Financial Distress and the Cross Section of Equity Returns

Transcription

1 Financial Distress and the Cross Section of Equity Returns Lorenzo Garlappi University of Texas Austin Hong Yan University of South Carolina National University of Singapore May 20, 2009

2 Motivation Empirical regularities in the cross section of equity returns Size effect Value premium Momentum Empirical evidence on the role of financial distress in the cross section Griffin and Lemmon (2002) (value premium stronger in distressed firms) Vassalou and Xing (2004) (size and value premium stronger for high default probability firms) Avramov et al (2007) (momentum profits stronger with low credit rating) Lack of a unified framework to understand these anomalies Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 1

3 Objectives Developing a theoretical framework to simultaneously account for major cross-sectional features of equity returns (value premium and momentum) and their interaction with financial distress Showing how financial leverage can enhance anomalies Demonstrating that potential recovery for shareholders upon financial distress plays an instrumental role in the cross-sectional patterns of stock returns Providing empirical implication using simulated data from a calibrated dynamic model Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 2

4 Background 1. Real options/neoclassical models of firms assets: [e.g., Berk, Green and Naik (1999), Gomes, Kogan and Zhang (2003), Zhang (2005), Carlson, Fisher and Giammarino (2004), Sagi and Seasholes (2006),... ] Size effect related to growth opportunities w.r.t. assets-in-place B/M effect related to the risk of assets-in-place Momentum driven by growth options 2. Limitations of ignoring financial leverage: Difficult to explain the effect of distress on the cross section Anomalies are significant for equity, not asset, returns [Hecht (2004), Charoenrook (2004), Choi (2008)] Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 3

5 Features of Our Approach 1. Introducing financial leverage in a real option model of equity value 2. Modeling the outcome of financial distress (e.g., potential shareholder recovery upon financial distress restructuring and debtequity swap, etc.) 3. Generating momentum in stock returns that arises endogenously in high-default-risk firms 4. Demonstrating the robustness of the intuition in a generalized framework with endogenous investment and financing choices Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 4

6 Basic Model Partial equilibrium, continuous-time model Two types of firms: mature and growth Firms have both operating (c) and financial (l) leverage Default may result in possible recovery to shareholders (e.g. Fan and Sundaresan (2000), Morellec, Nikolov and Schüroff (2008)). Unique source of risk: price of the good produced dp = µp dt + σp dw Constant risk premium λ associated with P. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 5

7 V m (P t ) = E Equity Value of a Mature Firm τl ξ: scale of operation. 0 }{{} payoff in default ( ξ(p t+s c) l)e rs ds + ηx }{{} m (P m )e rτ L operating profits τ L : default stopping time: τ L = inf {t : P t = P m } P m : endogenous default boundary X m (P m ): residual firm value (e.g., ξc/r: book value of assets) η: fraction of book value of assets captured by shareholders in financial distress (expected shareholder recovery upon financial distress) Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 6

8 Distribution of η in the cross section From Morellec, Nikolov and Schüroff (2008) structural estimation of η. Frequency Shareholder bargaining power (%) Shareholder recovery = η renegotiation surplus 20% of firm value. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 7

9 Beta and Momentum Measures Let V m (P ) denote equity value: 1. Beta sensitivity of equity return to the state variable P β = V m (P ) P P V m (P ). 2. Autocorrelation sensitivity of expected return to realized return AutoCorr = cov[ λβ, ln(e)] var[ ln(e)] = λ β/β P/P Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 8

10 Beta of a Mature Firm ( ) ( ) ( ) (ξc l)/r ξc + l (1 + η)ξc + l β = π V }{{ m ξc l ξc + l }}{{} BE/ME Leverage/Distress π: risk-neutral probability of default: (P/P ) φ, φ < 0. (ξc l)/r : book-to-market equity (BE/ME) V m The BE/ME effect captures all the cross sectional variation in beta (for no-growth firms), i.e. risk of assets in place (as in BGN and CFG) Beta and default probability If η = 0, β increases with default probability If η > 0 β hump-shaped or decreasing in default probability Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 9

11 Expected Return vs Default Probability No recovery (η = 0) Recovery (η = 5%) Expected Return Beta Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 10

12 B/M effect, value premium and default probability ( ) ( ) ( ) (ξc l)/r ξc + l (1 + η)ξc + l β = π V }{{ m ξc l ξc + l }}{{}}{{} BE/ME L > 1 D(η, π) 0 Leverage effect: L > 1 and in l = amplifying effect of leverage Book-to market effect If η = 0, D > 0 = β increases in BE/ME If η > 0 and π high, D < 0 = β may decrease in BE/ME Value premium: β high B/M β low B/M If η = 0 = Increasing with default probability If η > 0 = Declining or Hump-shaped in default probability: Positive/Increasing for low π, negative/decreasing for high π Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 11

13 Intuition for Value Premium Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 12

14 Intuition for Value Premium Expected return high B/M ratio Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 13

15 Intuition for Value Premium higher expected return Expected return high B/M ratio Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 14

16 Intuition for Value Premium low B/M ratio higher expected return Expected return high B/M ratio Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 15

17 Intuition for Value Premium low B/M ratio higher expected return Expected return lower expected return high B/M ratio Value Premium > Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 16

18 Intuition for Value Premium Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 17

19 Intuition for Value Premium high B/M ratio Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 18

20 Intuition for Value Premium high B/M ratio Expected return lower expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 19

21 Intuition for Value Premium high B/M ratio Expected return low B/M ratio lower expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 20

22 Intuition for Value Premium higher expected return high B/M ratio Expected return low B/M ratio lower expected return Value Premium < Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 21

23 Momentum and default probability The momentum measure for mature firms is AutoCorr = λ [ 1 β π ( γ1 ) ( l + ξc(1 + η) βe m r )], γ 1 < If η = 0 or low default prob. AutoCorr < 0, no momentum. 2. If η > 0 and high default prob. AutoCorr > 0, momentum. Potential recovery to shareholders crucial for momentum in highly levered firms. Mean reversion and growth options not necessary for generating this type of momentum. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 22

24 Intuition for Momentum Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 23

25 Intuition for Momentum Expected return negative realized return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 24

26 Intuition for Momentum higher expected return Expected return negative realized return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 25

27 Intuition for Momentum positive realized return higher expected return Expected return negative realized return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 26

28 Intuition for Momentum positive realized return higher expected return Expected return lower expected return negative realized return AutoCorr < Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 27

29 Intuition for Momentum Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 28

30 Intuition for Momentum negative realized return Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 29

31 Intuition for Momentum negative realized return Expected return lower expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 30

32 Intuition for Momentum negative realized return Expected return positive realized return lower expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 31

33 Intuition for Momentum higher expected return negative realized return Expected return positive realized return lower expected return AutoCorr > Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 32

34 V g (P t ) = E Equity Value of a Growth Firm τl τ G 0 op. profits {}}{ ( P t+s c l)e rs ds + (V m (P ) I)E [ ] e rτ GI {τg <τ L } + ηx g (P g )E[e rτ LI {τl <τ }{{} G }] }{{} growth option value expected payoff in default τ L : stopping time for default. τ L = inf {t : P t = P g } τ G : stopping time for growth. τ G = inf { t : P t = P } P g : endogenous default boundary. P : endogenous growth threshold X g (P g ) residual firm value (e.g., c/r: book value of assets) V m (P ): equity value of mature firm at P I: investment cost (borne by shareholders) η: recovery to shareholders Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 33

35 Growth vs. Mature firms: Autocorrelation Plot of return autocorrelation for growth vs. mature firms No recovery (η = 0) Recovery (η = 10%) Mature Growth 2 2 AutoCorr Mature Growth AutoCorr Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 34

36 Implications from the Basic Model Financial leverage and distress probability affects equity risk β dependent upon firm characteristics, thus time-varying Value premium vs. Default probability: Increasing if η = 0, i.e., no expected recovery for shareholders Humped if η > 0, i.e., positive expected shareholder recovery Momentum profits higher if: Default probability high, and High likelihood of shareholder recovery upon financial distress Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 35

37 The need for a general model Robustness of the implications Exogenous vs endogenous investment and financing decisions Static vs dynamic frameworks Consistency with existing empirical findings: A more general model that can be calibrated to produce moments to match the data Simulations of the model produce the appearance of α due to model misspecification for risk adjustment. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 36

38 Features of the general model Firm i s output at time t is described by Y i,t = K α i,t e X t+z i,t, X t : systematic, Z i,t : firm-specific Pricing kernel specified to allow for a counter-cyclical risk premium Frictions: capital adjustment costs and costs for equity financing Each period, the firm maximizes equity value when making decision on investment (level of capital) and choosing financing means Financial distress (or default) occurs when the equity value is below a threshold (ηr with R being the residual asset value at the time) Dynamic programming problem with 5 state variables. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 37

39 Sample moments Variable Model Data Annual risk-free rate Annual Sharpe ratio Annual volatility of real interest rate Annual equity premium Annual investment rate Market-to-book ratio Market leverage year EDF Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 38

40 Expected Returns and default probability 0.09 No recovery (η = 0) Recovery (η = 10%) Expected return Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 39

41 Value premium and default probability 0.08 No recovery (η = 0) Recovery (η = 10%) 10 x Value premium Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 40

42 Momentum and default probability 0 No recovery (η = 0) Recovery (η = 10%) 12 x Momentum profits Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 41

43 Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 42

44 Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = 0 2 FF-α Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 43

45 Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = 0 2 FF-α = = Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 44

46 Simulations: Alphas R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = 0 2 all FF-α = = Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 45

47 Factor loadings - β mkt R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = = 0.1 β mkt all = Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 46

48 Factor loadings - β smb R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = 0.1 β smb 0.4 = = all 0.4 Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 47

49 Factor loadings - β hml R j,t = α j + β mkt j (R m,t R f,t ) + β smb SMB t + β hml HML t + ɛ j,t j j = β hml = all 0.4 = Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 48

50 Conclusions Propose a new perspective for cross-sectional anomalies in equity returns. Expected outcome of financial distress affects the link between default probability and: 1. Beta/Expected returns 2. Value premium 3. Momentum A simple risk-based explanation for major cross-sectional features in returns Financial distress risk is reflected in beta and manifested in value premium and momentum A structural understanding, without having to introduce new risk factors Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 49

51 Additional Slides Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 50

52 Empirical Analysis Data Moody s KMV EDF: Expected Default Frequency TM Inspired by the Black-Scholes-Merton Model (Kealhofer (2003)) Time period: January 1969 December 2003 Number of observations: 1,430,713 firm-month No financial firms CRSP Monthly equity returns COMPUSTAT Accounting variables Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 51

53 Value Premium and Default Probability Full Sample Low EDF High EDF High-Low t-value B/M VW Returns Low Medium High High - Low t-value B/M EW Returns Low Medium High High - Low t-value Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 52

54 Value Premium and Default Probability Stocks with price $5 Low EDF High EDF High-Low t-value B/M VW Returns Low Medium High High - Low t-value B/M EW Returns Low Medium High High - Low t-value Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 53

55 Empirical Proxies for shareholder recovery (η) From Garlappi, Shu and Yan (2006): 1. Asset size. High asset size recovery more likely [Franks and Torous (1994) and Betker (1995)] 2. R&D expenditures/assets. High R&D recovery less likely [Opler and Titman (1994) and Fan and Sundaresan (2000)] 3. Herfindahl Index of sales. High Hfdl index recovery more likely [Shleifer and Vishny (1992)] Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 54

56 Momentum and Default Probability Methodology: Independently sort stocks into: 1. terciles of EDF 2. terciles of η proxy 3. and quintiles of losers/winners (past 6 month) Record equal-weight return over future 6-month period Report results in top EDF tercile. Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 55

57 Momentum and Default Probability Asset Value Loser Winner W-L t-stat Low Med High High-Low R&D Loser Winner W-L t-stat Low Med High Low-High SalesHfdl Loser Winner W-L t-stat Low Med High High-Low Garlappi & Yan Financial Distress and the Cross Section of Equity Returns 56