Firm Volatility in Granular Networks

Transcription

1 Firm Volatility in Granular Networks Bryan Kelly 1 Hanno Lustig 2 Stijn Van Nieuwerburgh 3 1 Chicago Booth and NBER 2 UCLA Anderson and NBER 3 NYU Stern, NBER, and CEPR

2 Introduction Size, Networks, and Volatility Recent research into aggregate volatility and Firm size distribution (Gabaix 2011) Network connectivity (Acemoglu et al. 2012, Carvalho 2010) Volatility of the firm? Affects investment, employment, stock prices How do inter-firm linkages and the size distribution interact to influence volatility of the firm? 1

3 Introduction Our Approach Data on specific network: Customer/supplier sales relationships Among firms and among industries Identify three prominent features of sales networks 1. Firm growth influenced by connected firms 2. Large firms connected to more firms 3. Large firms exert bigger influence on connected firms Propose model Simple statistical model based only on these features Rich implications for volatility (cross section and time series) New empirical facts: Strong comovement between FSD and FVD 2

4 Illustrative Networks Customer/Supplier Sales Relationships 1. Firms Customer/supplier linkages (Cohen and Frazzini 2008) Subset of CRSP/Compustat, firms are required to disclose the identity of any customer representing more than 10% of total reported sales 2. Industries BEA summary input/output tables 65 industries,

5 Illustrative Networks Customer/Supplier Sales Relationships 1. Supplier growth rates influenced by customer growth rates Transmission appears stronger upstream than downstream Network-based spatial AR fits significantly better than common factor model 2. Large suppliers have more customers 30% for firm-level data (truncation adjusted) 61% correlation between industry size and number of customers 3. Larger customers have stronger links with suppliers Size of customer j and the weight it exerts on its supplier i 20% correlation at firm level 37% correlation at industry level 4

6 A Network Model of Size and Volatility S i,t is size, with dynamics: S i,t+1 = S i,t e g i,t+1 Supplier i, connected to customers j, has growth rate: g i,t+1 = µ g + γ N w i,j,t g j,t+1 + ε i,t+1 Weight w i,j,t governs strength of firm j s influence on firm i, w i,i,t = 0 Idiosyncratic growth rate shocks ε i,t+1 N(0, σ 2 ε), i, t j=1 Parameter γ governs the rate of decay as shocks propagate through network/strength of the network effects g t+1 = (I γw t ) 1 (µ g + ε t+1 ): Model content is in W t 5

7 A Network Model of Size and Volatility g i,t+1 = γ N w i,j,t g j,t+1 + ε i,t+1 j=1 w i,j,t = b i,j,ts j,t j b i,j,ts j,t Does link exist? Link is iid Be(p i,t ) draw, b i,j,t = { 1 if i connected to j at time t 0 otherwise, p i,t = S i,t Z N ζ (i.e., N i p i N N 1 ζ ) Probability of connection depends on supplier size Number of links may increase more slowly than economy (ζ (0, 1]) If so, how strong? Depends on customer size Weights sum to one 6

8 Firm Volatility in a Granular Network As the number of firms in the economy N becomes large, firm i s volatility behaves as 1 V t (g i,t+1 ) σ 2 ε { ( κ0 1 + S i N 1 ζ + κ ) } 1 E[S 2 t ] N E[S t ] 2 + 2γ2 S i 1 γ NE[S t ] Factor structure in firm volatility dynamics Factor is firm size concentration Both mean and dispersion of firm volatility depend on concentration Special cases include { E[St 2 ] exp(σ 2 E[S = S ) if S LN(, σs) 2 t] 2 η/(η 2) if S PL(η) Larger firms have lower volatility level less variable volatility (smaller loading on factor) Scope for slower volatility decay than that due to pure granularity 7

9 Firm Volatility in a Granular Network As the number of firms in the economy N becomes large, firm i s volatility behaves as 1 V t (g i,t+1 ) σ 2 ε Proof intuition: One-Step Network { ( κ0 1 + S i N 1 ζ + κ ) } 1 E[S 2 t ] N E[S t ] 2 + 2γ2 S i 1 γ NE[S t ] g i,t+1 = µ g + γ V (g i,t+1 ) = σ 2 ε N j=1 ( w i,j,t 1 + γ 2 N g j,t+1 ε j,t+1 +ε i,t+1 j=1 H i N 1 p i E[S 2 ] NE[S] 2 V (g i ) σ 2 ε w 2 i,j,t } {{ } H i ) ( 1 + κ0 E[S 2 ] S i N 1 ζ E[S] 2 1 κ0 = γ 2 Z and κ 1 = 2γ3 1 γ + γ 4 (1 γ) 2 8 )

10 Other Implications 1. Variance of aggregate growth V t [g a t+1 ] depends on same factor σ2 s,t g a,t+1 = i S i,t i S i,t g i,t+1, with variance V t (g a,t+1 ) σε 2 E[St 2 ] NE[S t ] 2 ζ 2. Insufficiency of factor models in sparse networks N b i,j S j g i = γ j=1 k S g j +ε i γ k }{{} Avg. growth of links N S j j=1 k S g j k }{{} Avg. growth of economy 3. Idiosyncratic variance (g res i,t+1 = g i,t+1 β i g a,t+1 ) inherits same factor structure 4. Rich aggregate dynamics coming from network effects (γ 0) +ε i Firm size network structure firm volatility firm size Moments of FSD and FVD display substantial time variation 9

11 Empirical Facts 10

12 Data, Definitions, Etc. Market (CRSP) and fundamentals (Compustat) data Everything annual Firm size: Market cap or annual sales Firm volatility: Std. dev. of returns or sales growth Concentration: Standard deviation of log size 11

13 Average Firm Volatility and Dispersion in Firm Size Average Volatility and Dispersion in Firm Size, 0.72 correlation Mean Log Vol based on equity return Std log size based on mkt cap Firm size dispersion (mkt cap) Mean firm volatility (returns) 12

14 Dispersion in Firm Volatility and Dispersion in Firm Size Dispersion in Volatility and Dispersion in Firm Size, 0.79 correlation Std Log Vol based on equity return Std log size based on mkt cap Firm size dispersion (mkt cap) Firm volatility dispersion (returns) 13

15 Average Firm Volatility and Dispersion in Firm Size (2) Size and volatility based on sales data Average Volatility and Dispersion in Firm Size, 0.87 correlation Mean Log Vol based sales Std log size based on sales Firm size dispersion (sales) Mean firm volatility (sales growth) 14

16 Factor Structure in Volatility (Small) (Big) Average Log Return Volatility Volatility of Volatility Small Big 15

17 Factor Structure in Volatility log V i,t+1 = a i + b i factor t + e i,t+1 Panel A: Total Volatility Factors Panel B: Residual Volatility Factors σ s,t µ σ,t µ σ,t+1 σ s,t µ σ,t µ σ,t+1 Factor Model R 2, All Firms Return Volatility Sales Gr. Volatility Volatility Loadings by Size Quintile (1) Small (2) (3) (4) (5) Big

18 Network/Size Uniquely Important for Volatility Dependent Variable: Log Firm Volatility (1) (2) (3) (4) (5) (6) (7) (8) (9) Log Sales Netw. Conc Log Age... Leverage... Ind. Conc.... Inst. Hldg FE None None None Cohort Cohort Cohort Ind. Ind. Ind. Obs. 171,034 38,030 37, ,247 32,901 32, ,034 38,030 37,202 Adj. R

19 Model Calibration 18

20 Goals of Calibration Quantitative match of size, volatility, network data? 1. Amount of variability in FSD and FVD generated by model 2. Cross-correlations of moments of FSD and FVD 3. Cross-sectional correlation of network structure and size/volatility Dynamics (birth/death of firms, persistence in links) add further complexity Even this simple model produces complex, analytically intractable behavior Certain network features difficult to ascertain due to data truncation and selection 19

21 Benchmark Calibration 1 Model Dynamics Basic model setup as described earlier N g i,t+1 = w i,j,t g j,t ε i,t+1 j=1 w i,j,t = b i,j,ts j,t S i,t j b, b i,j,t iidbe(p i,t ), p i,t = i,j,ts j,t 0.35 j S j,t Initialize with log normal sizes, µ S,0 = 10.20, σ S,0 = 1.06 Extra persistence in links: p i,j,t = p i,t if i, j connected at t 1 Firm Death Exogenous rate δ = 5% Replace from initial distribution Addressing Data Limitations N = 2, 000, track largest 1,000 to treat selection (public firms only) w i,j,t < 0.1 is set to zero to treat truncation (only weights> 0.10) 20

22 Benchmark Calibration 2 Basic model setup as described earlier g i,t+1 = N w i,j,t g j,t+1 + σε,i,t 2 ε i,t+1 j=1 σ 2 ε,i,t = (0.4)2 0.9 log S i,t E[log(S t)] E[log(S t)] Large firms experience less volatile primitive shocks Motivated by internal diversification Network effects remain crucial. If γ = 0, focal moments change sign (higher size dispersion lowers average vol) 21

23 Size Distribution Moments All Top 1000 Model 1 Model 2 Cross-sectional Moments of Log Size Avg SD % % Med % % Time Series Properties of Size Distribution SD of σ S,t AR(1) σ S,t

24 Volatility Distribution Moments All Top 1000 Model 1 Model 2 Cross-sectional Moments of Firm Volatility Avg SD % % Med % % Cross Section Moments of Joint Size-Vol Distribution Corr(S i,t, V i,t+1 ) β(s i,t, V i,t+1 ) Time Series Properties of Volatility Distribution SD of µ σ 2,t SD of σ σ 2,t Corr(σ S,t, µ σ 2,t ) Corr(σ S,t, σ σ 2,t )

25 Network Moments All Top 1000 Model 1 Model 2 Cross-sectional Moments of Network median # customers th % # customers median H i th % H i Corr(H i, S i ) Corr(H i, V i )

26 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 25

27 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 26

28 Sample Composition Private vs. Public Firms Dynamics of FSD and FVD dispersion are similar for publicly-listed and privately-held firms Census Sample 1: Size concentration (measured from # employees) similar dynamics as Compustat sample Census Sample 2: TFP volatility (al mfg firms, Bloom et al. (2012)) has 50% correlation with sales growth volatility of Compustat firms Compustat Private Sample: Strong positive correlation between Size concentration of public firms and that of private firms Mean volatility of public firms and that of private firms 27

29 Sample Composition Stratified Samples # Firms ρ(σ subset,s,t, σ s,t) ρ(µ σ,t, σ s,t 1) ρ(σ σ,t, σ s,t 1) All stocks % 79.3% By sample period / exchange NYSE only % 62.1% 77.6% Non-NYSE % 58.1% 40.7% At least 50 yrs % 44.5% 62.7% Random % 64.9% 80.7% By size Smallest third % 71.7% 51.9% Middle third % 61.6% 69.8% Largest third % 55.9% 73.4% By industry Consumer Non-Dur % 64.4% 72.3% Consumer Durables % 33.4% 74.9% Manufacturing % 53.1% 79.8% Energy % 68.4% 67.9% Technology % 85.2% 58.2% Telecom % 14.3% 10.6% Retail % 69.0% 69.8% Healthcare % 69.4% 50.6% Utilities % 19.7% 64.8% Other % 63.3% 65.7% 28

30 Sample Composition Exit and Entry 0.14 Exit Entry Annual data, Source: U.S. Small Business Administration Office of Advocacy (based on data provided by the U.S. Census Bureau, Business Dynamics Statistics) 29

31 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 30

32 Internal vs. External Diversification Internal diversification alone is unable to match focal time series moments of data Calibration 2 described earlier: g i,t+1 = 0.95 N w i,j,t g j,t+1 + σε,i,t 2 ε i,t+1 j=1 σ 2 ε,i,t = (0.4)2 0.9 log S i,t E[log(S t)] E[log(S t)] If γ = 0, higher size dispersion lowers average volatility Internal diversification helps cross section spread in vols with less network concentration 31

33 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 32

34 Downstream Transmission of Shocks Model No change, reinterpret firm-level herfindahl as concentration of its Data suppliers Firm size and volatility distribution unaffected Model predicts in-herfindahl (supplier concentration) drives firm volatility, absent in data Does not generate correlation between out-herfindahl (customer concentration) and volatility, which is significant in data 33

35 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 34

36 Retail Sector? Retailers customers are households which are not modeled explicitly in network (leakage) But, if markets are incomplete, then some of the labor income risk that is specific to non-retail firms affects the consumption decisions of workers at these firms That in turn exposes retail firms to upstream risk from non-retail firms Let w l,m = 0, m = 1,..., N and v l,m denote the link strength of retailer l to customers working at supplier m. N+k g i,t+1 = µ g + γ w i,j,t g j,t+1 + ε i,t+1, i = 1,..., N. j=1 N+k g l,t+1 = µ g + ψ v l,m,t g m,t+1 + ε l,t+1, l = N + 1,.., N + k. m=1 ψ governs how much firm-specific idiosyncratic risk is transferred to consumption. 35

37 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks Amplifies size/vol dispersion with less idiosyncratic risk, but can overstate concentration High or low frequency dynamics? Micro Foundations 36

38 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations 37

39 Average Volatility and Size Concentration: Detrended 1.5 Average Volatility and Dispersion in Firm Size cyclical components, 0.29 correlation Mean Log Vol based on equity return Std log size based on mkt cap

40 Volatility Dispersion and Size Concentration: Detrended Dispersion in Volatility and Dispersion in Firm Size cyclical components, 0.66 correlation Std Log Vol based on equity return Std log size based on mkt cap

41 Average Volatility and Size Concentration: Detrended Sales and Sales Growth Volatiltiy Average Volatility and Dispersion in Firm Size cyclical components, 0.44 correlation Mean Log Vol based sales Std log size based on sales

42 Additional Considerations Sample composition Private vs. public firms Entry and exit Internal vs. external diversification Upstream vs. downstream shock transmission Retail sector Aggregate shocks High or low frequency dynamics? Micro Foundations Long and Plosser (1983) and emphasized in recent network settings (Acemoglu et al., Carvalho) GE network models analytically challenging, typically static We ve chosen a statistical route that embeds dynamics, size-dependent sparsity directly and offers tractability Gives us an edge to make empirical progress, establish foundation for next generation micro-founded network models 41

43 Conclusion New volatility insights due to network and firm size interaction Firms as aggregators of idiosyncratic shocks to other firms Factor structure in firm volatility Size concentration is factor governing all volatilities A firm s size determines its factor sensitivity Shocks are size-weighted, slow volatility decay granularity effect firm-by-firm (and in aggregate) Network sparsity slows this decay even further New empirical facts: FSD and FVD tightly linked Factor structure in firm vol, size concentration a successful factor Simple model unifies a wide range of size/network/volatility facts 42

44 Extra Slides 43

45 FSD Leads FVD: Granger Causality Tests in Data Dependent Variable Independent Variables Intercept µ σ,t 1 σ s,t 1 µ σ,t Coeff t-stat σ s,t Coeff t-stat Intercept σ σ,t 1 σ s,t 1 σ σ,t Coeff t-stat σ s,t Coeff t-stat

46 Firm Size Dispersion with Private Firms 4 Spliced Census Comp Census Comp Census 3.5 Comp Census Comp Cross-sectional variance of log employment in the Census and Compustat data. Data is annual for Source: U.S. Small Business Administration, Office of Advocacy, from data provided by the U.S. Census Bureau, Business Dynamics Statistics. Left panel: splices Census data together with Compustat data for firms with 10,000+ employees; correlation is 62%. The right panel does not; correlation is 65%. 45

47 Log-Normal Size/Vol Distributions Market All Years Skewness: 0.27 Kurtosis: 2.93 Fundamental All Years Skewness: 0.18 Kurtosis: 3.25 Probability Density Probability Density Size (log S/E[S]) All Years Skewness: 0.20 Kurtosis: Size (log S/E[S]) All Years Skewness: 0.26 Kurtosis: 3.25 Probability Density Probability Density Annual Volatility (log RV) Annual Volatility (log RV) 46

48 Simulated Size Dispersion and Mean Firm Variance Average Log Volatility Std. Dev. Log Size Average Volatility and Dispersion in Firm Size Benchmark Model (Last 300 Periods)

49 Simulated Size Dispersion and Variance Dispersion Std. Dev. Log Volatility Std. Dev. Log Size Dispersion in Volatility and Dispersion in Firm Size Benchmark Model (Last 300 Periods)

50 FSD Leads FVD: Granger Causality Tests in Model Dependent Variable Independent Variables Intercept µ σ,t 1 σ S,t 1 µ σ,t Coeff t-stat σ s,t Coeff t-stat Intercept σ σ,t 1 σ S,t 1 σ σ,t Coeff t-stat σ s,t Coeff t-stat Also: Model generates factor structure in volatility, quantitatively similar to data 49

51 Downstream Transmission: Network Moments All Top-33% All Top-33% Model Returns Returns Sales Sales Panel A: Out-degree Moments median K out th % K out median H out th % H out Corr(K out t, S t) Corr(H out t, S t) Corr(H out t, V t+1) Panel B: In-degree Moments median K in th % K in median H in th % H in Corr(K in t Corr(H in t Corr(H in t, St) , St) , Vt+1)

52 Downstream Transmission: Data on Supplier Networks w i,j,t log S i,t log S i,t log H i,t log H i,t S j,t K in i,t log H i,t log σ i,t (r) log σ i,t (s) Customer Firms (Compustat) Average t Customer Industries (BEA) Average t

53 Network/Size Uniquely Important for Volatility (Detail) Dependent Variable: Log Firm Volatility (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) Log Sales Netw. Conc Log Age Leverage Ind. Conc Inst. Hldg Constant FE None None None None None None None None None Cohort Cohort Cohort Ind. Ind. Ind. Obs. 171,034 38,030 37, ,070 32,887 32, ,425 31,318 31, ,247 32,901 32, ,034 38,030 37,202 Adj. R

54 Additional Considerations Private vs. public firms Stratified sample, Compustat private firm data, Census data Upstream vs. downstream shock transmission Bi-directional, but correlation of volatility with out-herfindahl statistically much stronger than with in-herfindahl Internal vs. external diversification Counterfactual implication: More size dispersion lowers average vol Aggregate shocks Amplifies size/vol dispersion with less idiosyncratic risk, can overstate concentration Entry and exit Our focus size/vol feedback, but interesting source of FSD variation Idiosyncratic vs. total volatility High or low frequency dynamics? Retail sector 53