The CAPM Strikes Back? An Investment Model with Disasters

Transcription

1 The CAPM Strikes Back? An Investment Model with Disasters Hang Bai 1 Kewei Hou 1 Howard Kung 2 Lu Zhang 3 1 The Ohio State University 2 London Business School 3 The Ohio State University and NBER Federal Reserve Bank of New York September 17, 2015

2 Introduction Insight An investment model with disasters replicates: The failure of the CAPM in capturing the value premium in nite samples in which disasters are not materialized; The relative success of the CAPM in samples in which disasters are materialized

3 Introduction Literature Early quantitative theories of cross-sectional asset pricing rely on single-factor models: Gomes, Kogan, and Zhang (2003); Carlson, Fisher, and Giammarino (2004); Zhang (2005); Cooper (2006) Recent quantitative theories introduce two-shock models: Ai and Kiku (2013); Kogan and Papanikolaou (2013); Belo, Lin, and Bazdresch (2014); Koh (2014) Prior disaster models: Rietz (1988); Barro (2006, 2009); Barro and Ursua (2008); Gourio (2012); Gabaix (2012); Wachter (2013)

4 Outline 1 Stylized Facts 2 The Model 3 Failing the CAPM 4 The Beta Anomaly

5 Outline 1 Stylized Facts 2 The Model 3 Failing the CAPM 4 The Beta Anomaly

6 Stylized Facts The CAPM regressions for the b/m deciles, July 1963June 2014 Fama and French (1992, 1993) L H H L m t m α t α β t β R

7 Stylized Facts The CAPM regressions for the b/m deciles, July 1926June 2014 Ang and Chen (2007) L H H L m t m α t α β t β R

8 80 60 Stylized Facts The value premium vs. MKT, July 1926June Aug 39Sep 60 The value premium Oct 98Aug 32May 87Oct 32Apr 31Sep 30Jun 31May 33Feb 37Sep 80Mar 08Oct 32Oct 40May 31Dec 38Mar 33May 34Jan 75Jan 76Jan 31Jun 38Jun 33Jun 38Apr 33Aug 28Nov 87Jan 74Oct 32Jul 33Apr The value premium The market excess return The market excess return

9 Stylized Facts Large swings in the stock market and the value premium MKT H L MKT H L November August October January June September May March June April September June December September April May May October July January August January October March February January April October May August June October

10 Stylized Facts The CAPM's general problem, the beta anomaly, July 1963June 2014, Fama and French (2006) L H H L m t m α t α β t β R

11 Stylized Facts The CAPM's general problem, the beta anomaly, July 1928June 2014, Fama and French (2006) L H H L m t m α t α β t β R

12 Outline 1 Stylized Facts 2 The Model 3 Failing the CAPM 4 The Beta Anomaly

13 The Model Highlights Embedding disasters into a standard investment model: Rare disasters in consumption (productivity) growth Asymmetric adjustment costs: Value rms are more exposed to disaster risk than growth rms Recursive preferences In a sample without disasters, estimated betas only reect risk in normal times, but the value premium is driven by disaster risk

14 The Model Recursive utility The pricing kernel: M t+1 = ι ( Ct+1 C t ) 1 ψ U1 γ [ t+1 E t U 1 γ t+1 ] 1/ψ γ 1 γ

15 The Model Consumption dynamics Log consumption growth: g ct = ḡ + g t Normal states follow a discretized autoregressive process: Five states: {g 1, g 2, g 3, g 4, g 5 } Transition matrix: p ij Prob(g t+1 = g i g t = g j ): p 11 p p 15 p 21 p p 25 P = p 51 p p 55

16 The Model Consumption dynamics Insert the disaster state, g 0 = λ D (disaster size < 0), and the recovery state, g 6 = λ R (recovery size > 0) Modify transition matrix: θ θ η p 11 η p p 15 0 η p 21 p 22 η... p 25 0 P = η p 51 p p 55 η 0 0 (1 ν)/5 (1 ν)/5... (1 ν)/5 ν η: disaster probability; θ: disaster persistence; ν: recovery persistence

17 The Model Firms, technology Operating prots: Π it = (X t Z it ) 1 ξ K ξ it fk it Aggregate productivity growth: g xt = g + φg t Firm-specic productivity: z it+1 = (1 ρ z ) z + ρ z z it + σ z e it+1

18 The Model Firms, asymmetric adjustment costs Capital accumulation: K it+1 = I it + (1 δ)k it Asymmetric capital adjustment costs: ( ) 2 a + K it + c+ Iit 2 K Kit for it I it > 0 Φ(I it, K it ) = 0 for I it = 0 ( ) 2 a K it + c Iit 2 K Kit for it I it < 0 in which c > c + > 0 and a > a + > 0 capture asymmetry

19 The Model Firms, value maximization Source of funds constraint: D it = Π it I it Φ(I it, K it ) Value maximization: ( V it = max {χ it } max {I it } D it + E t [M t+1 V (K it+1, X t+1, Z it+1 )], sk it in which s 0 is the liquidation value parameter Entry and exit, delisting return, reorganizational costs ),

20 Outline 1 Stylized Facts 2 The Model 3 Failing the CAPM 4 The Beta Anomaly

21 Failing the CAPM Calibration, preferences Parameters Value Description ι Time discount factor γ 5 The relative risk aversion ψ 1.5 The elasticity of intertemporal substitution

22 Failing the CAPM Calibration, consumption dynamics Parameters Value Description ḡ 0.019/12 The average consumption growth ρ g 0.6 The persistence of consumption growth σ g The conditional volatility of consumption growth η 0.028/12 The disaster probability λ D The disaster size θ /3 The disaster persistence λ R The recovery size ν 0.95 The recovery persistence

23 Failing the CAPM The impulse response of log consumption to a disaster shock mimics that in Nakamura, Steinsson, Barro, and Ursua (2013)

24 Failing the CAPM Calibration, technology Parameters Value Description ξ 0.65 The curvature parameter in the production function δ 0.01 The capital depreciation rate f Fixed costs of production φ 1 The leverage of productivity growth z 9.75 The long-run mean of log rm-specic productivity ρ z The persistence of log rm-specic productivity σ z 0.5 The conditional volatility of log rm-specic productivity a Upward nonconvex adjustment costs a 0.05 Downward nonconvex adjustment costs c + 75 Upward convex adjustment costs c 150 Downward convex adjustment costs s 0 The liquidation value parameter κ 0.25 The reorganizational cost parameter R The delisting return

25 Failing the CAPM The CAPM regressions for the b/m deciles, no-disaster samples G V V G m t m α t α β t β R

26 Failing the CAPM The CAPM regressions for the b/m deciles, disaster samples G V V G m t m α t α β t β R

27 Failing the CAPM Value is more exposed to disaster risk than growth Capital z Capital z 0

28 Failing the CAPM Impulse responses of risk and risk premiums for value and growth deciles to a disaster shock

29 Failing the CAPM Nonlinearity in the CAPM regressions The value premium The market excess return

30 Failing the CAPM Nonlinearity in the pricing kernel The pricing kernel The market excess return

31 Failing the CAPM Comparative statics λ D θ η ν λ R % 0.33% % 3.75% Disaster samples m t m α t α β t β No-disaster samples m t m α t α β t β

32 Failing the CAPM Comparative statics a + a c + c f Disaster samples m t m α t α β t β No-disaster samples m t m α t α β t β

33 Failing the CAPM Comparative statics s κ R γ ψ Disaster samples m t m α t α β t β No-disaster samples m t m α t α β t β

34 Outline 1 Stylized Facts 2 The Model 3 Failing the CAPM 4 The Beta Anomaly

35 The Beta Anomaly Deciles formed on rolling market betas, disaster samples L H H L m t m α t α β t β R

36 The Beta Anomaly Deciles formed on rolling market betas, no-disaster samples L H H L m t m α t α β t β R

37 The Beta Anomaly Measurement errors in rolling market betas

38 Conclusion Summary An investment model with disasters replicates the failure of the CAPM in capturing the value premium in no-disaster samples, and its relative success in disaster samples The beta anomaly largely due to measurement errors in pre-ranking rolling betas A rst step in integrating the disaster literature with investment-based asset pricing