Networks in Production: Asset Pricing Implications

Transcription

1 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 / 26

2 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 / 26

3 Introduction: input-output network Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

4 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 / 26

5 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 / 26

6 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 / 26

7 Multisector Model Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

8 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 / 26

9 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 / 26

10 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 / 26

11 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 / 26

12 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 / 26

13 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 / 26

14 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 / 26

15 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 / 26

16 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 / 26

17 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 / 26

18 Data Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

19 Network Factors 1.6 Level, 0.34 correlation Concentration Sparsity Innovations, 0.06 correlation Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

20 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 / 26

21 Sorted Portfolios Table: One Way Sorted Portfolios Panel A: Sparsity (1) (2) (3) (3)-(1) t-stat Avg. Exc. Returns (%) α CAP M α F F Volatility (%) Book/Market Avg. Market Value ($bn) Panel B: Concentration (1) (2) (3) (3)-(1) t-stat Avg. Exc. Returns (%) α CAP M α F F Volatility (%) Book/Market Avg. Market Value ($bn) more: ret Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

22 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 / 26

23 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 / 26

24 Annex Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26

25 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 / 26

26 Robustness: sorted portfolios Table: Return Spreads Sparsity-beta sort Concentration-beta sort (3)-(1) t-stat (3)-(1) t-stat Benchmark No level control All CRSP stocks Out of Sample R. TFP Cons No TFP year window year window year window year window year window back Networks in Production: Asset Pricing Implications Bernard Herskovic Dec / 26