Properties Yu Ren Department of Economics Queen s University Katsumi Shimotsu Department of Economics Queen s University

More information

Online Appendix (Not intended for Publication): Decomposing the Effects of Monetary Policy Using an External Instruments SVAR

Online Appendix (Not intended for Publication): Decomposing the Effects of Monetary Policy Using an External Instruments SVAR Online Appendix (Not intended for Publication): Decomposing the Effects of Monetary Policy Using an External Instruments SVAR Aeimit Lakdawala Michigan State University December 7 This appendix contains

More information

Comparing Forecast Accuracy of Different Models for Prices of Metal Commodities

Comparing Forecast Accuracy of Different Models for Prices of Metal Commodities Comparing Forecast Accuracy of Different Models for Prices of Metal Commodities João Victor Issler (FGV) and Claudia F. Rodrigues (VALE) August, 2012 J.V. Issler and C.F. Rodrigues () Forecast Models for

More information

Multivariate forecasting with VAR models

Multivariate forecasting with VAR models Multivariate forecasting with VAR models Franz Eigner University of Vienna UK Econometric Forecasting Prof. Robert Kunst 16th June 2009 Overview Vector autoregressive model univariate forecasting multivariate

More information

DISCUSSION PAPERS IN ECONOMICS

DISCUSSION PAPERS IN ECONOMICS STRATHCLYDE DISCUSSION PAPERS IN ECONOMICS UK HOUSE PRICES: CONVERGENCE CLUBS AND SPILLOVERS BY ALBERTO MONTAGNOLI AND JUN NAGAYASU NO 13-22 DEPARTMENT OF ECONOMICS UNIVERSITY OF STRATHCLYDE GLASGOW UK

More information

Introduction to Algorithmic Trading Strategies Lecture 3

Introduction to Algorithmic Trading Strategies Lecture 3 Introduction to Algorithmic Trading Strategies Lecture 3 Pairs Trading by Cointegration Haksun Li haksun.li@numericalmethod.com www.numericalmethod.com Outline Distance method Cointegration Stationarity

More information

Volatility, Information Feedback and Market Microstructure Noise: A Tale of Two Regimes

Volatility, Information Feedback and Market Microstructure Noise: A Tale of Two Regimes Volatility, Information Feedback and Market Microstructure Noise: A Tale of Two Regimes Torben G. Andersen Northwestern University Gökhan Cebiroglu University of Vienna Nikolaus Hautsch University of Vienna

More information

Panel Data Exercises Manuel Arellano. Using panel data, a researcher considers the estimation of the following system:

Panel Data Exercises Manuel Arellano. Using panel data, a researcher considers the estimation of the following system: Panel Data Exercises Manuel Arellano Exercise 1 Using panel data, a researcher considers the estimation of the following system: y 1t = α 1 + βx 1t + v 1t. (t =1,..., T ) y Nt = α N + βx Nt + v Nt where

More information

Chapter 6. Maximum Likelihood Analysis of Dynamic Stochastic General Equilibrium (DSGE) Models

Chapter 6. Maximum Likelihood Analysis of Dynamic Stochastic General Equilibrium (DSGE) Models Chapter 6. Maximum Likelihood Analysis of Dynamic Stochastic General Equilibrium (DSGE) Models Fall 22 Contents Introduction 2. An illustrative example........................... 2.2 Discussion...................................

More information

Introduction to Regression Analysis. Dr. Devlina Chatterjee 11 th August, 2017

Introduction to Regression Analysis. Dr. Devlina Chatterjee 11 th August, 2017 Introduction to Regression Analysis Dr. Devlina Chatterjee 11 th August, 2017 What is regression analysis? Regression analysis is a statistical technique for studying linear relationships. One dependent

More information

Lecture 8: Multivariate GARCH and Conditional Correlation Models

Lecture 8: Multivariate GARCH and Conditional Correlation Models Lecture 8: Multivariate GARCH and Conditional Correlation Models Prof. Massimo Guidolin 20192 Financial Econometrics Winter/Spring 2018 Overview Three issues in multivariate modelling of CH covariances

More information