Risk-Adjusted Capital Allocation and Misallocation

Transcription

1 Risk-Adjusted Capital Allocation and Misallocation Joel M. David Lukas Schmid David Zeke USC Duke & CEPR USC Summer / 18

2 Introduction In an ideal world, all capital should be deployed to its most productive use! But, σmpk 2 0 capital misallocation, large losses in TFP, output Why doesn t capital flow to the most productive firms? Sources of dispersion still unclear, e.g., sizable persistent component Our analysis: with aggregate risk 1 = E t [M t+1 (MPK it δ)] E t [MPK it+1 ] = α t + β i λ t Expected discounted MPK s should be equalized MPK it depends on exposure to agg risk factors CS return predictability: persistent deviations σmpk 2 depends on dispersion in risk exposures (σβ) 2 and price of risk (λ t) TS return predictability: countercyclical variation Novel link between nature of agg shocks, asset pricing and resource allocations 2 / 18

3 Introduction In an ideal world, all capital should be deployed to its most productive use! But, σmpk 2 0 capital misallocation, large losses in TFP, output Why doesn t capital flow to the most productive firms? Sources of dispersion still unclear, e.g., sizable persistent component Our analysis: with aggregate risk 1 = E t [M t+1 (MPK it δ)] E t [MPK it+1 ] = α t + β i λ t Expected discounted MPK s should be equalized MPK it depends on exposure to agg risk factors CS return predictability: persistent deviations σmpk 2 depends on dispersion in risk exposures (σβ) 2 and price of risk (λ t) TS return predictability: countercyclical variation Novel link between nature of agg shocks, asset pricing and resource allocations 2 / 18

4 This paper Neoclassical growth model w idiosyncratic and aggregate risk Firms with greater exposure to agg risk offer higher MPK MPK dispersion increases when price of risk is high (i.e., is countercyclical) Verify predictions for US firms Quantitative analysis: how much MPK dispersion from risk premium effects? More structure: connect agg risk to technology shocks Empirical strategy: use link with stock market returns Key result: σ 2 E[mpk] σ2 E[r] Findings: important role for risk considerations Accounts for 40% of σ 2 MPK reduces long-run TFP 8% Adds countercyclical component to σ 2 MPK amplifies agg shocks 3 / 18

5 This paper Neoclassical growth model w idiosyncratic and aggregate risk Firms with greater exposure to agg risk offer higher MPK MPK dispersion increases when price of risk is high (i.e., is countercyclical) Verify predictions for US firms Quantitative analysis: how much MPK dispersion from risk premium effects? More structure: connect agg risk to technology shocks Empirical strategy: use link with stock market returns Key result: σ 2 E[mpk] σ2 E[r] Findings: important role for risk considerations Accounts for 40% of σ 2 MPK reduces long-run TFP 8% Adds countercyclical component to σ 2 MPK amplifies agg shocks 3 / 18

6 This paper Neoclassical growth model w idiosyncratic and aggregate risk Firms with greater exposure to agg risk offer higher MPK MPK dispersion increases when price of risk is high (i.e., is countercyclical) Verify predictions for US firms Quantitative analysis: how much MPK dispersion from risk premium effects? More structure: connect agg risk to technology shocks Empirical strategy: use link with stock market returns Key result: σ 2 E[mpk] σ2 E[r] Findings: important role for risk considerations Accounts for 40% of σ 2 MPK reduces long-run TFP 8% Adds countercyclical component to σ 2 MPK amplifies agg shocks 3 / 18

7 Cues from the basic neoclassical growth model Continuum of firms, only capital, idio. + agg. risk Production: Y it = X β it t Z it Kit θ, X t correlated with SDF M t K accumulation: K it+1 = I it + (1 δ) K it Dividends: D it = Y it I it Firm problem: V (X t, Z it, K it ) = max K it+1 X β it t Z it Kit θ K it+1 +(1 δ) K it +E t [M t+1v (X t+1, Z it+1, K it+1 )] Optimality: 1 = E t [M t+1 (MPK it δ)], MPK it+1 = θ Y it+1 K it+1 E t [MPK it+1 ] = α t + β it λ t, σ 2 E t [MPK t+1 ] = σ 2 βλ 2 t where β it = covt(mpk it+1,m t+1) var t (M t+1, λ ) t = vart (M t+1) E t [M t+1 ] 4 / 18

8 Cues from the basic neoclassical growth model Continuum of firms, only capital, idio. + agg. risk Production: Y it = X β it t Z it Kit θ, X t correlated with SDF M t K accumulation: K it+1 = I it + (1 δ) K it Dividends: D it = Y it I it Firm problem: V (X t, Z it, K it ) = max K it+1 X β it t Z it Kit θ K it+1 +(1 δ) K it +E t [M t+1v (X t+1, Z it+1, K it+1 )] Optimality: 1 = E t [M t+1 (MPK it δ)], MPK it+1 = θ Y it+1 K it+1 E t [MPK it+1 ] = α t + β it λ t, σ 2 E t [MPK t+1 ] = σ 2 βλ 2 t where β it = covt(mpk it+1,m t+1) var t (M t+1, λ ) t = vart (M t+1) E t [M t+1 ] 4 / 18

9 Examples 1. No aggregate risk (or risk neutrality): M t+1 = ρ E t [MPK it+1 ] = 1 ρ (1 δ) = r f + δ 2. CAPM: M t+1 = a br mt+1 E t [MPK it+1 ] = α t + covt (rmt+1, MPK it+1) var t (r mt+1) } {{ } β it E t [r mt+1 r ft+1 ] }{{} λ t ( ) γ Ct+1 3. CCAPM: M t+1 = ρ C t E t [MPK it+1 ] = α t + covt ( ct+1, MPK it+1) var t ( c t+1) } {{ } β it γvar t ( c t+1) }{{} λ t 5 / 18

10 Empirical Predictions E t [MPK it+1 ] = α t + β it λ t, σ 2 E t [MPK t+1 ] = σ 2 βλ 2 t 1. Predictions on expected MPK (Empk) Cross-section: exposure to risk factors is a determinant of expected MPK (Empk) Time-series: predictable variation in λ t leads to predictable variation in Empk 2. Predictions on MPK dispersion Cross-section: cross-sectional MPK dispersion is related to β dispersion Time-series: MPK dispersion increases with λ t We find evidence supporting these predictions using data on US publicly traded firms 6 / 18

11 Prediction 1 - standard risk factors are determinants of Empk (1/2) Relate mpk to expected stock market returns Sort firms into 10 portfolios based on mpk it = y it k it, calculate E [r t+1] Low mpk High mpk HML E [r t+1 ], not industry-adjusted 6.84* 13.82*** 6.98*** (1.94) (3.43) (3.10) E [r t+1 ], industry-adjusted 9.18* 13.48*** 4.29*** (1.95) (3.16) (3.24) High mpk firms offer high expected stock returns Robust to using Contemporaneous or long-term (3 year) returns Unlevered returns Double sorting on mpk and other variables, e.g., size, book-to-market 7 / 18

12 Prediction 1 - standard risk factors are determinants of Empk (2/2) Directly relate mpk it+1 to measures of β it Compute β mpk and β r using CAPM, Fama French 3 factor model Estimate regressions: mpk it+1 = ψ 0 + ψ 1β it + controls + ζ it+1 (1) (2) (3) (4) β mpk,mkt 0.020*** (6.74) β mpk,ff 1.008*** (9.62) β r,mkt *** (4.14) β r,ff 0.005*** (5.59) Observations Firms R High mpk firms have high betas 8 / 18

13 Prediction 3 - mpk dispersion is related to β dispersion Relate σmpk 2 to σβ 2 and σ 2 E[r] across industries By firm: estimate E t [r t+1] and β t s from Fama French 3 factor model By industry: calculate σ (mpk t+1) and σ (E t [r t+1]) Regress: σ (mpk t+1) j = ψ 0 + ψ 1σ (E t 1 [r t]) j + ζ jt+1 (1) (2) (3) σ(e[r]) 2.54*** (34.14) σ(e[r β ]) 11.63*** (31.43) σ(β MKT ) 0.24*** (12.22) σ(β HML ) 0.12*** (10.63) σ(β SMB ) 0.12*** (8.54) Observations R Industries w high expected return/β dispersion have high mpk dispersion 9 / 18

14 Prediction 4 - mpk dispersion increases with λ Relate σ 2 mpk, r hml to (lagged) indicators of price of risk Estimate regressions: σ mpk,t+1 = ψ 0 + ψ 1x t + ζ t+1 r hml,t+1 = ψ 0 + ψ 1x t + ζ t+1 σ (mpk) HML Spread (%) PD Ratio ** * (-3.01) (-1.70) GZ Spread 0.012*** 0.384** (3.69) (2.31) EB Premium 0.027*** 0.580** (4.41) (2.36) Observations R mpk dispersion increases when λ t is high (i.e., is countercyclical) 10 / 18

15 Quantitative model 1. Technology Production: Y it = X ˆβ i t Ẑ it K θ 1 it Nθ 2 it Π it = X β i t Z it Kit θ Productivity components follow AR(1) (in logs): ( ) x t+1 = ρ xx t + ε t+1, ε t+1 N 0, σε 2 ( ) z it+1 = ρ zz it + ε it+1, ε it+1 N 0, σ 2 ε For now, no other frictions (later: adj. costs, other frictions/distortions) 2. Stochastic discount factor m t+1 log M t+1 = log ρ γ tε t γ2 t σ 2 ε γ t = γ 0 + γ 1x t, γ 1 0 Constant risk-free rate: r f = log ρ Countercyclical price of risk: var t (m t+1) = γ 2 t σ 2 ε in x t Maximum Sharpe ratio: SR t = σ mt = γ tσ ε 11 / 18

16 Quantitative model 1. Technology Production: Y it = X ˆβ i t Ẑ it K θ 1 it Nθ 2 it Π it = X β i t Z it Kit θ Productivity components follow AR(1) (in logs): ( ) x t+1 = ρ xx t + ε t+1, ε t+1 N 0, σε 2 ( ) z it+1 = ρ zz it + ε it+1, ε it+1 N 0, σ 2 ε For now, no other frictions (later: adj. costs, other frictions/distortions) 2. Stochastic discount factor m t+1 log M t+1 = log ρ γ tε t γ2 t σ 2 ε γ t = γ 0 + γ 1x t, γ 1 0 Constant risk-free rate: r f = log ρ Countercyclical price of risk: var t (m t+1) = γ 2 t σ 2 ε in x t Maximum Sharpe ratio: SR t = σ mt = γ tσ ε 11 / 18

17 Risk premia and misallocation Optimal investment: k it+1 = 1 ( ) α + β i ρ xx t + ρ zz it β i γ tσε 2 1 θ Conditional on (expected) fundamentals, high β firms choose lower k Expected mpk: E t [mpk it+1 ] = α + β i γ tσ 2 ε σ 2 E t [mpk] = σ 2 β ( ) 2 γ tσε 2 Dispersion in Empk depends on σ 2 β, price of risk (so is countercyclical) Aggregate TFP: a t+1 = at+1 1 θ 1 (1 θ 2) σmpk,t+1 2 = at+1 1 θ 1 (1 θ 2) σβ θ 1 + θ θ 1 + θ 2 ( ) 2 γ tσε 2 Heterogeneity in risk premia depresses TFP, amplifies underlying shocks 12 / 18

18 Risk premia and misallocation Optimal investment: k it+1 = 1 ( ) α + β i ρ xx t + ρ zz it β i γ tσε 2 1 θ Conditional on (expected) fundamentals, high β firms choose lower k Expected mpk: E t [mpk it+1 ] = α + β i γ tσ 2 ε σ 2 E t [mpk] = σ 2 β ( ) 2 γ tσε 2 Dispersion in Empk depends on σ 2 β, price of risk (so is countercyclical) Aggregate TFP: a t+1 = at+1 1 θ 1 (1 θ 2) σmpk,t+1 2 = at+1 1 θ 1 (1 θ 2) σβ θ 1 + θ θ 1 + θ 2 ( ) 2 γ tσε 2 Heterogeneity in risk premia depresses TFP, amplifies underlying shocks 12 / 18

19 Risk premia and misallocation Optimal investment: k it+1 = 1 ( ) α + β i ρ xx t + ρ zz it β i γ tσε 2 1 θ Conditional on (expected) fundamentals, high β firms choose lower k Expected mpk: E t [mpk it+1 ] = α + β i γ tσ 2 ε σ 2 E t [mpk] = σ 2 β ( ) 2 γ tσε 2 Dispersion in Empk depends on σ 2 β, price of risk (so is countercyclical) Aggregate TFP: a t+1 = at+1 1 θ 1 (1 θ 2) σmpk,t+1 2 = at+1 1 θ 1 (1 θ 2) σβ θ 1 + θ θ 1 + θ 2 ( ) 2 γ tσε 2 Heterogeneity in risk premia depresses TFP, amplifies underlying shocks 12 / 18

20 Adjustment costs Add capital adjustments costs: Φ (I it, K it ) = ξ 2 ( Iit K it δ) 2 Kit Optimal investment (first order approx): k it+1 = φ 00 + φ 1β i x t + φ 2z it + φ 3k it φ 01β i Key effects of ξ: φ 3 and φ 01 in ξ No closed-forms for E t [mpk it+1 ], focus on E [mpk it+1 ]: E [mpk it+1 ] = α + 1 θ ( ) 2 φ 01β i σ 2 1 θ E[mpk] = φ 2 01σβ 2 1 φ 3 1 φ 3 On their own, adj. costs do not generate persistent dispersion in mpk But, they amplify persistent risk premium effects! (φ 3 and φ 01 in ξ) 13 / 18

21 Adjustment costs Add capital adjustments costs: Φ (I it, K it ) = ξ 2 ( Iit K it δ) 2 Kit Optimal investment (first order approx): k it+1 = φ 00 + φ 1β i x t + φ 2z it + φ 3k it φ 01β i Key effects of ξ: φ 3 and φ 01 in ξ No closed-forms for E t [mpk it+1 ], focus on E [mpk it+1 ]: E [mpk it+1 ] = α + 1 θ ( ) 2 φ 01β i σ 2 1 θ E[mpk] = φ 2 01σβ 2 1 φ 3 1 φ 3 On their own, adj. costs do not generate persistent dispersion in mpk But, they amplify persistent risk premium effects! (φ 3 and φ 01 in ξ) 13 / 18

22 MPK dispersion and stock market returns How to quantify...? Our approach: use link with stock market returns To a first-order approximation: E t [r e it+1] log E t [R e it+1] = ψβ i γ tσ 2 ε σ 2 E t [r] = ψ 2 σ 2 β σ 2 E t [mpk] σ2 E t [r] ψ depends on prod. parameters, ind. of γ 0, decreasing in γ 1 ( ) 2 γ tσε 2 Suggests empirical strategy: Market portfolio (perfectly diversified): SR mt = γ tσ ε E [SR mt] = γ 0σ ε E t [r e mt+1] = ψβγ tσ 2 ε E [r e mt+1] = ψβγ 0σ 2 ε Estimates of γ 0 and γ 1 σ 2 E t [r] estimate of σβ 2 (compute E t [rit+1] e using FF 3 factor model) σ 2 E t [r],ff = σ ˆβ = 5 14 / 18

23 MPK dispersion and stock market returns How to quantify...? Our approach: use link with stock market returns To a first-order approximation: E t [r e it+1] log E t [R e it+1] = ψβ i γ tσ 2 ε σ 2 E t [r] = ψ 2 σ 2 β σ 2 E t [mpk] σ2 E t [r] ψ depends on prod. parameters, ind. of γ 0, decreasing in γ 1 ( ) 2 γ tσε 2 Suggests empirical strategy: Market portfolio (perfectly diversified): SR mt = γ tσ ε E [SR mt] = γ 0σ ε E t [r e mt+1] = ψβγ tσ 2 ε E [r e mt+1] = ψβγ 0σ 2 ε Estimates of γ 0 and γ 1 σ 2 E t [r] estimate of σβ 2 (compute E t [rit+1] e using FF 3 factor model) σ 2 E t [r],ff = σ ˆβ = 5 14 / 18

24 Main results - risk premia and misallocation Baseline Only Risk Constant Risk Only Constant Risk MPK Implications EσEmpk EσEmpk 2 σ mpk 2 EσEmpk 2 σ 2 mpk a ) corr (σempk,t 2, xt Risk premium effects lead to substantial mpk dispersion 44% of observed σmpk, 2 two-thirds of perm. component Reduces long-run TFP 8% Adds countercyclical element to σmpk 2 E.g., -1% shock to x t generates 1.2% fall in a t 15 / 18

25 Other Forms of Heterogeneity Adj. Costs Large Adj. Costs θ δ ρ z σz 2 (1) (2) (3) (4) (5) (6) Min. Er Mean Er Max. Er Spread Unobserved variation in technological parameters unlikely to account for large spreads in expected returns observed in the data 16 / 18

26 Robustness/extensions 1. Other distortions (e.g., markups, financial frictions, policies, etc.) Add idiosyncratic output tax 1 τ it, τ it = νz it η it+1 mpk it+1 = α + β i ε t+1 + ε it+1 + νρ zz it + η it+1 + β i γ tσε 2 }{{}}{{}}{{} uncertainty distortions risk premium Risk premium, expected stock returns unaffected, analysis unchanged! 2. Are we picking up adj. costs, other forms of heterogeneity? Set β i = β, compute σ 2 E[r] with adj. costs, firm-specific parameters (e.g., θ) Do not generate large dispersion in expected returns 3. Alternative measure of β s using production-side data Estimate: β i x t + z it = κ i + x t + ζ it Gives value of σβ 2 similar to baseline 17 / 18

27 Conclusion Theory connecting misallocation to exposure to agg risk Persistent firm-level mpk deviations and countercyclical dispersion Accounts for substantial portion of measured mpk dispersion New link between CS asset pricing, agg fluctuations and long-run outcomes Next steps Other countries - developing economies more volatile Sources of β dispersion... Private firms and idiosyncratic risk 18 / 18

28 Variation in β - example 1

29 Variation in β - example 2

30 Variation in β - example 3