Growth Opportunities, Investment-Specific Technology Shocks and the Cross-Section of Stock Returns
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1 Growth Opportunities, Investment-Specific Technology Shocks and the Cross-Section of Stock Returns Leonid Kogan 1 Dimitris Papanikolaou 2 1 MIT and NBER 2 Northwestern University Boston, June 5, 2009 Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
2 Outline 1 Introduction 2 The Model 3 Empirical Analysis 4 Numerical Simulation 5 Conclusion 6 Supplementary Exhibits Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
3 Motivation Growth opportunities and the cross-section of returns. Growth opportunities are real options: leverage; Arrival, expiration, and exercise of growth opportunities: time-series predictability in risk returns; Growth opportunities may be subject to different risk factors than assets in place: cross-sectional differences in expected returns. Growth opportunities are not observable directly: Market-to-book ratio is a popular empirical proxy; Some research advocates firm size as a proxy; Limited ability to predict firms investment; Agency problems, financial constraints, etc. A better empirical measure of growth opportunities would help understand their impact on stock returns, other applications in asset pricing and corporate finance. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
4 Intuition Present value of growth opportunities depends on the cost of investment goods. Exercise price of an option. A decline in the price of investment goods implies Present value of growth opportunities increases; Value of assets in place unchanged or reduced due to lower replacement cost. Use sensitivity of stock returns to investment-specific productivity shocks (I-shocks) to identify the value growth opportunities. Investment-specific shocks are a priced risk factor (Papanikolaou 2008) growth opportunities generate a spread in returns. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
5 Contribution Propose a theoretically motivated method for measuring growth opportunities using stock-market data. Empirical evidence on firm investment and stock returns supports theoretical predictions. Empirical findings are quantitatively consistent with a structural model of investment. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
6 Outline Main focus on consumption-good producers. Reduced-form model of investment-good producers. Key findings: Risk premium depends linearly on the weight of growth opportunities in firm value; Return on a long-short portfolio (IMC) long investment-good producers and short consumption-good producers mimics investment-specific shocks; Individual firms beta with respect to IMC returns can be used to measure the fraction of growth opportunities in its value. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
7 Assets in Place Each firm operates a finite portfolio of projects. Projects arrive and expire randomly, produce a stochastic stream of cash flows. Cash flow from a single project j is y jt = ε ft u jt x t K α j K j: physical capital, invested irreversibly; ε ft : firm-specific productivity; u jt : project-specific productivity; x t: aggregate productivity. Aggregate productivity grows stochastically; firm- and project-specific productivity components are stationary and stochastic. Details Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
8 Investment Projects arrive exogenously at rate λ ft = λ f λ f,t. λft follows a two-state Markov process with transition rates (µ L, µ H ) E[ λ f,t ] = 1 implies λ L + µh µ H+µ L (λ H λ L ) = 1. At time t, firm chooses the scale of investment K j (irreversibly) and pays the cost z t x t K j. Efficiency (quality-adjusted) unit cost of investment z t declines stochastically over time. Details Project-specific productivity is initiated at one: u jt = 1. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
9 Valuation Assume that aggregate productivity shocks and investment specific shocks have constant price of risk β x and β z (constant expected return compensation per unit risk). Present value of single-project cash flows is p(ε ft, u jt, x t, K j ) = A(ε ft, u jt )x t K α j Value of asset is place (VAP) is a sum of individual project values: VAP = j p(ε ft, u jt, x t, K j ) Investment follows the NPV rule: max p(ε ft, u jt, x t, K j ) z t x t K j K j }{{}}{{} PV(Cash Flows) Cost Investment in new projects generates positive NPV. Present value of growth opportunities (PVGO) is PVGO ft = z α α 1 t x t G(ε ft, λ ft ) Details Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
10 Growth Opportunities and Expected Returns Firm value is a sum of the value of assets in place and the value of growth opportunities V ft = VAP ft + PVGO ft = x t j A(ε ft, u jt )K α j + z α α 1 t x t G(ε ft, λ ft ) VAP and PVGO have different risk premia. Firm risk premium is a weighted average of the two: E (R ft ) r f = β x σ x α ( ) 1 α β PVGOft zσ z Risk premium depends on the fraction of firm value represented by growth opportunities. V ft Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
11 Investment-Good Producers Assume profit is a fixed fraction φ of sales. Value of investment-good producers V It φx t z α α 1 t Define the beta of firm f s stock return with respect to the IMC portfolio as β imc is proportional to the PVGO: β imc ft β imc ft = cov t(r ft, R I t R C t ) var t (R I t RC t ) ( ) PVGOft = β 0t, β 0t = V t V ft VAP t Theoretical basis for using β imc as a proxy for growth opportunities. Connection with expected returns. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
12 Data and Procedures CRSP, COMPUSTAT, NIPA tables. Identify investment- and consumption-good producers using NIPA Input-Output tables. Drop firms in investment and financial sectors, missing data, outliers. Estimate β imc : one-year moving-window regressions with weekly returns. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
13 Summary Statistics β imc sort I/K CASH/A D/A Tobin s Q log(k) R&D/A DIV/CF Low 19.4% 10.2% 18.5% % 23.8% % 9.5% 18.6% % 25.4% % 9.6% 18.5% % 24.0% % 9.7% 18.2% % 27.5% % 9.5% 18.4% % 29.8% % 9.7% 18.5% % 23.0% % 10.4% 18.4% % 21.1% % 10.5% 19.0% % 19.2% % 11.5% 19.4% % 17.7% High 24.8% 13.4% 19.1% % 14.9% Tobin s Q is the ratio of market value to replacement cost of assets. Details Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
14 Investment Response to R imc Estimate investment response (i ft = I ft /K f,t 1 ): i ft = a d=2 a d D(β imc f,t 1) d + b 1 ( Rimc t 1) + + cx f,t 1 + γ f + u t 5 d=2 b d D(β imc f,t 1) d ( Rimc t 1) D(β imc i,t 1 ) n is a dummy for quintile n. X f,t 1 is a vector of controls. Coefficients on D(β imc f,t 1 ) d measure average investment rate differences between quintiles. Coefficients on D(β imc f,t 1 ) d ( Rimc t 1 ) measure differences in investment response to R imc. Two sets of controls. Controls 1: i t 1. Controls 2: (Q t 1, CF t 1, K t 1, E t 1 /A t 1 ). Normalize all variables to zero mean and unit variance. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
15 Investment Response to R imc : Sorted on β imc Dependent variable i t (1) (2) (3) (4) (5) (6) Constant (-7.71) (-5.88) (-5.04) (-4.55) (-0.54) D(β imc ) (6.22) (4.99) (4.40) (3.71) (1.78) D(β imc ) H (9.65) (8.43) (8.10) (6.39) (2.10) R t 1 imc (4.86) (4.10) (3.64) (3.90) (3.86) (3.71) D(β imc ) 3 ( Rimc t 1) (1.26) (1.24) (1.51) (1.36) (2.07) D(β imc ) H ( Rimc t 1) (4.27) (6.87) (4.72) (7.66) (5.01) Observations R Industry/Firm FE N N N I I F Controls 1 N N Y N Y N Controls 2 N N N Y Y Y Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
16 Robustness Checks Investment sensitivity to shocks to cost of equipment. Investment sensitivity to credit shocks (Baa-Aaa spread shocks). Sort firms on Tobin s Q ( M/B ). Investment response to equipment price shocks is much smaller. Sort firms on β mkt instead of β imc. Investment response is very weak. Adjust for leverage in β imc estimates. Investment response is similar. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
17 Equipment Prices 0 Equipment Price 0.5 log Price Year Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
18 Equipment Prices log Price HP Filtered Equipment Price Year Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
19 Investment Response to Equipment Price Shocks Use the annual series of quality-adjusted prices of new equipment, Cummins and Violante (2002), covering Remove low-frequency components using Hodrick-Prescott (HP) filter. Extract shocks from the filtered series: Correlate with IMC returns: z t = p hp t p hp t 1 z t = R imc,t R imc,t 1 + e t R 2 = 11.4% (1.85) (2.41) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
20 Investment Response to Equipment Price Shocks Estimate investment response (i ft = I ft /K f,t 1 ): i ft = a d=2 a d D(β imc f,t 1) d + b 1 ( z t 1 ) + + cx f,t 1 + γ f + u t 5 d=2 b d D(β imc f,t 1) d ( z t 1 ) Coefficients on D(β imc f,t 1 ) d ( z t 1 ) measure differences in investment response to equipment price shocks. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
21 Investment Response to Equipment Price Shocks Dependent variable i t (1) (2) (3) (4) (5) (6) Constant (-6.04) (-4.93) (-3.61) (-3.41) (0.89) D(β imc ) (6.99) (5.47) (4.32) (3.64) (1.84) D(β imc ) H (10.40) (8.18) (8.41) (6.44) (2.55) z t (1.47) (-0.48) (-1.05) (-0.57) (-1.29) (0.39) D(β imc) 3 ( z t 1) (2.10) (3.09) (1.46) (2.01) (0.71) D(β imc) H ( z t 1) (3.57) (4.12) (2.41) (2.40) (1.86) Observations R Industry/Firm FE N N N I I F Controls 1 N N Y N Y N Controls 2 N N N Y Y Y Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
22 Investment Response to Credit Spread Shocks Investment sensitivity to credit shocks (Baa-Aaa spread shocks). Credit shocks have low correlation with I-shocks (33% in sample); Changes in credit conditions should affect investment rate of high-growth firms more; Empirical results are supportive: investment response to credit shocks is higher for high-β imc firms. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
23 Investment Response to Credit Spread: Sorted on β imc Dependent variable i t (1) (2) (3) (4) (5) (6) Constant (-7.29) (-6.54) (-4.60) (-4.65) (-0.41) D(β imc ) (6.49) (5.09) (4.54) (3.79) (1.85) D(β imc ) H (9.84) (7.22) (8.23) (5.77) (2.72) s t (5.29) (3.38) (4.44) (2.39) (3.80) (2.35) D(β imc ) 3 ( s t 1) (1.66) (1.78) (1.59) (1.71) (2.18) D(β imc ) H ( s t 1) (2.45) (2.42) (2.06) (2.04) (2.22) Observations R Industry/Firm FE N N N I I F Controls 1 N N Y N Y N Controls 2 N N N Y Y Y Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
24 Summary β imc predicts investment response to investment-specific shocks. Portfolios sorted on β imc have many characteristics consistent with differences in growth opportunities. Results persist when we control for traditional predictors of investment. Multiple robustness checks. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
25 Model Calibration Calibrate model parameters to match simultaneously moments of returns and fundamentals. Simulate 5,000 firms for 50 years. Average coefficient estimates and t-statistics over 1,000 simulations. parameter r µ x σ x β x µ z σ z β z φ α δ value parameter θ ɛ σ e θ u σ u µ λ σ λ µ H µ L λ H λ L value Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
26 Model Calibration Moment Data Model µ(d t) σ(d t) µ(i t) σ(i t) E(R mkt ) r f σ(r mkt ) E(R imc ) σ(r imc ) ρ(r imc, R mkt r f ) Market Cap of I relative to C Investment over Capital (mean) Investment over Capital (IQR) Cashflows over Capital (mean) Cashflows over Capital (IQR) Market-to-Book Equity (median) Market-to-Book Equity (IQR) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
27 Investment Response to R imc : Model Dependent variable i t (1) (2) (3) (4) (5) Constant (-20.33) (-20.71) (-5.17) (4.27) D(β imc ) (12.30) (11.85) (3.08) (-5.57) D(β imc ) H (15.71) (14.89) (10.77) (-4.20) R t 1 imc (3.09) (4.20) (4.19) (2.13) (-3.04) D(β imc ) 3 Rimc t (3.26) (3.22) (2.63) (-1.40) D(β imc ) H Rimc t (3.81) (3.77) (3.76) (1.83) R Controls (i t 1) N N Y Y Y Controls (CF t 1, K t 1) N N N Y Y Controls (Q t 1) N N N N Y Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
28 Stock Returns We calibrate the model so that I-shocks have a negative price of risk. Intuition: states of the world with high real investment opportunities are states with high marginal value of money. IMC pays off more in these states negative price of risk. Growth stocks have higher β imc and lower average returns. Compare model predictions to empirical estimates. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
29 Stock Returns: β imc Portfolios Data β imc Lo Hi Hi - Lo E(R) r f (%) σ(%) (2.83) (2.96) (3.56) (1.88) (1.49) (0.89) (-0.76) β mkt α(%) (19.19) (25.18) (31.44) (44.38) (33.19) (26.29) (8.56) (1.59) (1.79) (3.04) (-0.76) (-1.45) (-2.18) (-2.26) R 2 (%) β mkt (23.54) (40.14) (58.99) (42.81) (36.84) (31.59) (2.81) β imc α(%) (-10.79) (-13.44) (-16.37) (5.81) (12.51) (13.32) (20.43) (0.22) (-0.04) (1.69) (0.57) (0.74) (0.12) (-0.05) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
30 Stock Returns: β imc Portfolios Model β imc Lo Hi Hi - Lo E(R) r f σ(%) (3.72) (3.50) (3.30) (2.15) (1.81) (1.34) (-2.50) β mkt α(%) (22.83) (29.91) (37.78) (75.40) (48.45) (30.98) (5.02) (4.63) (4.80) (4.73) (-3.33) (-4.39) (-4.70) (-4.85) R 2 (%) β mkt (52.55) (68.83) (80.04) (87.59) (84.15) (83.47) (2.43) β imc α(%) (-11.57) (-12.57) (-12.16) (6.03) (11.85) (21.23) (18.19) (0.92) (1.07) (0.92) (-0.36) (-0.45) (-0.23) (-0.79) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
31 Stock Returns: Hi - Lo β imc Portfolios Data Model E(R) r f (%) σ(%) β mkt α(%) R 2 (%) β mkt β imc α(%) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
32 Stock Returns: B/M Portfolios Data B/M Lo Hi Hi - Lo E(R) r f (%) σ(%) (1.44) (2.18) (2.55) (3.79) (3.94) (3.85) (2.87) β mkt α(%) (43.46) (52.78) (53.02) (25.42) (22.68) (20.03) (-1.88) (-1.89) (-0.27) (0.95) (3.36) (3.59) (3.05) (2.94) R 2 (%) β mkt (36.12) (53.48) (54.19) (33.81) (27.66) (20.39) (0.09) β imc α(%) (6.37) (-1.43) (-3.98) (-7.69) (-6.25) (-2.53) (-4.85) (-0.93) (-0.11) (0.24) (2.41) (2.64) (2.56) (2.22) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
33 Stock Returns: B/M Portfolios Model B/M Lo Hi Hi - Lo E(R) r f (%) σ(%) (1.21) (1.76) (2.12) (3.31) (3.53) (3.83) (2.98) β mkt α(%) (29.75) (48.67) (75.39) (38.70) (31.12) (24.01) (-4.71) (-5.16) (-4.88) (-3.70) (4.94) (5.18) (5.33) (5.41) R 2 (%) β mkt (78.45) (76.73) (81.33) (81.18) (69.01) (54.13) (-1.30) β imc α(%) (20.54) (9.92) (4.84) (-11.97) (-12.06) (-11.42) (-17.24) (-0.92) (-1.22) (-1.09) (1.06) (1.47) (1.83) (1.69) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
34 Stock Returns: Hi - Lo B/M Portfolios Data Model E(R) r f (%) σ(%) β mkt α(%) R 2 (%) β mkt β imc α(%) R 2 (%) Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
35 Summary The model generates cross-sectional dispersion in average returns because of heterogeneity in growth opportunities. Cross-sectional distribution of returns on β imc portfolios is very close to the data. Large spread in CAPM alphas between IMC decile portfolios. A two-factor model (MKT, IMC) explains the cross-section of returns on the IMC decile portfolios. The model captures a portion of the empirical value premium: The model replicates failure of CAPM very accurately; A two-factor model (MKT, IMC) does not explain the cross-section of B/M portfolios in the data. Does much better in the model. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
36 Conclusion Develop an empirical procedure for measuring growth opportunities. Empirical test are encouraging: predict heterogeneity in investment response to I-shocks, stock returns, other firm characteristics. Improvement over standard measures. A stylized structural model provides good quantitative account of empirical findings. Related research: Use our paradigm to interpret and extend evidence on the relationship between investment and stock returns; Develop a general-equilibrium model to endogenize pricing of I-shocks. Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
37 Productivity and Investment-Specific Shocks ε ft : firm-specific productivity; u jt : project-specific productivity; x t : aggregate productivity; z t : efficiency investment cost. dε ft = du jt = θ ε (ε ft 1) dt + σ ε εft db ft θ u (u jt 1) dt + σ u ujt db jt dx t = µ x x t dt + σ x x t db xt, dz t = µ z z t dt + σ z z t db zt db ft, db jt, db xt and db zt are independent standard Brownian motions. Back to Productivity Back to Investment Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
38 Valuation Details Stochastic discount factor dπt π t = r dt β x d B xt β z d B zt. Project PV(Cash Flows) [ p(ε ft, u jt, x t, K j ) = E t e δ(s t) π ] s ε fs u js x s K α j ds = A(ε ft, u jt )x t K α j, π t where t A(ε, u) = (ε 1) + r + δ µ X r + δ µ X + θ e 1 (u 1) r + δ µ X + θ u 1 + (ε 1)(u 1) r + δ µ X + θ e + θ u Continued on next slide... Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
39 Valuation Details Optimal investment scale ( ) 1 K αa(εft 1 α, 1) (ε ft, z t ) =. z t PVGO where and PVGO ft = z α α 1 t x t G(ε ft, λ ft ), G(ε ft, λ ft ) = C E t [ t e ρ(s t) λ fs A(ε fs ) 1 1 α ds ]. ρ = r + α 1 α (µ z σ 2 z/2) µ x α2 σ 2 z 2(1 α), C = α ( α α 1 1 ). Back to Valuation Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
40 Data Definitions Variable Source Investment (I) Compustat item128 Capital (K) Compustat item8 Book Assets (A) Compustat item6 Book Debt (D) Compustat item9 Book Preferred Equity (EP) Compustat item56 Book Common Equity (EC) Compustat item60 Operating Cashflows (CF) Compustat item14+item18 Inventories (INV) Compustat item76-78 Market Capitalization (MKCAP) CRSP R&D Expenditures (R&D) Compustat item46 Cash Holdings (CASH) Compustat item1 Dividends (DIV) Compustat item19+item21 Share Repurchases (REP) Compustat item115 Tobin s Q (Q) (MKCAP + EP + D-INV)/(EC+EP + D) Quality Adjusted Price of Investment Goods Cummins and Violante (2002) Consumption Deflator NIPA Back Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
41 Inv Response to Equipment Price Shocks: (Q) Dependent variable i t (1) (2) (3) (4) (5) (6) Constant (-11.03) (-8.96) (-9.08) (-7.22) (-9.05) D(Q) (6.96) (5.46) (5.11) (3.73) (7.27) D(Q) H (23.72) (20.26) (9.19) (7.25) (13.01) z t (1.47) (-0.01) (-1.23) (0.08) (-1.19) (0.52) D(Q) 3 ( z t 1) (1.78) (1.67) (1.45) (1.36) (1.16) D(Q) H ( z t 1) (2.27) (3.40) (2.74) (3.66) (1.48) Observations R Industry/Firm FE N N N I I F Controls 1 N N Y N Y N Controls 2 N N N Y Y Y Kogan, Papanikolaou (2009) Growth Opportunities and Investment-Specific Shocks Boston, June 5, / 47
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