Commodity Connectedness

Transcription

1 Commodity Connectedness Francis X. Diebold (Penn) Laura Liu (Penn) Kamil Yılmaz (Koç) November 9, / 29

2 Financial and Macroeconomic Connectedness Portfolio concentration risk Credit risk Counterparty and gridlock risk Systemic risk (including MES, CoVaR, system-wide,...) Business cycle risk This paper: Commodities Crucial part of the global economy Partly financial, partly real Key inputs and key outputs Static and dynamic aspects Real-time monitoring of commodity market volatility Real-time monitoring for real-time policy 2 / 29

3 Covariance So pairwise... So linear... So Gaussian... 3 / 29

4 A Very General Environment x t = B(L) ε t ε t (0, Σ) C(x, B(L), Σ) 4 / 29

5 A Natural Economic Connectedness Question: What fraction of the H-step-ahead prediction-error variance of variable i is due to shocks in variable j, j i? Non-own elements of the variance decomposition: d H ij, j i C(x, H, B(L), Σ) 5 / 29

6 Variance Decompositions for Connectedness N-Variable Connectedness Table x 1 x 2... x N From Others to i x 1 d11 H d12 H d1n H Σ N j=1 d 1j H, j 1 x 2 d21 H d22 H d2n H Σ N j=1 d 2j H, j x N dn1 H dn2 H dnn H Σ N j=1 d Nj H, j N To Others Σ N i=1 d i1 H Σ N i=1 d i2 H Σ N i=1 d in H Σ N i,j=1 d ij H From j i 1 i 2 i N i j Upper-left block is variance decomposition matrix, D Connectedness involves the non-diagonal elements of D 6 / 29

7 Connectedness Measures From others to i: C H i = To others from j: C H j = N j=1 j i N i=1 i j d H ij d H ij ( i s total imports ) ( j s total exports ) Pairwise Directional: Ci j H = d ij H ( i s imports from j ) Net: Cij H = Cj i H C i j H ( ij bilateral trade balance ) - Total Directional: Net: Ci H = C i H C i H ( i s multilateral trade balance ) - Total System-Wide: C H = 1 N dij H ( total world exports ) N i,j=1 i j 7 / 29

8 Background Recent paper: Diebold, F.X. and Yilmaz, K. (2014), On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms, Journal of Econometrics, 182, Recent book: Diebold, F.X. and Yilmaz, K. (2015), Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring, Oxford University Press. With K. Yilmaz. 8 / 29

9 Network Representation: Graph and Matrix A = Symmetric adjacency matrix A A ij = 1 if nodes i, j linked A ij = 0 otherwise 9 / 29

10 Network Connectedness: The Degree Distribution Degree of node i, d i : N d i = j=1 Discrete degree distribution on 0,..., N 1 Mean degree, E(d), is the key connectedness measure A ij 10 / 29

11 Network Representation II (Weighted, Directed) A = to i, from j 11 / 29

12 Network Connectedness II: The Degree Distribution(s) A ij [0, 1] depending on connection strength Two degrees: d from i = d to j = N j=1 N i=1 from-degree and to-degree distributions on [0, N 1] Mean degree remains the key connectedness measure A ij A ij 12 / 29

13 Variance Decompositions as Weighted, Directed Networks Variance Decomposition / Connectedness Table x 1 x 2... x N From Others x 1 d11 H d12 H d1n H j 1 d 1j H x 2 d21 H d22 H d2n H j 2 d 2j H x N dn1 H dn2 H dnn H j N d Nj H To Others i 1 d H i1 i 2 d H i2 i N d H in i j d H ij Total directional from, Ci H = N j=1 dij H: from-degrees j i Total directional to, C j H = N i=1 dij H: to-degrees i j Total system-wide, C H = 1 N N i,j=1 i j dij H : mean degree 13 / 29

14 Estimating Connectedness Thus far we ve worked under correct specification, in population: C(x, H, B(L), Σ) Now we want: ( ) Ĉ x, H, B(L), Σ, M(L; ˆθ), and similarly for other variants of connectedness 14 / 29

15 Many Interesting Issues / Choices x objects: Returns? Return volatilities? x universe: How many and which ones? (Major commodity sub-indexes) x frequency: Daily? Monthly? Quarterly? Specification: Approximating model M: VAR? DSGE? Estimation: Classical? Bayesian? Hybrid? Selection: Information criteria? Stepwise? Lasso? Shrinkage: BVAR? Ridge? Lasso? Identification (of variance decompositions): Assumptions: Cholesky? Generalized? SVAR? DSGE? Horizon H: 10-day? Others? Understanding: Network summarization and visualization Estimation: Static vs. dynamic 15 / 29

16 Selection and Shrinkage via Penalized Estimation of High-Dimensional Approximating Models ˆβ = argmin β T t=1 ( ( T ˆβ = argmin β y t t=1 i y t ) 2 β i x it s.t. i β i x it ) 2 + λ K β i q c i=1 K β i q i=1 Concave penalty functions non-differentiable at the origin produce selection. Smooth convex penalties produce shrinkage. q 0 produces selection, q = 2 produces ridge, q = 1 produces lasso. 16 / 29

17 Lasso ( T ˆβ Lasso = argmin β y t t=1 i ( T ˆβ AEnet = argmin β y t t=1 i β i x it ) 2 + λ β i x it ) 2 + λ K β i i=1 K ( w i α βi + (1 α)βi 2 i=1 where w i = 1/ ˆβ i ν, ˆβ i is OLS or ridge, and ν > 0. Choices: α = 0.5 ; w i from OLS regression; ν = 1; 10-fold cross validation for λ, separately for each equation. ) 17 / 29

18 Network Visualization via Spring Graphs Node shading: Total directional connectedness to others Node location: Average pairwise directional connectedness (Equilibrium of repelling and attracting forces, where (1) nodes repel each other, but (2) edges attract the nodes they connect according to average pairwise directional connectedness to and from. ) Link thickness: Average pairwise directional connectedness Link arrow sizes: Pairwise directional to and from 18 / 29

19 Commodity Contracts Commodity Designated Contract Exchange Natural Gas Henry Hub Natural Gas NYMEX WTI Crude Oil Light, Sweet Crude Oil NYMEX Unleaded Gasoline RBOB NYMEX ULS Diesel (Heating Oil) ULS Diesel NYMEX Live Cattle Live Cattle CME Lean Hogs Lean Hogs CME Wheat Soft Wheat CBOT Corn Corn CBOT Soybeans Soybeans CBOT Soybean Oil Soybean Oil CBOT Aluminum High Grade Primary Aluminum LME Copper Copper COMEX Zinc Special High Grade Zinc LME Nickel Primary Nickel LME Gold Gold COMEX Silver Silver COMEX Sugar World Sugar No. 11 NYBOT Cotton Cotton NYBOT Coffee Coffee C NYBOT 19 / 29

20 Time Series Plots of Log Commodity Sub-Indices 20 / 29

21 Time Series Plots of Log Realized Volatilities 21 / 29

22 Gaussian Q-Q Plots for Realized Volatilities 22 / 29

23 Gaussian Q-Q Plots for Log Realized Volatilities 23 / 29

24 Autocorrelation Functions of Log Realized Volatilities 24 / 29

25 Full-Sample Spring Graph 25 / 29

26 Full-Sample Spring Graph, Six-Group Aggregation 26 / 29

27 Rolling-Sample System-Wide Connectedness 27 / 29

28 Rolling-Sample Net Total Directional Connectedness 28 / 29

29 Conclusion 29 / 29