Networks in Production: Asset Pricing Implications Bernard Herskovic UCLA Anderson Third Economic Networks and Finance Conference London School of Economics December 2015 Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 1 / 26
Introduction Input-output network and technology How are changes in the input-output network priced? Theory general equilibrium model Network factors: priced sources of risk Data new asset pricing factors Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 2 / 26
Introduction: input-output network Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 3 / 26
Introduction: concentration and sparsity Concentration (nodes/circles) Large sectors concentrated network Output concentration Decreases output Sparsity (edges/arrows) Few thick arrows sparse network Input specialization Increases output (a) Low Concentration Low Sparsity (b) High Concentration High Sparsity (c) Low Concentration High Sparsity Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 4 / 26
Introduction: how are the network factors priced? Concentration innovations Decrease consumption growth and increase marginal utility Negative price of risk more exposure to concentration lower returns Return spread of 4% with similar FF/CAPM alpha Sparsity innovations Increase consumption growth and decrease marginal utility Positive price of risk more exposure to sparsity higher returns Return spread of 6% with similar FF/CAPM alpha Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 5 / 26
Related Papers Multisector models, input-output and aggregation: Long and Plosser (1983) Acemoglu, Carvalho, Ozdaglar, and Tahbaz-Salehi (2012) Networks and asset pricing: Ahern (2012) Kelly, Lustig, and Van Nieuwerburgh (2012) Production-based asset pricing: Papanikolaou (2011) Loualiche (2012) Kung and Schmid (2013) Sectoral composition risk: Martin (2013) Cochrane, Longstaff, and Santa-Clara (2008) Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 6 / 26
Multisector Model Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 7 / 26
Representative Household n goods Epstein-Zin recursive preferences U t = [ ( (1 β) C 1 ρ t + β (E t U 1 γ t+1 )) 1 ρ ] 1 1 ρ 1 γ w/ Cobb-Douglas consumption aggregator: C t = n i=1 cα i i,t Budget constraint n n P i,t c i,t + ϕ i,t+1 (V i,t D i,t ) = i=1 i=1 n ϕ i,t V i,t i=1 V i,t cum-dividend price of firm i ϕ i,t share holding of firm i D i,t dividend of firm i c i,t consumption of good i Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 8 / 26
Firms n firms and n goods: firm i produces good i i buys inputs {y i1,t,..., y in,t } from other firms Final output Y i,t : combination of inputs Maximization problem D t = max {yij,t } j,i i,t P i,t Y i,t n j=1 P j,ty ij,t s.t. Y i,t = ε i,t I η i,t η < 1 diminishing returns ε i,t sector specific productivity I i,t = n j=1 yw ij,t ij,t w ij,t network weight of firm i on firm j alt. Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 9 / 26
Network I i,t = w n 11,t w 1n,t y w ij,t ij,t W t =..... w n1,t w nn,t j=1 Network Weights w ij,t : fraction i spends on inputs from j w ij,t : elasticity of I i,t with respect to input j Network Properties n w ij,t = 1 and w ij,t 0 j=1 W t : exogenous, stochastic, arbitrary dynamics n n Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 10 / 26
Competitive Equilibrium Definition A competitive equilibrium consists of spot market prices (P 1,t,, P n,t ), value of the firms (V 1,t,, V n,t ), consumption bundle (c 1,t,, c n,t ), shares holdings (ϕ 1,t,, ϕ n,t ) and inputs bundles (y ij,t ) ij such that 1. Given prices, household and firms maximize 2. Markets clear c i,t + n j=1 y ji,t = Y i,t i, t (goods) ϕ i,t = 1 i, t (assets) Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 11 / 26
Output Shares Output share of firm i δ i,t = P i,t Y i,t n j=1 P j,ty j,t In equilibrium n δ j,t = (1 η)α j + η w ij,t δ i,t i=1 = (1 η)α j + n n n η α i w ij,t + η 2 α i w ik,t w kj,t +... i=1 i=1 k=1 Feedback effects: decaying rate η Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 12 / 26
Theorem In equilibrium, consumption growth is given by 1 [ (et+1 e t ) (1 η)(nt+1 C Nt C ) + η(nt+1 S Nt S ) ] 1 η where e t = n i=1 δ i,t log ε i,t (residual TFP) N C t = n i=1 δ i,t log δ i,t (concentration) N S t = n i=1 δ i,t n j=1 w ij t log w ij,t (sparsity) and δ j,t is the equilibrium output share of firm j n n n δ j,t = (1 η)α j + η α i w ij,t + η 2 α i w ik,t w kj,t +... i=1 i=1 k=1 Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 13 / 26
Network Concentration N C t = n δ i,t log δ i,t i=1 Sectoral Output Concentration Min if δ j,t = 1 n (equal shares) Max if δ s,t = 1 and δ j,t = 0 j s (concentrated shares) Good news for consumption? No Decreases consumption Production relies on fewer sectors: diminishing returns Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 14 / 26
Network Sparsity N S t = i δ i,t w ij,t log w ij,t j } {{ } Ni,t S High Ni,t S High Nt S = row i with few high entries (thick arrows) = sparse network w 11,t 0 w 1n,t W t =..... w n1,t 0 w nn,t n n Dispersion of marginal product and output elasticities Gains from input specialization Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 15 / 26
Example: why does sparsity increase consumption? Firm i has $ k to buy inputs, what is the optimal output? ε j = 1, P j = 1 for every j = 1,..., n Scenario 1: high sparsity w ij = 1 for some j and w is = 0 for every s j y ij = k for some j and y is = 0 for every s j Y i = k η Scenario 2: low sparsity w ij = 1 n y ij = k n Y i = kη n η Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 16 / 26
Why Does Sparsity Increase Consumption? (Partial eq.) If i spends $k, then ( k ε i,t j wwij,t y ij,t = w ij,t = Y i,t = ( P j,t ) η k η j P wij,t j,t substitution of inputs: input specialization changes in marginal cost: different input bundle (General eq.) Sparsity increases output log i P i,t+1 Y i,t+1 = η 1 η i keeping network concentration constant δ i,t+1 log j ) η w wij,t+1 ij,t+1 Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 17 / 26
Data Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 18 / 26
Network Factors 1.6 Level, 0.34 correlation Concentration Sparsity 3 1.8 3.05 2 3.1 1980 1985 1990 1995 2000 2005 2010 0.2 Innovations, 0.06 correlation 0.05 0.1 0 0 0.05 0.1 1980 1985 1990 1995 2000 2005 2010 Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 19 / 26
Constructing Beta-Sorted Portfolios 1. CRSP monthly data: form annual returns for each stock 2. For each stock, regress excess returns on the factors innovations over a 15 year window: r i t+1 r f t = αi + β i N S N S t+1 + β i N C N C t+1 + Controls + ξ i t β i N S and β i N : exposure of stock i to factors innovations C Sample: stocks with network data Controls: factors in level and orthogonalized TFP 3. Form portfolios sorted by β i and β i terciles N S N C 4. Compute subsequent year s return for the sorted portfolio 5. Verify return spread Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 20 / 26
Sorted Portfolios Table: One Way Sorted Portfolios Panel A: Sparsity (1) (2) (3) (3)-(1) t-stat Avg. Exc. Returns (%) 5.24 8.61 11.25 6.01 2.26 α CAP M 3.15 2.29 4.78 7.92 3.11 α F F 3.21 1.47 3.84 7.04 2.91 Volatility (%) 17.60 13.78 15.13 11.60 Book/Market 0.76 0.67 0.70 Avg. Market Value ($bn) 1.53 2.18 1.23 Panel B: Concentration (1) (2) (3) (3)-(1) t-stat Avg. Exc. Returns (%) 10.23 8.51 6.19 4.04 2.19 α CAP M 2.62 2.43 1.60 4.21 2.26 α F F 2.00 1.64 2.00 4.01 2.12 Volatility (%) 16.18 13.60 16.27 8.05 Book/Market 0.74 0.69 0.70 Avg. Market Value ($bn) 0.91 2.03 2.00 more: ret Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 21 / 26
Why do sectors have different network betas? Dividend growth: D i,t = (1 η)δ i,t z t = d i,t+1 = log δ i,t+1 + log z t+1. Cross-sectional heterogeneity: changes in output shares Concentration beta Network centrality / size Sparsity beta N S t n δ i,t i=1 j=1 n w ijt log w ij,t = n j=1 i=1 n δ i,t w ijt log w ij,t }{{} out-sparsity of sector j Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 22 / 26
Concluding Remarks New production-based asset pricing factors - Network sparsity and concentration Sources of aggregate risk Sparsity-beta sorted portfolios 6% return spread per year on avg Concentration-beta sorted portfolios -4% return spread per year on avg Spreads not explained by CAPM or Fama French factors Calibrated model replicates return spreads Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 23 / 26
Annex Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 24 / 26
Firms Maximization problem D t = max {yij,t } j,i i,t P i,t Y i,t n j=1 P j,ty ij,t s.t. Y i,t = ε i,t I η i,t L i,t 1 η η < 1 diminishing returns ε i,t sector specific productivity I i,t = n j=1 yw ij,t ij,t w ij,t network weight of firm i on firm j L i,t = 1 back Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 25 / 26
Robustness: sorted portfolios Table: Return Spreads Sparsity-beta sort Concentration-beta sort (3)-(1) t-stat (3)-(1) t-stat Benchmark 6.01 2.26 4.04 2.19 No level control 4.47 1.90 3.50 1.55 All CRSP stocks 5.78 2.17 3.83 2.13 Out of Sample 0.31 0.14 3.25 1.61 R. TFP Cons. 6.03 2.09 3.42 1.64 No TFP 5.49 1.92 4.89 2.51 16-year window 5.51 1.92 5.35 2.73 17-year window 4.91 1.46 6.00 2.52 18-year window 4.57 1.22 5.15 2.19 19-year window 8.54 2.02 5.93 2.45 20-year window 6.48 1.73 3.60 1.63 back Networks in Production: Asset Pricing Implications Bernard Herskovic Dec. 2015 26 / 26